Customer Privacy Policy

Last Modified: January 23, 2026 | Update History

Most recent update: This Privacy Policy has been updated to address additional rights for individuals in the European Union/UK.

We advise you to read this Privacy Policy in its entirety, including the jurisdiction-specific provisions in the appendix. Click here to review Our U.S. Notice At Collection.

Customer Privacy Policy: K–12 Schools

Who We Are

Amplify Education, Inc. (“Amplify”) is leading the way in next-generation curriculum and assessment. Amplify’s programs provide teachers with powerful tools that help them understand and respond to the needs of each student and use data in a way that is safe, secure, and effective.

Our Products and Services

Amplify’s products support classroom instruction and learning and include Amplify CKLA, Amplify ELA, Amplify Caminos, Amplify Science, Amplify Desmos Math, Boost Reading, Boost Math, mCLASS, Mathigon, associated professional development and tutoring services, and services at classroom.amplify.com (for creating and assigning activities) and student.amplify.com (for use of the activities or curricula as directed by an instructor), and any other product or service that links to this Privacy Policy (together, the “Products”).

Our Approach to Student Data Privacy 

In the course of providing the Products to Schools and their Authorized School Users, Amplify collects, receives, generates, or has access to Student Data (defined below). We consider Student Data to be confidential and we collect and use Student Data solely for educational purposes in connection with providing our Products to, or on behalf of the School as described in this Privacy Policy and our Agreements (defined below). We work to maintain the security and confidentiality of Student Data that we collect or store, and we enable Schools to control the use, access, sharing, and retention of Student Data.

Our Products are geared towards K–12 students (“Students”), and the educators, agents and staff members who use the Products as authorized by their School (“Educators”). Information that directly relates to an identifiable Student (“Student Data”) is owned and controlled by the School, and Amplify receives Student Data as a “school official” under Section 99.31 of the Family Educational Rights and Privacy Act of 1974 (“FERPA”) for the purpose of providing the Products hereunder. In addition, we rely on the School acknowledging that it is acting as the parent’s agent and consenting on the parent’s behalf to process personal information of Students under the age of 13 (“Child Users”) in accordance with the Children’s Online Privacy Protection Act (“COPPA”).

Our collection and use of Student Data is governed by our Agreements with Schools, including this Privacy Policy (“Privacy Policy”), and applicable laws which may include FERPA, COPPA, the Protection of Pupil Rights Amendment (“PPRA”), as well as other applicable federal, state, and local privacy laws and regulations (“Applicable Laws”). As noted above, with respect to FERPA, Amplify receives Student Data as a “school official” under Section 99.31 of FERPA for the purpose of providing its Products, and such Student Data is owned and controlled by the School.

Schools may provide authorization in two ways:

  1. by the School agreeing to our Customer Terms and Conditions located at amplify.com/customer-terms or another written agreement between Amplify and the School, as applicable; or
  2. by an Educator agreeing to the Acceptable Use Policy located at amplify.com/acceptable-use-policy/ (“AUP”) on behalf of the School as outlined in the AUP.

In each case, we collect Student Data and provide these Products solely for the use and benefit of the School and for no other commercial purpose. We require all Schools to review this Privacy Policy, available at amplify.com/customer-privacy, and to make a copy of the Privacy Policy available to the parents or guardians of Child Users.

We also provide limited opportunities for individual users to sign up for an account for use of our Products at-home or otherwise outside of the authorization of a School (“Home Users”). See the Appendix–Supplemental Disclosures for additional information that applies to our Home Users.

What This Privacy Policy Covers 

This Customer Privacy Policy (“Privacy Policy”) describes how Amplify collects, uses, and discloses personal information through the provision of Products.

For purposes of this Privacy Policy, “you” and “your” means Authorized Users (defined below).

This Privacy Policy does not apply to Amplify’s handling of:

  • information collected from users of Amplify’s company website, which is governed by our Website Privacy Policy.
  • job applicant data that we process in accordance with our applicant privacy notice.

There may be different contractual terms or privacy policies in place with some Schools. Such other terms or policies supersede this Privacy Policy for information collected or released under those terms. If you have any questions as to which legal agreement or privacy policy controls the collection and use of your personal information, please contact us using the information provided below. Unless expressly superseded, this Privacy Policy is incorporated into and is subject to the Agreement that governs your use of the Products.

Our Role

Amplify as a processor/service provider: Our School customers are the controllers of Student Data (as well as certain other Educator personal information to the extent required by law or Amplify’s agreement with the School) (together “School Data”).

Amplify acts as a processor/service provider for our School customers with respect to School Data, which means when we use School Data, we do so solely on the instruction of the School. School Data is subject to the School’s privacy policies; therefore, you will need to contact the School directly if you have any questions or would like to exercise your rights with respect to School Data.

Amplify as a controller: We are the controller of all other personal information we collect from non-Student Authorized Users (“Amplify Data”) and can be reached by email at privacy@amplify.com or by mail at Amplify Education, Inc., 55 Washington St.#800, Brooklyn, NY, 11201.

Policy

1. Definitions

Capitalized terms not defined in this section or elsewhere in this Privacy Policy will have the meaning set forth by Applicable Laws.

Agreement” means the underlying contractual agreement between Amplify and the School.

Authorized Users” means all users of our Products, including Authorized School Users, parents and legal guardians, and Home Users.

Authorized School Users” means Students and Educators.

Local Education Authority” means a local education agency or authority, school district, school network, independent school, or other regional education system.

Non-Student Data” means information that is linked or linkable to Authorized Users who are not Students.

School” means the Local Education Authority or State Agency.

State Agency” means the educational agency primarily responsible for the supervision of public elementary and secondary schools in any of the 50 states, the Commonwealth of Puerto Rico, the District of Columbia, or other territories and possessions of the United States, as well as a national or regional ministry or department of education in other countries, as applicable.

2. What personal information do we collect?

When you access or use our Products, you may choose to provide us with personal information, including Student Data. This information may be provided to us directly (e.g. when an account is created or through communications with us) or through your interactions with our Products.

Student Data. Below is a list of the categories of Student Data that may be collected by Amplify or its Products, either directly or through the Authorized School User’s use of the various features and configurations of the Products:

  • Identifier and Enrollment Data, such as name, email, school / state ID number, username and password, grade level, homeroom, courses, teacher names.
    • Why? Most of Amplify’s Products require some basic information about who is in a classroom and who teaches the class—Student or teacher Identifier and Enrollment data. This information is provided to Amplify by the School, either directly from the School’s student information system or via a third party with whom the School contracts to provide that information.
  • Demographic Data, such as date of birth, socioeconomic status, race, national origin, and preferred or primary language.
    • Why? To support school instructional and reporting requirements, Amplify’s Products allow Schools to view reports and analyze data using Demographic Data. Generally, Demographic Data is provided on a voluntary basis by the School. For example, a School may wish to analyze Student literacy assessment results based on English Language Learner status to better tailor classroom instruction, and in that case, the School may provide Demographic Data to enable that reporting.
  • School Records, such as grades, attendance, assessment results, and whether an Individualized Education Plan (IEP or local equivalent) is in place.
    • Why? Some of our Products support grading assignments and administering formative, diagnostic, and curriculum-based assessments. Teachers use that information to support Students’ progress in the program or help with instructional decisions. We do not collect specific details from an IEP, nor do we collect protected health information or other sensitive information.
  • Schoolwork and Student Generated Content, which includes any information contained in Student assignments and assessments, including information in response to instructional activities and participation in collaborative or interactive features of our Products, such as Student responses to academic questions and Student-written essays, as well as images, video, and audio recordings.
    • Why? As part of the digital learning experience, some of our Products may enable Students to write text and create and upload images, video, and audio recordings. For example, in Amplify ELA, students may write essays or submit short-form responses in our platform as part of a lesson on literature. As another example, in Boost Reading, student interactions with reading skills games are recorded to keep track of the student’s progress to level up in the program and to provide visibility to teachers on how students are mastering the skills.
  • Teacher Comments and Feedback, such as scores, written comments, or other feedback that Educators may provide about Student responses or student course performance.
    • Why? To enable teachers to track the performance and provide feedback to their students.
  • Non-Student Data. We may collect the following types of personal information from all other Authorized Users:
    • Contact Information, such as name and email address, as well as grade level taught, school name and school location, whether you are an Educator or Home User that creates an account or uses our Products or communicates with us.
    • Account Information, such as user login and password, for account creation and access purposes.
    • Survey Responses, which you provide in response to surveys or questionnaires.
  • Device and Usage Data. Depending on the Product, we may collect certain information about the device used to connect to our Product, such as device type and model, browser configurations, and persistent identifiers, such as IP addresses and unique device identifiers. We may collect device diagnostic information, such as battery level, usage logs, and error logs, as well as usage, viewing, and technical information (e.g., email open rates), such as the number of requests a device makes, to ensure proper system capacity for all Authorized Users. We may collect IP addresses and use that information to approximate device location to support operation of the Product. To the extent that we collect this information, this data is solely used to support operation of the Product and is not linked to Student Data. For purposes of clarity, Amplify does not use Student Data for marketing or advertising purposes (see section 6 of this Privacy Policy for more information about our commitments regarding Student Data).
    • Why? We use this information to remember returning users and facilitate ease of login, to customize the function and appearance of the Products, and to improve the learning experience. This information also helps us track product usage for various purposes, including website optimization, to ensure proper system capacity, troubleshoot and fix errors, provide technical assistance and customer support, provide and monitor the effectiveness of our Products, monitor and address security concerns, and compile analytics for product improvement and other internal purposes.
    • How? Cookies and Similar Technologies. We collect device and usage data through “cookies,” Web beacons, HTML5 local storage, and other similar technologies, which are used in some of our Products solely to support operation of the Products as described above. While we may use third party cookies and similar technologies for advertising and marketing purposes on our website (in accordance with our Website Privacy Policy), we do not permit such tracking technologies to be present on Student-facing portions of the Products. In particular, we only use the following types of cookies in our Products:
      • Strictly necessary cookies – These are cookies that are required for the operation of our websites and applications that host our Products. They include, for example, cookies that enable you to log into secure areas of our Products. These cookies are not generally stored beyond the browser session and are less likely to include personal information. This category of cookies cannot be disabled.
      • Functionality Cookies – We use these cookies so that we recognize you on the websites and apps that host our Products and remember your previously selected preferences. These cookies are stored on your device between browsing sessions but expire after a pre-defined period. These cookies enable us to “recognize” you when you use our Products, including your preferences such as your preferred language, time, and location. A mix of first party (placed by us) and third-party cookies (placed by third parties) are used.
      • Performance Cookies – These cookies help us and service providers acting on our behalf compile statistics and analytics about users of our Products that are accessed via websites and apps, including Device and Usage Information.
    • Learn how to opt out of cookies and similar technologies by reading the “What Rights and Choices Do You Have?” section of this Privacy Policy below.

3. How do we use personal information?

Student Data. Amplify uses Student Data for educational purposes, to provide the Products, and to ensure secure and effective operation of our Products, including:

  • to provide and improve our educational Products;
  • to support School and Authorized School Users’ activities;
  • to ensure secure and effective operation of our Products;
  • for purposes requested or authorized by the School or Authorized School User or as otherwise permitted by Applicable Laws;
  • for customer support purposes, to respond to the inquiries and fulfill the requests of the School and their Authorized School Users;
  • to enforce Product access and security controls; and
  • to conduct system audits and improve protections against the misuse of our Products, or to detect and prevent fraud and other harmful activities.
  • to enable the adaptive and personalized learning features of the Products.

Non-Student Data. Amplify may use Non-Student Data for the purposes for which Student Data is used as set forth above. In addition, Amplify may use Non-Student Data to provide customized content, advertising and marketing in limited circumstances (e.g. to periodically send newsletters and other promotional materials) directed to Educators and Home Users. For sake of clarity, we do not use Student Data for marketing purposes and we do not direct marketing to Students. Amplify may also use Non-Student Data for internal research and analytics, including generating insights on the use of our Products by Educators in certain Schools so that we can better serve those communities. We will also use Non-Student Data as otherwise required or permitted by law, or as we may notify you at the time of collection. Learn how to opt out of these communications by reading the “What Rights and Choices Do You Have?” section of this Privacy Policy below.

Amplify may use aggregate or de-identified data as described in the Aggregate/De-identified Data section below.

4. To whom do we disclose personal information?

Student Data. We disclose Student Data to third parties only as needed to provide the Products under the Agreement, as directed or permitted by the School or Authorized School User, and as required by law. Such disclosures may include but are not limited to the following:

  • to other Authorized School Users of the School entitled to access such data in connection with the Products;
  • to our service providers, subprocessors, or vendors who have a legitimate need to access such data in order to assist us in providing or supporting our Products, such as platform, infrastructure, and application software. We contractually bind such parties to protect Student Data in a manner consistent with those practices set forth in this Privacy Policy and in accordance with Applicable Laws. A list of Amplify subprocessors is available at https://www.amplify.com/subprocessors;
  • to comply with the law, respond to requests in legal or government enforcement proceedings (such as complying with a subpoena), protect our rights in a legal dispute, or seek assistance of law enforcement in the event of a threat to our rights, security, or property or that of our affiliates, customers, Authorized Users, or others;
  • in the event Amplify or all or part of its assets are acquired or transferred to another party, including in connection with any bankruptcy or similar proceedings, provided that successor entity will be required to comply with the privacy protections in this Privacy Policy with respect to information collected under this Privacy Policy, or we will provide the School with notice and an opportunity to opt out of the transfer of such data prior to the transfer; and
  • except as restricted by Applicable Laws or contracts with the School, we may also share Student Data with Amplify’s affiliated education companies, provided that such disclosure is solely for the purposes of providing Products and at all times is subject to this Policy.

Non-Student Data. Amplify discloses Non-Student Data for the purposes for which Student Data is used as set forth above. Amplify may also disclose Non-Student Data as otherwise required or permitted, or as disclosed at the time of collection. Please note that we do not share mobile information or opt-in consent with third parties / affiliates for their own marketing or promotional purposes.

5. Aggregate/De-identified data

Amplify may use de-identified or aggregate data for purposes allowed under FERPA and other Applicable Laws, to research, develop, and improve educational sites, services, and applications and to demonstrate the effectiveness of the Amplify Products. Amplify will not attempt to re-identify de-identified data. We may use aggregate information (which is information that has been collected in summary form such that the data cannot be associated with any individual) for analytics and reports. For example, our promotional materials may note the total number of students served by our programs in the prior year, but that information cannot be used to identify any one student. We may also share de-identified or aggregate data with research partners to help us analyze the information for product improvement and development purposes.

Records and information are de-identified when all personal information has been removed or obscured, such that the remaining information does not reasonably identify a specific individual. We de-identify Student Data in compliance with Applicable Laws and in accordance with the guidelines of NIST SP 800-122. Amplify has implemented internal procedures and controls to protect against the re-identification of de-identified Student Data. Amplify does not disclose de-identified data to its research partners unless that party has agreed in writing not to attempt to re-identify such data.

6. Data prohibitions, Advertising, Advertising limitations

Amplify will not:

  • sell Student Data to third parties;
  • use or disclose Student Data to inform, influence, or enable targeted advertising to a Student based on Student Data or information or data inferred over time from the Student’s usage of the Products;
  • use Student Data to develop a profile of a Student for any purpose other than providing the Products to a School or Authorized School User, or as authorized by a parent or legal guardian;
  • use Student Data for any commercial purpose other than to provide the Products to the School or Authorized School User, or as permitted by Applicable Laws.

7. External third-party services

This Privacy Policy applies solely to Amplify’s Products and practices. Schools and other Authorized Users may choose to connect or use our Products in conjunction with third-party services and Products. Additionally, our sites and Products may contain links to third-party websites or services . This Privacy Policy does not address, and Amplify is not responsible for, the privacy, information, or other practices of such third parties. Schools should carefully consider which third-party applications to include among the Products and services they provide to Students and vet the privacy and data security standards of those providers.

Authorized Users may be able to log in to our Products using third-party sign-in services such as Clever, ClassLink or Google. These services authenticate your identity and provide you with the option to share certain personal information with us, including your name and email address, to pre-populate our account sign-up form. If you choose to enable a third party to share your third-party account credentials with Amplify, we may obtain personal information via that mechanism. You may configure your accounts on these third-party platform services to control what information they share.

8. Security

Amplify maintains a comprehensive information security program and uses industry standard administrative, technical, operational, and physical measures to safeguard Student Data in its possession against loss, theft and unauthorized use, disclosure, or modification. Amplify performs periodic risk assessments of its information security program and prioritizes the remediation of identified security vulnerabilities. Please see https://amplify.com/security for a detailed description of Amplify’s security program.

In the event Amplify discovers or is notified that Student Data within our possession or control was disclosed to, or acquired by, an unauthorized party, we will investigate the incident, take steps to mitigate the potential impact, and notify the School in accordance with Applicable Laws.

Non-Student Data

Outside of Student Data, Amplify uses commercially reasonable administrative, technical, personnel, and physical measures to safeguard personal information in its possession against loss, theft, and unauthorized use, disclosure or modification.

9. Data Storage and Transfers

We are a United States Company, and our servers are hosted, managed, and controlled by us in the United States. If you are outside of the United States, we use industry standards to protect your data when it leaves your country of residence and your data will always be protected in accordance with this Privacy Policy, Applicable Laws and our Agreement regardless of the storage location.

Additionally, where we transfer your personal information to service providers outside of the United Kingdom (UK), European Economic Area (EEA), or other region that offers similar protections, we use specific appropriate safeguards to contractually obligate such service providers to protect personal information in accordance with Amplify’s commitment to privacy and security and applicable data protection laws.

If you have questions or wish to obtain more information about the international transfer of your personal information or the implemented safeguards, please contact us using the contact information below.

10. Data Retention / Deletion

Student Data

Upon request, we provide the School the opportunity to review and delete the personal information collected from Students. We will retain Student Data for the period necessary to fulfill the purposes outlined in this Privacy Policy and our Agreement with the School. We do not knowingly retain Student Data beyond the time period required to support the School or Authorized School User’s educational purpose, unless authorized by the School or Authorized School User. Upon request, Amplify will return, delete, or destroy Student Data stored by Amplify in accordance with applicable law and customer requirements. We may not be able to delete all data in all circumstances, such as information retained in technical support records, customer service records, back-ups, and similar business records. All such information will be protected in accordance with this Privacy Policy and our Agreement until it has been permanently deleted. Unless otherwise notified by the School, we will delete or de-identify Student Data after termination of our Agreement with the School.

Non-Student Data

Outside of Student Data, we keep personal information as long as it is necessary or relevant for the practices described in this Privacy Policy or as otherwise required by our Agreement with the School, if applicable. We determine the appropriate retention period for personal information on the basis of the amount, nature and sensitivity of the personal information being processed, the potential risk of harm from unauthorized use or disclosure of the personal information, whether we can achieve the purposes of the processing through other means, and on the basis of applicable legal requirements (such as applicable statutes of limitations).

11. What rights and choices do you have?

What Choices Do You Have?

Marketing/Advertising

As noted above, we do not use Student Data for marketing purposes and we do not direct marketing to Students. Amplify does not use third party cookies and similar technologies for advertising and marketing purposes on Student-facing portions of the Products. The choices below apply to Non-Student Authorized Users.

Opt-out of Marketing Communications. If you want to stop receiving promotional materials from Amplify, you can follow the unsubscribe instructions at the bottom of each email or email us at privacy@amplify.com. Amplify does not send marketing communications to Students.

Opt-out of Cookies and Similar Tracking Technologies. With respect to cookies, you may be able to reject cookies through your browser or device controls. Note that you have to opt-out of cookies on each browser or device that you use. If you replace, change, or upgrade your browser or device, or delete your cookies, you may need to use these opt-out tools again. Please be aware that disabling cookies may negatively impact your experience as some features may not work properly. To learn more about browser cookies, including how to manage or delete them, check the “Help,” “Tools,” or similar section of your browser.

What Rights Do You Have?

Individuals in the U.S.

  • What Rights Do You Have With Respect to Student Data?
    • Review and Correction. FERPA requires schools to provide parents with access to their children’s education records, and parents may request that the school correct records that they believe to be inaccurate or misleading.
    • If you are a parent or guardian and would like to review, correct, or update your child’s data stored in our Products, contact your School. Amplify will work with your School to enable your access to and, if applicable, correction of your child’s education records.
    • If you have any questions about whom to contact or other questions about your child’s data, you may contact us using the information provided below.
    • Other Privacy Rights? Please see section 3 of our supplemental disclosures: “Additional U.S. State Privacy Law Rights” for more information about your U.S. privacy rights

Individuals in the EU/UK

Please see section 4 of our supplemental disclosures: “Notice for European Economic Area and United Kingdom Customers” for more information about your EU/UK privacy rights.

12. COPPA

We do not knowingly collect personal information from a Child User unless and until a School or Educator, with the permission of the School, has authorized us to collect such information to provide the Products. Amplify relies on the School acknowledging that it is acting as the parent’s agent and consenting on the parent’s behalf to process personal information of Child Users in accordance with all applicable provisions of COPPA. To the extent COPPA applies to the information we collect, we process such information for educational purposes only, and no other commercial purpose, at the direction of the School and on the basis of the School’s authorization. If you are a parent or guardian and have questions about your child’s use of the Products and any personal information collected, please direct these questions to your child’s school.

Please refer to the Appendix–Supplemental Disclosures if you are a Home User.

13. Updates to this Privacy Policy

We may change this Privacy Policy in the future. For example, we may update it to comply with new laws or regulations, to conform to industry best practices, or to reflect changes in our product offerings. When these changes do not reflect material changes in our practices with respect to use and/or disclosure of Authorized Users’ personal information, including Student Data, such changes to the Privacy Policy will become effective when we post the revised Privacy Policy on our website. In the event there are material changes in our practices that would result in Authorized Users’ personal information being used in a materially different manner than was disclosed when the information was collected, with respect to Student Data, we will notify the School, and with respect to other information, we will notify you via email and provide an opportunity to opt out before such changes take effect.

14. Contact us

If you have questions about this Privacy Policy, please contact us at:

Email: privacy@amplify.com
Mail: Amplify Education, Inc.
55 Washington St.#800
Brooklyn, NY, 11201
Phone: (800) 823-1969
Attn: General Counsel

To report a security vulnerability, visit https://amplify.com/report-a-vulnerability/.

Appendix – Supplemental Disclosures

1. Mathigon and Amplify Classroom accounts

While our Products are geared towards Schools we do provide a limited opportunity for Home Users to use the Products at home—outside of the school context. We do not allow persons under the age of 13 (or those under the age of consent in any applicable jurisdiction) to register for an account with us outside the school context.

If you are a Home User, you are prohibited from collecting or providing any personal information from students or minors. You are permitted to access the platform for instructional purposes, but you may not enroll or roster minors, create accounts for minors, or input any personal information of minors into the Product.

Please note that most parts of Mathigon can be used without creating an account or providing any personal information that directly identifies you.

What Rights Do You Have? If you are a Child User who is 13 or older with a legacy Mathigon account (or the parent or guardian of a Child User with a legacy Mathigon account), you may request that we provide for your review, delete from our records, or cease collecting any Child User personal information. To the extent that you are unable to exercise these rights through self-service features within your account with us, please contact us by sending an email to: help@amplify.com and we will provide assistance.

2. U.S. Notice at Collection

Personal Information We Collect How We Use Personal Information

Student Data, which includes:

  • Roster Information
  • Demographic Data, such as race and national origin
  • School Records
  • Account Information
  • Schoolwork and Student Generated Content
  • Teacher Comments and Feedback
  • Device and Usage Data
  • To provide and improve our educational Products;
  • To support Schools’ and Authorized School Users’ activities;
  • To ensure secure and effective operation of our Products;
  • For purposes requested or authorized by the School or Authorized School Users, or as otherwise permitted by Applicable Laws;
  • For adaptive or personalized learning features of the Products; provided that Student Data is not disclosed;
  • For customer support purposes, to respond to the inquiries and fulfill the requests of the School and their Authorized School Users;
  • To enforce product access and security controls; and
  • To conduct system audits and improve protections against the misuse of our Products, or to detect and prevent fraud and other harmful activities.

Authorized Users, which includes:

  • Contact Information
  • Account Information
  • Survey Responses
  • Device and Usage Data
  • For the purposes for which Student Data is used as set forth above;
  • For marketing purposes in limited circumstances (e.g. to periodically send newsletters and other promotional materials), which will not be based on Student Data or directed to K–12 students;
  • For internal research and analytics; and
  • As otherwise required or permitted, or as we may notify you at the time of collection.

Some of the information described above may be considered “sensitive” under the laws of certain jurisdictions (i.e., account credentials and race/national origin) (“Sensitive Information”). We use Sensitive Information for necessary or reasonably expected purposes – specifically, to provide you with our Services (i.e., account credentials are used to allow account logins and race/national origin are used for the School’s reporting purposes when voluntarily provided by the School).

We do not sell or share your personal information, as described in California law.

We retain your personal information for as long as reasonably necessary for the purposes disclosed in the chart above. Additional information about our retention of Student Data and personal information from other Authorized Users can be found in Section 10 of this Privacy Policy.

Please see the Additional U.S. State Privacy Law Rights section of this appendix for information about your privacy rights pursuant to applicable U.S. law.

Notice of Financial Incentive

From time to time, to support our services, we offer opportunities to complete surveys and questionnaires. As an incentive for completing the survey or questionnaire, you can voluntarily provide personal information as an entry into a raffle drawing or to obtain other benefits, discounts, offers, or deals that may constitute a financial incentive under California law (“Financial Incentive”). The categories of personal information required for us to provide the Financial Incentives include: contact information and any other information that you choose to provide when you complete the survey.

Participation is voluntary and you can opt out at any time before the survey is complete. We do not allow students to participate in our surveys.

The value of the personal information we collect in connection with our Financial Incentives is equivalent to the value of the benefit offered.

3. Additional U.S. State Privacy Law Rights

Note for Requests Relating to Student Data: Because Amplify provides the Products to Schools as a “School Official,” we collect, retain, use, and disclose Student Data only for or on behalf of the School for educational purposes, including the purpose of providing the Products specified in our Agreement with the School and for no other commercial purpose. Accordingly, we act as a “service provider” for the School with respect to School Data. We work with the School to support and assist them in addressing privacy requests relating to School Data. Please reach out to your School directly if you wish to exercise any privacy rights that may be available to you.

For all other requests: With respect to Amplify Data, individuals residing in certain U.S. states have the following rights, regarding your personal information (each of which is subject to various exceptions and limitations):

  • Access. You have the right to request, up to two times every 12 months, that we disclose to you the categories of personal information collected about you; the categories of sources from which the personal information is collected; the categories of personal information sold or shared; the business or commercial purpose for collecting, selling, or sharing the personal information; the categories of third parties with whom personal information was shared; and the specific pieces of personal information collected about you.
  • Correction. You have the right to request that we correct inaccurate personal information collected from you.
  • Deletion. You have the right to request that we delete the personal information that we maintain about you. Even after the deletion of your account, some personal information may remain on our servers, such as in technical support logs, server caches, data backups, or email conversations. These will be automatically deleted after a reasonable amount of time, unless we are legally required to retain information for longer, or unless there is a legitimate business reason (e.g. security and fraud prevention or financial record-keeping). We are not required to delete any information which has been aggregated or de-identified in accordance with Section 5.
  • No Discrimination. You have the right not to be discriminated against for exercising these rights.
  • Appeals. You have a right to appeal decisions concerning your ability to exercise your consumer rights.

See Submitting Requests section below for details on submitting a request to exercise these rights.

4. Notice for European Economic Area (EEA) and United Kingdom (UK) Customers

As detailed at the beginning of our Privacy Policy (under the section titled “Our Role”), Amplify operates primarily as a processor that collects personal information on behalf of the School, and we act as a controller in limited circumstances where we offer Products outside the school context.

If you represent a School in the EEA or the UK, please note that we process personal information in accordance with this Privacy Policy, our Acceptable Use Policy, and our standard Data Protection Agreement, which sets out our responsibilities when it comes to our processing activities. Schools must send an email to privacy@amplify.com to enter into that DPA.

Lawful Basis for Processing

We rely on the following lawful bases for our processing activities:

  • Consent;
    • We obtain your consent to use cookies to collect and process device and usage data to understand how individuals use our Products.
  • Pursuant to a contract for use of our Products;
    • We process School Data to provide our Products (e.g., to create, authenticate and manage your account, to verify your identity, to manage our Products) pursuant to the Agreement between us and the School, as required in order for us to perform our obligations.
  • To comply with our legal obligations;
    • We process all categories of personal information that we collect to ensure the safety and security of our Products where we are complying with security requirements under data protection and cyber and information security law.
    • We process all categories of personal information that we collect to comply with our legal obligations which includes, for example, to access, retain or share certain personal information where we receive a valid request from a government body, law enforcement body, judicial body regulator or similar, to deal with legal claims and prospective legal claims, and to ensure we are complying with applicable laws.
  • When we have a legitimate interest in doing so, which is not outweighed by the risks to the individual.
    • We process all categories of personal information that we collect to support the provision, effective management, and improvement of our Products where such activities are not strictly required under our contract. This is in our legitimate interests to ensure that we are providing the best possible service.
    • We process all categories of personal information that we collect to ensure the safety and security of our services where this is important but not required under the data protection law or cyber and information security laws. This is in our legitimate interests to ensure the security of our services and systems, to prevent threats, abuse or fraudulent or unlawful activity, to promote safety and security and to ensure our Products are used in accordance with our terms and conditions.
    • We process the contact information of Non-Student Authorized Users to manage our relationship, including to respond to queries or otherwise communicate with you in relation to our Products and the operation of our business where this is not strictly required under a contract with you. This is in our legitimate interests to communicate with and resolve queries from users of our Products and to ensure that we are providing the best possible service.

We process the contact information and survey data of Non-Student Authorized Users for internal research and marketing purposes in limited circumstances (e.g. to periodically send newsletters and other promotional materials), which will not be based on Student Data or directed to Students. This is in our legitimate interests to understand our customers and prospective customers, understand how our products and services are perceived in the market, to promote our products, and to grow and develop our business.

Your Data Subject Rights

Note for Requests Relating to School Data: Amplify acts as processor to its School customers with respect to all School Data. We work with our School customers to support and assist them in addressing privacy requests relating to School Data. Please reach out to your School directly if you wish to exercise any privacy rights that may be available to you.

For all other Requests With respect to Amplify Data, you have the following rights if you are in the EEA or UK, subject to certain exceptions:

  • Right of access: You have the right to ask us for confirmation on whether we are processing your personal information and access to that personal information.
  • Right to correction: You have the right to have your personal information corrected.
  • Right to erasure: You have the right to ask us to delete your personal information.
  • Right to withdraw consent: You have the right to withdraw consent that you have provided.
  • Right to lodge a complaint with a supervisory authority: You have the right to lodge a complaint with a supervisory authority.
  • Right to restriction of processing: You have the right to request the limiting of our processing under limited circumstances.
  • Right to data portability: You have the right to receive the personal information that you have provided to us, in a structured, commonly used, and machine-readable format, and you have the right to transmit that information to another controller, including to have it transmitted directly, where technically feasible.
  • Right to object: You have the right to object to our processing of your personal information

See Submitting Requests section below for details on submitting a request to exercise these rights.

5. Submitting Requests

To exercise any of the rights described in sections 2 and 3 of this appendix, email us at privacy@amplify.com and specify which privacy right you intend to exercise. We may require additional information from you to allow us to confirm your identity. The verification steps will vary depending on the sensitivity of the personal information and whether you have an account with us. Please note that your rights may not apply in all cases. For example, we may need to retain your personal information to comply with our legal obligations, resolve disputes, prevent fraud and enforce our agreements. We will inform you if we are not able to fully respond to your requests. You may designate an authorized agent to make a request on your behalf. When submitting the request, please ensure the authorized agent identifies himself/herself/itself as an authorized agent and can show written permission from you to represent you. We may contact you directly to confirm that you have authorized the agent to act on your behalf or confirm your identity.

Complaints

If you have any issues, you have the right to lodge a complaint with an EEA or UK supervisory authority. We would, however, appreciate the opportunity to address your concerns before you approach a data protection regulator and would welcome you directing an inquiry first to us. To do so, please contact us by email at privacy@amplify.com or by mail at Amplify Education, Inc., 55 Washington St.#800, Brooklyn, NY, 11201.

6. Google APIs

Amplify uses Google’s Application Programming Interface (API) Services to enable Authorized Users to log in to Amplify, import classes and rosters from Google Classroom, create assignments in Google Classroom, and copy, edit, and publish Amplify content using Google Slides. Amplify will use and transfer information received from Google’s API in accordance with Google API Service User Data Policy, including the Limited Use requirements.

Update History:

Update: 6/13/2025: This Policy has been updated to align with product updates and to provide additional context for authorized educational use of Amplify’s Products.

Update 6/27/2024: The Policy has been updated to include an explanation regarding Google APIs in the Appendix — Supplemental Disclosures section.

Update 6/30/2023: This Privacy Policy has been updated to address new state law data privacy requirements.

Grade 6

Unit 1: Area and Surface Area

Illustrative MathematicsDesmos Math 6–A1
Topic A: Reasoning to Find Area 
Lesson 1: Tiling the PlaneUnit 1
Lesson 1: Shapes on a Plane [Free lesson]
Lesson 2: Finding Area by Decomposing and Rearranging
Lesson 3: Reasoning to Find Area
Unit 1
Lesson 2: Letters
Topic 2: Parallelograms
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Unit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Topic 3: Triangles
Lesson 7: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 8: Area of TrianglesUnit 1
Lesson 5: Exploring Triangles (Print available)
Lesson 9: Formula for the Area of a Triangle
Lesson 10: Bases and Heights of Triangles
Unit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Topic 4: Polygons
Lesson 11: PolygonsUnit 1
Lesson 2: Letters
Lesson 8: Pile of Polygons
Practice Day 1 (Print available)
Unit 7
Lesson 11: Polygon Maker
Topic 5: Surface Area
Lesson 12: What is Surface Area?Unit 1
Lesson 9: Renata´s Stickers [Free lesson]
Lesson 13: PolyhedraUnit 1Lesson 10: Plenty of Polyhedra
Lesson 14: Nets and Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 13: Take It To Go
Lesson 15: More Nets, More Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Practice Day 2 (Print available)
Lesson 16: Distinguishing Between Surface Area and Volume
Topic 6: Squares and Cubes 
Lesson 17: Squares and CubesUnit 6
Lesson 12: Squares and Cubes
Lesson 18: Surface Area of a Cube 
Topic 7: Let’s Put It to Work 
Lesson 19: Designing a TentUnit 1
Lesson 13: Take It To Go (Print available)

Unit 2: Introducing Ratios

Topic 1: Introducing Ratios
Lesson 1: Introducing Ratios and Ratio LanguageUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)
Lesson 2: Representing Ratios with DiagramsUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)Lesson 3: Rice Ratios (Print available)
Topic 2: Equivalent Ratios
Lesson 3: RecipesUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 3: Rice Ratios (Print available)
Lesson 4: Color MixturesUnit 2Lesson 7: Mixing Paint, Part 1Lesson 12: Mixing paint, Part 2
Lesson 5: Defining Equivalent RatiosUnit 2Lesson 3: Rice Ratios (Print available)Lesson 4: Fruit Lab [Free lesson]Lesson 11: Community LifePractice Day 1 (Print available)
Topic 3: Representing Equivalent ratios
Lesson 6: Introducing Double Number Line DiagramsUnit 2Lesson 5: Balancing Act
Lesson 7: Creating Double Line DiagramsUnit 2Lesson 5: Balancing ActLesson 6: Product prices (Print available)
Lesson 8: How Much for One?Unit 2Lesson 6: Product prices (Print available)
Lesson 9: Constant SpeedUnit 2Lesson 8: World Records (Print available)
Lesson 10: Comparing Situations by Examining RatiosUnit 2Lesson 7: Mixing Paint, Part 1 
Topic 4: Solving Ratio and Rate Problems
Lesson 11: Representing Ratios with TablesUnit 2Lesson 9: Disaster Preparation [Free lesson]
Lesson 12: Navigating a Table of Equivalent Ratios
Lesson 13: Tables and Double Line Diagrams
Unit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1
Lesson 14: Solving Equivalent Ratio ProblemsUnit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1Lesson 10: BalloonsLesson 11: Community Life (Print available)
Topic 5: Part-Part-Whole Ratios
Lesson 15: Part-Part-Whole RatiosUnit 2Lesson 12: Mixing paint, Part 2Lesson 13: City Planning
Lesson 16: Solving More Ratio ProblemsUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Topic 6: Let’s Put It to Work 
Lesson 17: A Fermi ProblemUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)Practice Day 2 (Print available)

Unit 3: Rates and Percentages

Topic 1: Units of Measurement 
Lesson 1: The Burj KhalifaUnit 3
Lesson 4: Model Trains
Topic 2: Unit Conversion
Lesson 2: Anchoring Units of MeasurementUnit 3
Lesson 1: Many Measurements (Print available) [Free lesson]
Lesson 3: Measuring with Different-Sized Units
Lesson 4: Converting Units
Unit 3
Lesson 2: Counting Classrooms
Lesson 3: Pen Pals
Topic 3: Rates
Lesson 5: Comparing Speeds and PricesUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 6: Interpreting Rates
Lesson 7: Equivalent Ratios Have the Same Unit Rates
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 8: More About Constant SpeedUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 9: Solving Rate ProblemsUnit 3
Lesson 7: More Soft Serve
Topic 4: Percentages
Lesson 10: What Are percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 11: Percentages and Double Number LinesUnit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing? (Print available)
Lesson 12: Percentages and Tape DiagramsUnit 3
Lesson 10: What’s Missing? (Print available)
Lesson 13: Benchmark percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 14: Solving Percentage Problems
Lesson 15: Finding This Percent of That
Lesson 16: Finding the Percentage
Unit 3
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Topic 5: Let’s Put It to Work 
Lesson 17: Painting a RoomUnit 3
Lesson 13: A Country as a Village
Lesson 7: Equivalent Ratios Have the Same Unit RatesUnit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]

Unit 4: Dividing Fractions

Topic 1: Making Sense of Division 
Lesson 1: Size of Divisor and Size of Quotient
Lesson 2: Meanings of Division
Unit 4Lesson 1: Cookie Cutter
Lesson 3: Interpreting Division SituationsUnit 4Lesson 2: Making Connections (Print available)
Topic 2: Meanings of Fraction Division
Lesson 4: How Many Groups (Part 1)Unit 4Lesson 3: Flour Planner [Free lesson]Lesson 4: Flower Planters 
Lesson 5: How Many Groups (Part 2)Unit 4Lesson 5: Garden Bricks (Print available)
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4Lesson 5: Garden Bricks (Print available)Lesson 6: Fill the Gap [Free lesson]
Lesson 7: What Fraction of a Group?
Lesson 8: How Much in Each Group? (Part 1)
Lesson 9: How Much in Each Group? (Part 2)
Unit 4Lesson 8: Potting Soil
Topic 3: Algorithm for Fraction Division
Lesson 10: Dividing by Unit and Non-Unit FractionsUnit 4Lesson 7: Break It DownLesson 8: Potting SoilLesson 9: Division Challenges 
Lesson 11: Using an Algorithm to Divide FractionsUnit 4Lesson 9: Division ChallengesPractice Day
Topic 4: Fractions in Lengths, Areas, and Volumes
Lesson 12: Fractional LengthsUnit 4Lesson 11: Classroom Comparisons
Lesson 13: Rectangles with Fractional Side LengthsUnit 4Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 14: Fractional Lengths in Triangles and Prisms
Lesson 15: Volume of PrismsUnit 4Lesson 13: Volume Challenges
Topic 5: Let’s Put It to Work
Lesson 16: Solving Problems with FractionsUnit 4Lesson 10: Swap Meet (Print available)
Lesson 17: Fitting Boxes into BoxesUnit 4Lesson 14: Planter Planner (Print available)

Unit 5: Arithmetic in Base Ten

Topic 1: Warming Up to Decimals 
Lesson 1: Using Decimals in a Shopping ContextUnit 5Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Topic 2: Adding and Subtracting Decimals
Lesson 2: Using Decimals to Represent Addition and SubtractionUnit 5Lesson 3: Fruit by the PoundLesson 4: Missing Digits
Lesson 3: Adding and Subtracting Decimals with Few Non-Zero DigitsUnit 5Lesson 4: Missing Digits
Lesson 4: Adding and Subtracting Decimals with Many Non-Zero Digits 
Topic 3: Multiplying Decimals
Lesson 5: Decimal Points in ProductsUnit 5Lesson 5: Decimal Multiplication
Lesson 6: Methods for Multiplying DecimalsUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with AreasLesson 7: Multiplication methods (Print available)
Lesson 7: Using Diagrams to Represent MultiplicationUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with Areas
Lesson 8: Calculating Products of DecimalsUnit 5Lesson 6: Multiplying with Areas
Topic 4: Dividing Decimals
Lesson 9: Using the Partial Quotients MethodUnit 5Lesson 8: Division Diagrams
Lesson 10: Using Long DivisionUnit 5Lesson 8: Division DiagramsLesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Lesson 11: Dividing Numbers That Result in Decimals
Lesson 12: Dividing Decimals by Whole Numbers
Lesson 13: Dividing Decimals by Decimals
Unit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Topic 5: Let’s Put It to Work
Lesson 14: Using Operations on Decimals to Solve ProblemsUnit 5Lesson 11: Movie Time [Free lesson]
Lesson 15: Making and Measuring Boxes
Lesson 12: Dividing Decimals by Whole Numbers 
Lesson 13: Dividing Decimals by DecimalsUnit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and Equations
Lesson 2: Truth and Equations
Unit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)
Lesson 3: Staying in BalanceUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging Around
Lesson 4: Practice Solving Equations and Representing Situations with EquationsUnit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Lesson 5: A New Way to Interpret a and bUnit 6Lesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Topic 2: Equal and Equivalent
Lesson 6: Write Expressions Where Letters Stand for NumbersUnit 6Lesson 6: Vari-applesLesson 7: Border Tiles
Lesson 7: Revisit PercentagesUnit 3Lesson 10: What’s Missing?Lesson 11: Cost BreakdownLesson 12: More Bicycle Goals
Lesson 8: Equal and EquivalentUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging AroundLesson 6: Vari-apples
Topic 9: The Distributive Property, Part 1Unit 6Lesson 8: Products and Sums [Free lesson]
Lesson 10: The Distributive Property, Part 2
Lesson 11: The Distributive Property, Part 3
Unit 6Lesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences (Print available)
Topic 3: Expressions with Exponents
Lesson 12: Meaning of ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)
Lesson 13: Expressions with Exponents
Lesson 14: Evaluating Expressions with Exponents
Lesson 15: Equivalent Exponential Expressions
Unit 6Lesson 11: Exponent Expressions (Print available)Lesson 12: Squares and Cubes
Topic 4: Relationships Between Quantities 
Lesson 16: Two Related Quantities, Part 1
Lesson 17: Two Related Quantities, Part 2
Lesson 18: More Relationships
Unit 6Lesson 13: Turtles All the WayLesson 14: Representing RelationshipsLesson 15: Connecting Representations (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Tables, Equations, and Graphs, Oh My!Unit 6Lesson 16: Subway fares (Print available) [Free lesson]

Unit 7: Rational Numbers

Topic 1: Positive and Negative Numbers
Lesson 1: Positive and Negative NumbersUnit 7Lesson 1: Can You Dig In [Free lesson]Lesson 2: Digging Deeper
Lesson 2: Points on the Number LineUnit 7Lesson 2: Digging Deeper
Lesson 3: Comparing Positive and Negative Numbers
Lesson 4: Ordering Rational Numbers
Unit 7Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 5: Using Negative Numbers to make Sense of ContextsUnit 7 Lesson 4: Sub-Zero
Lesson 6: Absolute Value of Numbers
Lesson 7: Comparing Numbers and Distance from Zero
Unit 7Lesson 5: Distance on the Number Line
Topic 2: Inequalities
Lesson 8: Writing and Graphing InequalitiesUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Solutions of Inequalities
Lesson 10: Interpreting Inequalities
Unit 7Lesson 6: Tunnel Travel [Free lesson]Lesson 7: Comparing WeightsLesson 8: Shira´s Solutions
Topic 3: The Coordinate Plane
Lesson 11: Points on the Coordinate Plane
Lesson 12: Constructing the Coordinate Plane
Unit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate Plane
Lesson 13: Interpreting Points on a Coordinate PlaneUnit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate PlaneLesson 11: Polygon Maker
Lesson 14: Distances on a Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Lesson 15: Shapes on the Coordinate PlaneUnit 1Lesson 1: Shapes on a Plane [Free lesson]Lesson 2: LettersLesson 5: Exploring Triangles (Print available)Lesson 6: Triangles and ParallelogramsUnit 7Lesson 3: Exploring Parallelograms (Print available)Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Topic 4: Common Factors and Common Multiples
Lesson 16: Common FactorsUnit 5Lesson 15: Common factors
Lesson 17: Common MultiplesUnit 5Lesson 14: Common Multiples
Lesson 18: Using Common Multiples and Common FactorsUnit 5Lesson 14: Common MultiplesLesson 15: Common factorsPractice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Drawing on the Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)

Unit 8: Data Sets and Distributions

Topic 1: Data, Variability, and Statistical Questions
Lesson 1: Got Data?
Lesson 2: Statistical Questions
Unit 8Lesson 1: Screen TimeLesson 2: Dot Plots
Topic 2: Dot Plots and Distributions
Lesson 3: Representing Data Graphically
Lesson 4: Dot Plots
Lesson 5: Using Dot Plots to Answer Statistical Questions
Unit 8Lesson 2: Dot PlotsLesson 3: Minimum Wage (Print available) [Free lesson]Lesson 4: Lots More Dots
Lesson 6: Interpreting Histograms
Lesson 7: Using Histograms to Answer Statistical Questions
Lesson 8: Describing Distributions on Histograms
Unit 8Lesson 5: The Plot Thickens [Free lesson]Lesson 6: DIY Histograms (Print available)
Topic 3: Measures of Center and Variability
Lesson 9: Mean
Lesson 10: Finding and Interpreting the Mean as a Balance Point
Unit 8Lesson 7: Snack Time
Lesson 11: Variability and MADUnit 8Lesson 8: Pop It!
Lesson 12: Using Mean and MAD to Make ComparisonsUnit 8Lesson 9: Hoops
Topic 4: Median and IQR
Lesson 13: MedianUnit 8Lesson 11: Toy Cars [Free lesson]Lesson 12: In the News
Lesson 14: Comparing Mean and MedianUnit 8Lesson 12: In the News
Lesson 15: Quartiles and Interquartile RangeUnit 8Lesson 13: Pumpkin Patch
Lesson 16: Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 17: Using Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)Lesson 15: Hollywood Part 2Lesson 16: Hollywood Part 3 (Print available)Practice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 18: Using Data to Solve ProblemsUnit 8Lesson 16: Hollywood Part 3 (Print available)

Unit 9: Putting It All Together

Topic 1: Making Connections
Lesson 1: Fermi Problems
Lesson 2: In Our Class Were the World
Unit 3Lesson 13: A Country as a Village
Lesson 3: Rectangle MadnessUnit 5Lesson 14: Common MultiplesLesson 15: Common factors
Topic 2: Voting
Lesson 4: How Do We Choose?Unit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Lesson 5: More than Two ChoicesUnit 3Lesson 13: A Country as a Village
Lesson 6: Picking RepresentativesUnit 8Lesson 16: Hollywood Part 3 (Print available)

Grade 7

Unit 1: Scale Drawings

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Scaled Copies 
Lesson 1: What are Scaled Copies?Unit 1Lesson 1: Scaling Machines [Free lesson]
Lesson 2: Corresponding Parts and Scale FactorsUnit 1Lesson 2: Scaling Robots Unit 3Lesson 1: Toothpicks
Lesson 3: Making Scaled Copies
Lesson 4: Scaled Relationship
Unit 1Lesson 3: Make It Scale Unit 4Lesson 3: Sticker Sizes
Lesson 5: The Size and the Scale FactorUnit 1Lesson 4: Scale Factor Challenges
Lesson 6: Scaling and AreaUnit 1Lesson 5: TilesPractice Day 1 (Print available)
Topic 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1Lesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scale Drawings and Maps 
Lesson 9: Creating Scale Drawings
Lesson 10: Changing Scales in Scale Drawings
Unit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)
Lesson 11: Scales without Units 
Lesson 12: Units in Scale DrawingsUnit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)Practice Day 2 (Print available)
Topic 3: Let’s Put It to Work
Lesson 13: Draw It to ScaleUnit 1Lesson 10: Room Redesign (Print available)

Unit 2: Introducing Proportional Relationships

Topic 1: Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the OthersUnit 2Lesson 1: Paint [Free lesson] 
Lesson 2: Introducing Proportional Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 3: More About Constant of ProportionalityUnit 2Lesson 3: Sugary Drinks (Print available)Unit 4Lesson 3: Sticker Sizes
Topic 2: Representing Proportional Relationships with Equations 
Lesson 4: Proportional Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of Equations
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Unit 2Lesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsPractice Day
Topic 3: Comparing Proportional and Nonproportional Relationships 
Lesson 7: Comparing Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 8: Comparing Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsLesson 11: Four RepresentationsLesson 12: Water Efficiency
Lesson 9: Solving Problems About Proportional RelationshipsUnit 2Lesson 12: Water Efficiency
Topic 4: Representing Proportional Relationships with Graphs
Lesson 10: Introducing Graphs of Proportional Relationships
Lesson 11: Interpreting Graphs of Proportional Relationships
Lesson 12: Using Graphs to Compare Relationships
Lesson 13: Two Graphs for Each Relationship
Unit 2Lesson 8: Dino Pops [Free lesson]Lesson 9: Gallon ChallengeLesson 10: Three TurtlesLesson 11: Four RepresentationsLesson 12: Water Efficiency
Topic 5: Let’s Put It to Work
Lesson 14: For RepresentationsUnit 2Lesson 11: Four Representations (Print available)
Lesson 15: Using Water EfficiencyUnit 2Lesson 12: Water Efficiency

Unit 3: Measuring Circles

Topic 1: Circumference of a Circle 
Lesson 1: How Well Can You Measure?Unit 3Lesson 1: Toothpicks
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Unit 3Lesson 2: Is It a Circle?Lesson 3: Measuring Around [Free lesson]
Lesson 5: Circumference and Wheels 
Topic 2: Area of a Circle
Lesson 6: Estimating AreasUnit 3Lesson 5: Area Strategies
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Unit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi?Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. SquarePractice Day 2 (Print available)
Lesson 9: Applying Area of CirclesUnit 3Lesson 6: Radius Squares (Print available)
Topic 3: Let’s Put It to Work
Lesson 10: Distinguishing Circumference and AreaUnit 3Lesson 7: Why Pi?
Lesson 11: Stained-Glass WindowsUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)

Unit 4: Proportional Relationships and Percentages

Topic 1: Proportional Relationships with Fractions 
Lesson 1: Lots of Flags
Lesson 2: Ratios and Rates with Fractions
Lesson 3: Revisiting Proportional Relationships
Lesson 4: Half as Much Again
Unit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 5: Say It with Decimals 
Topic 2: Percent Increase and Decrease 
Lesson 6: Increasing and DecreasingUnit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 7: One Hundred percentUnit 4Lesson 6: 100% (Print available)
Lesson 8: Percent Increase and Decrease with EquationsUnit 4Lesson 5: All the Equations
Lesson 9: More and Less than 1% 
Topic 3: Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Unit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 12: Finding the PercentagesUnit 4Lesson 4: More and Less
Lesson 13: Measurement Error
Lesson 14: Percent Error
Lesson 15: Error Intervals
Unit 4Lesson 11: Bookcase Builder
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Percent ProblemsUnit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]Practice Day

Unit 5: Rational Number Arithmetic

Topic 1: Interpreting Negative Numbers 
Lesson 1: Interpreting Negative NumbersUnit 5Lesson 1: Floats and Anchors [Free lesson]
Topic 2: Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Unit 5Lesson 2: More Floats and AnchorsLesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 4: Money and Debts 
Lesson 5: Representing SubtractionUnit 5Lesson 5: Number Puzzles
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Unit 5Lesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]Lesson 5: Number PuzzlesLesson 10: Integer Puzzles [Free lesson]Lesson 11: Changing TemperaturesLesson 13: Solar Panels and More (Print available)Practice Day 1 (Print available)
Topic 3: Multiplying and Dividing Rational Numbers
Lesson 8: Position, Speed, and Direction
Lesson 9: Multiplying Rational Numbers
Lesson 10: Multiply!
Unit 5Lesson 7: Back in Time
Lesson 11: Dividing Rational NumbersUnit 5Lesson 8: Speeding Turtles
Lesson 12: Negative Rates 
Topic 4: Four Operations with Rational Numbers 
Lesson 13: Expressions with Rational NumbersUnit 5Lesson 9: Expressions (Print available)
Lesson 14: Solving Problems with Rational NumbersLesson 11: Changing Temperatures
Lesson 12: Arctic Ice Sea (Print available)
Lesson 13: Solar Panels and More (Print available)
Topic 5: Solving Equations When There Are Negative Numbers 
Lesson 15: Making and Measuring Boxes 
Lesson 16: Representing Contexts with Equations 
Topic 6: Let’s Put It to Work 
Lesson 17: The Stock market

Unit 6: Expressions, Equations, and Inequalities

Topic 1: Representing Situations of the Form px + q and p(+ q) = r
Lesson 1: Relationships Between Quantities
Unit 2 Lesson 1: Paint [Free lesson] Lesson 2: Balloon Float
Unit 4 Lesson 1: Mosaics [Free lesson] Lesson 2: Peach Cobbler (Print available)
Unit 6 Lesson 1: Toothpicks and Tiles
Lesson 2: Reasoning about Contexts with Tape Diagrams
Lesson 3: Reasoning about Equations with Tape Diagrams
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
Unit 6Lesson 2: Smudged ReceiptsLesson 3: EquationsLesson 4: Seeing Structure (Print available)
Lesson 6: Distinguishing between Two Types of SituationsUnit 6Lesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)
Topic 2: Solving Equations of the Form px + q and p(+ q) = and Problems That lead to Those Equations 
Lesson 7: Reasoning about Solving Equations (Part 1)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available) 
Lesson 8: Reasoning about Solving Equations (Part 2)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 9: Always-Equal Machines
Topic 9 Dealing with Negative Numbers 
Lesson 10: Different Options for Solving One EquationUnit 6Lesson 7: Keeping It True (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)
Lesson 11: Using Equations to Solve ProblemsUnit 6Lesson 12: Community Day (Print available)
Lesson 12: Solving Problems about Percent Increase or DecreaseUnit 4Lesson 10: Cost of College (Print available)
Topic 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6Lesson 13: I Saw the SignsLesson 15: BudgetingLesson 16: Shira the Sheep [Free lesson]
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiency Solving Inequalities
Unit 6Lesson 14: Unbalanced HangersLesson 15 Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Unit 6Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)Practice Day 2 (Print available)
Topic 4: Writing Equivalent Expressions 
Lesson 18: Subtraction in Equivalent ExpressionsUnit 6Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available) 
Lesson 19: Expanding and FactoringUnit 6Lesson 8: Factoring and Expanding (Print available)Lesson 11: Equation Roundtable (Print available)
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Unit 6Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 8: Factoring and Expanding (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Practice Day 1 (Print available)
Topic 5: Let’s Put It to Work
Lesson 23: Applications of ExpressionsUnit 6Lesson 12: Community Day (Print available)

Unit 7: Angles, Triangles, and Prisms

Topic 1: Angle Relationships
Lesson 1:Relationships of Angles
Unit 7 Lesson 1: Pinwheels Lesson 2: Friendly Angles [Free lesson] Lesson 3: Angle Diagrams
Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Unit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle Diagrams
Lesson 4: Solving for Unknown AnglesUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available)
Lesson 5: Using Equations to Solve for Unknown AnglesUnit 7Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Topic 2: Drawing Polygons with Given Conditions 
Lesson 6: Building Polygons (Part 1)
Lesson 7: Building Polygons (Part 2)
Unit 7Lesson 6: Is It Enough?
Lesson 8: Triangles with 3 Common MeasuresUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Unit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Topic 3: Solid Geometry
Lesson 11: Slicing SolidsUnit 7Lesson 9: Slicing Solids
Lesson 12: Volume of Right PrismsUnit 7Lesson 10: Simple Prisms
Lesson 13: Decomposing Bases for AreasUnit 7Lesson 11: More Complicated Prisms
Lesson 14: Surface Area of Right PrismsUnit 7Lesson 10: Simple PrismsLesson 11: More Complicated PrismsLesson 12: Surface Area Strategies (Print available)
Lesson 15: Distinguishing Volume and Surface Area
Lesson 16: Applying Volume and Surface AreaUnit 7Lesson 13: Popcorn Possibilities
Topic 4: Let’s Put It to Work
Lesson 17: Building Prisms

Unit 8: Probability and Sampling

Topic 1: Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Unit 8 Lesson 1: How Likely? (Print available) [Free lesson] Lesson 2: Prob-bear-bilities [Free lesson] Lesson 3: Mystery Bag
Lesson 4: Estimating Probabilities Through Repeated ExperimentsUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Lesson 5: More Estimating ProbabilitiesUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 9: Car, Bike, or Train? (Print available)
Lesson 6: Estimating Probabilities Using SimulationUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 2: Probabilities of Multi-step Events
Lesson 7: Simulating Multi-step EventsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Lesson 8: Keeping Track of All Possible OutcomesUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Topic 9: Multi-step experiments
Lesson 10: Designing SimulationsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 3: Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Unit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Topic 4: Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Unit 8 Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 11: HeadlinesLesson 12: Flower Power
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations with Friends
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)
Topic 5: Let’s Put It to Work
Lesson 20: Memory TestUnit 8Lesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)

Grade 8

Unit 1: Rigid Transformations and Congruence

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Rigid Transformations 
Lesson 1: Moving in the PlaneUnit 1Lesson 1: Transformers [Free lesson]
Lesson 2: Naming the MovesUnit 1Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Grid MovesUnit 1Lesson 3: Transformation GolfLesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting CoordinatedUnit 3Lesson 6: Translations
Lesson 4: Making the MovesUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 5: Coordinate MovesUnit 1Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 6: Describing TransformationsUnit 1Lesson 5: Getting CoordinatedLesson 6: Connecting the Dots [Free lesson]
Topic 2: Properties of Rigid Transformations 
Lesson 7: No Bending or StretchingUnit 1Lesson 7: No Bending, No Stretching
Lesson 8: Rotation PatternsUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 9: Moves in Parallel
Lesson 10: Composing Figures
Unit 1 Lesson 10: Transforming Angles
Topic 3: Congruence 
Lesson 11: What is the Same?
Lesson 12: Congruent Polygons
Lesson 13: Congruence
Unit 1 Lesson 7: Are They the Same?Lesson 9: Are They Congruent?Practice Day (Print available)
Topic 4: Angles in a Triangle
Lesson 14: Alternate Interior Angles
Lesson 15: Adding the Angles in a Triangle
Unit 1 Lesson 11: Tearing It Up (Print available)
Lesson 16: Parallel Lines and the Angles in a TriangleUnit 1 Lesson 10: Transforming Angles
Topic 5: Let’s Put It to Work
Lesson 17: Rotate and TessellateLesson 13: Tessellate [Free lesson]

Unit 2: Dilations, Similarity, and Introducing Slope

Topic 1: Dilations
Lesson 1: Projecting and ScalingUnit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]
Lesson 2: Circular Grid
Lesson 3: Dilations with No Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]Lesson 3: Match My DilationLesson 4: Dilations on a Plane
Topic 2: Similarity 
Lesson 6: SimilarityUnit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 7: Similar Polygons 
Lesson 8: Similar Triangles
Lesson 9: Side Length Quotients in Similar Triangles
Unit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Topic 3: Slope
Lesson 10: Meet SlopeUnit 2Lesson 9: Water SlideLesson 10: Points on a PlanePractice Day (Print available)Unit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations Unit 4Lesson 8: When Are They the Same?
Lesson 11: Writing Equations of LinesUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: SolutionsLesson 11: Pennies and Quarters Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 12: Using Equations of LinesUnit 3Lesson 9: Coin Capture
Topic 4: Let’s Put It to Work
Lesson 13: The Shadow KnowsUnit 2Lesson 8: Shadows

Unit 3: Linear Relationships

Topic 1: Proportional Relationships 
Lesson 1: Understanding Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Graphs of Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water Tank Unit 5Lesson 4: Window Frames
Lesson 3: Representing Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 4: Window FramesLesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 4: Comparing Proportional RelationshipsUnit 3Lesson 3: Posters
Topic 2: Representing Linear Relationships
Lesson 5: Introduction to Linear RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 4: Stacking CupsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: More Linear RelationshipsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 7: Representations of Linear RelationshipsUnit 3Lesson 5: Flags [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 8: Translating mx + bUnit 3Lesson 3: PostersLesson 6: Translations
Topic 3: Finding Slopes 
Lesson 9: Slopes Don’t Have to be PositiveUnit 3Lesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 8: Landing Planes
Lesson 10: Calculating SlopeUnit 3Lesson 7: Water CoolerLesson 8: Landing Planes
Lesson 11: Equations of All Kinds of LinesUnit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Topic 4: Linear Equations 
Lesson 12: Solutions to Linear EquationsUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: Solutions Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 13: More Solutions to Linear EquationsUnit 3 Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 10: Solutions
Topic 5: Let’s Put It to Work 
Lesson 14: Using Linear Relations to Solve ProblemsUnit 3 Lesson 11: Pennies and Quarters

Unit 4: Linear Equations and Linear Systems

Topic 1: Puzzle Problems 
Lesson 1: Number PuzzlesUnit 4Lesson 1: Number machines
Topic 2: Linear Equation in One Variable 
Lesson 2: Keeping the Equation BalancedUnit 4Lesson 2: Keep It Balanced
Lesson 3: Balanced MovesUnit 4Lesson 3: Balanced Moves
Lesson 4: More Balanced MovesUnit 4Lesson 4: More Balanced Moves (Print available)
Lesson 5: Solving Any Linear EquationUnit 4Lesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 6: Strategic SolvingUnit 4Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or No Solutions
Lesson 8: How many Solutions?
Unit 4Lesson 7: All, Some, or None?
Lesson 9: When Are They the SameUnit 4Lesson 8: When Are They the Same?
Topic 3: Systems of Linear Equations
Lesson 10: On or Off the Line?Unit 4Lesson 7: All, Some, or None?Lesson 8: When Are They the Same?Lesson 13: All, Some, or None? Part 2
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Unit 4 Lesson 9: On or Off the Line?Lesson 10: On Both LinesLesson 11: Make Them Balance [Free lesson]Lesson 12: Line Zapper [Free lesson]Lesson 13: All, Some, or None? Part 2Practice Day 2 (Print available)
Lesson 14: Solving More Systems 
Lesson 15: Writing Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Problems with Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)

Unit 5: Functions and Volume

Topic 1: Inputs and Outputs 
Lesson 1: Inputs and OutputsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Introduction to FunctionsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]Lesson 3: Function or Not?
Topic 2: Representing and Interpreting Functions 
Lesson 3: Equations of FunctionsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 3: Function or Not?Lesson 4: Window Frames
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Unit 5Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: Even More Graphs of Functions 
Lesson 7: Connecting Representations of FunctionsUnit 5Lesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: (Print available)Charge!
Topic 3: Linear Functions and Rates of Change
Lesson 8: Linear FunctionsUnit 2Lesson 9: Water SlideLesson 10: Points on a PlaneUnit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 9: Linear ModelsUnit 5Lesson 3: PostersLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 10: Piecewise Linear FunctionsUnit 5Lesson 9: Piecing It Together
Topic 4: Cylinder and Cones 
Lesson 11: Filling Containers 
Lesson 12: How Much Will Fit? 
Lesson 13: The Volume of a CylinderUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling Cylinders
Lesson 14: Finding Cylinder DimensionsUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling CylindersLesson 14: Missing Dimensions (Print available)
Lesson 15: The Volume of a ConeUnit 5Lesson 10: Volume LabLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 16: Finding Cone DimensionsUnit 5Lesson 12: Scaling CylindersLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Topic 5: Dimensions and Spheres 
Lesson 17: Scaling One DimensionUnit 5Lesson 12: Scaling Cylinders
Lesson 18: Scaling Two Dimensions 
Lesson 19: Estimating a Hemisphere 
Lesson 20: The Volume of a Sphere
Lesson 21: Cylinders, Cones, and Spheres
Unit 5Lesson 15: SpheresPractice Day 2 (Print available)
Topic 6: Let’s Put It to Work 
Lesson 22: Volume As a Function of …Unit 5Lesson 15: Spheres

Unit 6: Associations in Data

Topic 1: Does This Predict That? 
Lesson 1: Organizing DataUnit 6 Lesson 1: Click Battle
Lesson 2: Plotting DataUnit 6 Lesson 2: Wing Span
Topic 2: Associations in Numerical Data 
Lesson 3: What a Point in a Scatter Plot MeansUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 4: Fitting a LineUnit 6 Lesson 4: Dapper Cats [Free lesson]Lesson 5: Fit Fights [Free lesson]Lesson 6: Interpreting SlopesLesson 8: Animal BrainsPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 5: Describing Trends in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City(Print available)Practice Day 1 [Free lesson]
Lesson 6: The Slope of a Fitted LineUnit 6 Lesson 6: Interpreting SlopesLesson 7: Scatter Plot CityPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 7: Observing More patterns in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 8: Analyzing Bivariate DataUnit 6Lesson 9: Tasty Fruit
Topic 3: Associations in Categorical data 
Lesson 9: Looking for AssociationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 11: Federal BudgetsPractice Day 3 (Print available)
Lesson 10: Using Data Displays to Find associationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 9: Tasty Fruit
Topic 4: Let’s Put It to Work
Lesson 11: Gone in 30 SecondsUnit 6Lesson 11: Federal Budgets

Unit 7: Exponents and Scientific Notation

Topic 1: Exponent Review 
Lesson 1: Exponent ReviewUnit 7 Lesson 1: Circles [Free lesson]Lesson 2: Combining Exponents
Topic 2: Exponent Rules 
Lesson 2: Multiplying Powers of 10
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Unit 7 Lesson 3: Power Pairs (Print available) [Free lesson]Lesson 4: Rewriting Powers  
Lesson 5: Negative Exponents with Powers of 10Unit 7 Lesson 5: Zero and Negative ExponentsLesson 6: Write a Rule (Print available)Practice Day 1 (Print available)
Lesson 6: What about Other Bases? 
Lesson 7: Practice with Rational Bases
Lesson 8: Combining Bases 
Topic 3: Scientific Notation 
Lesson 9: Describing Large and Small Numbers using Powers of 10Unit 7 Lesson 7: Scales and Weights
Lesson 10: Representing Large Numbers on the Number Line
Lesson 11: Representing Small Numbers on the Number Line
Unit 7 Lesson 8: Point Zapper
Lesson 12: Applications of Arithmetic with Powers of 10Unit 7  Lesson 8: Point ZapperLesson 9: Use Your Powers
Lesson 13: Defining Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Unit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 13: Star Power
Lesson 15: Adding and Subtracting with Scientific NotationUnit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 12: City LightsLesson 13: Star Power
Topic 4: Let’s Put It to Work
Lesson 16: Is a Smartphone Smart Enough to Go to the Moon?Lesson 13: Star Power Practice Day 2 (Print available)

Unit 8: Pythagorean Theorem and Irrational Numbers

Topic 1: Side Lengths and Areas of Squares
Lesson 1: The Areas of Squares and Their Side LengthsUnit 8Lesson 1: Tilted Squares
Lesson 2: Side Lengths and AreasUnit 8Lesson 2: From Squares to RootsLesson 3: Between Squares
Lesson 3: Rational and Irrational Numbers
Lesson 4: Square Roots on the Number Line
Lesson 5: Reasoning about Square RootsUnit 8Lesson 2: From Squares to RootsLesson 3: Between SquaresLesson 4: Root Down [Free lesson]Practice Day 1 (Print available)
Topic 2: The Pythagorean Theorem
Lesson 6: Finding Side Lengths of TrianglesUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove ItLesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 7: A Proof of the Pythagorean TheoremUnit 8Lesson 7: Pictures to Prove It
Lesson 8: Finding Unknown Side LengthsUnit 8Lesson 11: Pond Hopper
Lesson 9: The ConverseUnit 8Lesson 9: Make It Right
Lesson 10: Applications of the Pythagorean TheoremUnit 8Lesson 10: Taco Truck [Free lesson]
Lesson 11: Finding Distances in the Coordinate PlaneUnit 8Lesson 11: Pond Hopper
Topic 3: Side Lengths and Volumes of Cubes
Lesson 12: Edge Lengths and Volumes
Lesson 13: Cube Roots
Unit 8Lesson 5: Filling Cubes
Topic 4: Decimal Representation of Rational and Irrational Numbers
Lesson 14: Decimal Representation of Rational and Numbers
Lesson 15: Infinite Decimal expansions
Unit 8Lesson 12: Fractions to DecimalsLesson 13: Decimals to Fractions
Topic 5: Let’s Put It to Work
Lesson 16: When Is the Same Size Not the Same Size?Unit 8Lesson 10: Taco Truck [Free lesson]

Unit 9: Putting It All Together

Topic 1: Tessellations
Lesson 1: Tessellations of the Plane
Lesson 2: Regular Tessellations
Lesson 3: Tessellating Polygons
Topic 2: The Weather
Lesson 4: What Influences Temperature?
Lesson 5: Plotting the Weather
Lesson 6: Using and Interpreting a Mathematical Model

Website Terms of Use

Description of Site Services; Acceptance of Terms of Use

Welcome to www.amplify.com (together with any successor sites and the Site Services and Company Content (each as defined below), in whole and in part, the “Site”). The Site is operated by Amplify Education, Inc. (“Company” or “we”). The services that Company makes available on or through the Site include education-related articles, information and instructional services, purchasing functionality, support chat functionality and any other features, content, services, functionality and applications offered from time to time by Company on or through the Site (collectively, “Site Services”).

BY ACCESSING OR USING THE SITE, YOU REPRESENT AND WARRANT THAT YOU ARE OF LEGAL AGE TO ENTER INTO THIS TERMS OF USE AGREEMENT (“AGREEMENT”) AND YOU AGREE TO BE BOUND BY THE TERMS AND CONDITIONS OF THIS AGREEMENT. BY PURCHASING GOODS AND SERVICES ON THE SITE, YOU ARE ACCEPTING THE PRACTICES DESCRIBED IN THIS AGREEMENT AS WELL AS ANY ADDITIONAL TERMS OF USE THAT MAY BE ASSOCIATED WITH THE PARTICULAR GOODS AND SERIVICES YOU ARE PURCHASING.

Please read this Agreement carefully. If you are an employee or other representative of a school or other organization who is accessing or using the Site on behalf of such organization, then you are agreeing to this Agreement on behalf of yourself and such organization. We may modify this Agreement at any time in our discretion, and we may provide such modifications to you by any reasonable means, including by posting the revised version of this Agreement on the Site. You can determine when this Agreement was last revised by referring to the “LAST UPDATED” legend at the top of this Agreement. Your access to or use of the Site following any changes to this Agreement will constitute your acceptance of those changes. Notwithstanding the foregoing, any changes to this Agreement shall not apply to any dispute between you and us arising prior to the date on which we posted the revised version of this Agreement incorporating such changes or otherwise notified you of such changes. If you do not agree to be bound by this Agreement, you must not access or use the Site. Your access to and use of certain parts of the Site may require you to accept additional terms and conditions, and may require you to download certain Software or Content (each as defined below).

Jurisdictional Issues

The Site is controlled and operated by Company from the United States, and is not intended to subject Company to the laws or jurisdiction of any state, country or territory other than that of the United States. Company does not represent or warrant that the Site is appropriate or available for use in any particular jurisdiction other than the United States. In choosing to access and use the Site, you do so on your own initiative and at your own risk, and you are responsible for complying with all local laws, rules and regulations. You are also subject to United States export controls and are responsible for any violations of such controls, including any United States embargoes and other federal rules and regulations restricting exports. We may limit the Site’s availability to any person, geographic area or jurisdiction we choose, at any time and in our discretion. Not all products or services described on the Site are available in all states or territories.

Company content

The Site contains information, text, files, images, video, sounds, musical works, computer code, works of authorship, applications, and other materials and content (collectively, “Content”) of Company or its licensors (“Company Content”). The Site (including the Company Content) is protected by copyright, trademark, trade secret and other laws, and as between you and Company, Company owns and retains all rights in the Site. Company hereby grants to you a limited, revocable, non-sublicensable license, during the term of the Agreement, to access, display and perform the Company Content (excluding any computer code) solely for your personal, non-commercial use and solely as necessary to access and use the Site. Except as expressly permitted by Company in this Agreement or on the Site, you may not copy, download, stream, capture, reproduce, duplicate, archive, upload, modify, translate, create derivative works based upon, publish, broadcast, transmit, retransmit, distribute, perform, display, sell or otherwise use or transfer any Content. You may not, either directly or through the use of any device, software, online resource or other means, remove, alter, bypass, avoid, interfere with or circumvent any copyright, trademark or other proprietary notice on the Content or any digital rights management mechanism, device, or other content protection or access control measure associated with the Content.

User content

You may not access or use the Site for any commercial purpose. You are responsible for all Content that you post, upload, transmit, e-mail or otherwise make available on, through or in connection with the Site (collectively, “User Content”). Please choose carefully the Content that you make available on, through or in connection with the Site. Company does not control any Content other than Company Content, and as such you may be exposed to offensive, indecent, inaccurate or otherwise objectionable Content by accessing or using the Site. Company is not responsible or liable for any Content or the conduct of any Site user. If you become aware of any misuse of the Site, please report such misuse immediately to Company at general@amplify.com. Company reserves the right (but has no obligation) to monitor the Site, including for inappropriate Content or conduct, and to remove any Content in Company’s discretion and without liability to you or any third party.

Your proprietary rights

You retain any ownership rights that you have in your User Content. You hereby grant to Company and its affiliates, licensees and authorized users, a perpetual, non-exclusive, fully paid-up and royalty-free, sublicensable (through multiple tiers), transferable (in whole or in part), worldwide license to use, modify, excerpt, adapt, create derivative works and compilations based upon, publicly perform, publicly display, reproduce and distribute such User Content on, through or in connection with the Site and/or any other commercial or non-commercial endeavor of Company or any of its affiliates, including in connection with any distribution or syndication thereof to Third Party Services (as defined below), on and through all media formats now known or hereafter devised, for any and all purposes including promotional, marketing, trade and commercial purposes. The exercise of such rights shall not require any further permission or notice, payment or attribution to you or any third party. Company reserves the right to limit the storage capacity made available for User Content.

You represent and warrant that: (a) you own the User Content made available by you, or otherwise have the right to grant the license set forth in this Section, and (b) the posting of such User Content through or in connection with the Site does not violate the privacy rights, publicity rights, copyrights, contract rights or any other rights of any person or entity. You agree to pay for all royalties, fees and any other monies owing to any person or entity by reason of the use of such User Content.

Use of the site

You agree not to:

  • Post, upload or otherwise transmit or link to Content that is: unlawful; threatening; harmful; abusive; pornographic or includes nudity; offensive; harassing; excessively violent; tortious; defamatory; false or misleading; obscene; vulgar; libelous; hateful; or discriminatory.
  • Violate the rights of others, including patent, trademark, trade secret, copyright, privacy, publicity, contract or other proprietary rights.
  • Harass or harm another person.
  • Exploit or endanger a minor.
  • Impersonate any person or entity.
  • Introduce or engage in activity that involves the use of viruses, bots, worms, Trojan horses, Easter eggs, time bombs, spyware or any other computer code, files or programs that interrupt, destroy or limit the functionality of any computer software or hardware or telecommunications equipment, or otherwise permit the unauthorized access to or use of a computer or a computer network.
  • Interfere with, damage, disable, disrupt, impair, create an undue burden on, or gain unauthorized access to the Site or any Account, or Company’s servers or networks;
  • Restrict or inhibit any other person from using the Site (including by hacking or defacing the Site). Cover, remove, disable, block or obscure the Site (including advertisements on the Site).
  • Use technology or any automated system, such as scripts or bots, to collect user names, passwords, e-mail addresses or any other data from or through the Site, or to circumvent or modify any security technology or software that is part of the Site.
  • Send or cause to send (directly or indirectly) unsolicited bulk messages or other unsolicited bulk communications of any kind through the Site. If you do so, you acknowledge you will have caused substantial harm to Company, and that the amount of such harm would be extremely difficult to measure. As a reasonable estimation of such harm, you agree to pay to Company $50.00 for each actual or intended recipient of such communication.
  • Modify, adapt, translate, reverse engineer, decompile or disassemble the Site.
  • Solicit, collect or request any information for commercial or unlawful purposes.
  • Post, upload or otherwise transmit an image or video of another person without that person’s consent.
  • Use the Site to advertise, promote or engage in any commercial activity (including engaging in sales, contests or sweepstakes) without Company’s prior written consent.
  • Frame or mirror the Site without Company’s express prior written consent.
  • Use the Site in a manner inconsistent with any applicable law, rule or regulation.
  • Use any robot, spider, site search/retrieval application or other manual or automatic device to retrieve, index, “scrape,” “data mine,” or in any way gather content of the Site or reproduce or circumvent the navigational structure or presentation of the Site without Company’s express prior written consent. Notwithstanding the foregoing, Company grants to the operators of public search engines the permission to use spiders to copy material from the Site for the sole purpose of, and solely to the extent necessary for, creating publicly-available searchable indices of such material, but not caches or archives of such material. Company reserves the right to revoke these exceptions either generally or in specific cases.
  • Attempt, facilitate or encourage others to do any of the foregoing.

Company reserves the right to investigate and take appropriate legal action against anyone who, in Company’s discretion, violates this Agreement or attempts to do so, including terminating or suspending a user’s Account or access to or use of the Site, or reporting any User Content or conduct to law enforcement authorities.

You (and not Company) are responsible for obtaining and maintaining all telecommunications, broadband and computer hardware, equipment and services needed to access and use the Site, and for paying all charges related thereto.

User disputes

You are solely responsible for your interactions with other users of the Site, providers of Third Party Services (as defined below) or any other third parties with whom you interact on, through or in connection with the Site.

Purchases

Company may make available products and services for purchase through the Site, and may use third-party suppliers and service providers to enable e-commerce functionality on the Site. You may only purchase products and services that appear on the Site and that are delivered to an address located in the United States. You may only purchase products and services for personal, non-commercial use by you, your educational institution or students of your educational institution. We may limit quantities or refuse any order for any reason or no reason, including if we have reasonable cause to believe an order is for onward sale or resale other than through distribution channels approved by us. We make no promise that products or services available on the Site are appropriate or available for use in locations outside the United States, and purchasing products or services for delivery to or use in territories where their contents are unlawful is prohibited. If you choose to purchase products or services from locations outside the United States, you do so at your own risk. It is your responsibility to ascertain and obey all applicable local, state, federal and international laws (including minimum age requirements) in regard to the possession, use and sale of any product or service made available through the Site.

If you wish to purchase any product or service made available through the Site, you may be asked to supply certain information relevant to your transaction, including your credit card number, the expiration date of your credit card, your billing address and your shipping information. YOU REPRESENT AND WARRANT THAT YOU HAVE THE LEGAL RIGHT TO USE ANY CREDIT CARD(S) USED IN CONNECTION WITH ANY TRANSACTION. By submitting such information, you grant to Company the right to provide such information to third parties for purposes of facilitating the completion of transactions initiated by you or on your behalf. Verification of information may be required prior to the acknowledgement or completion of any transaction. While it is our practice to confirm orders by e-mail, the receipt of an e-mail order confirmation does not constitute our acceptance of an order or our confirmation of an offer to sell a product or service.

Details of the products and services available for purchase are set forth on the Site. All prices are displayed exclusive of all taxes and shipping/freight charges. Available payment methods, methods of shipping and shipping charges (including charges for expedited shipping, if available) are detailed on the Site. Company may also collect and remit sales tax on your purchase as required by United States law. If you are a tax-exempt entity, please enter the appropriate information where requested on your order form and we will not collect sales tax on your purchase.

Generally, credit and debit cards are not charged until we either ship the product(s) or confirm store availability (at which time you will be charged only for the products we have actually shipped along with any applicable taxes and shipping charges). However, we may pre-authorize your order amount with your credit or debit card issuer at the time you place the order, which may have an effect on your available credit line. When paying for a preorder with a debit card, you will be charged at the time you place your preorder. Please contact your credit or debit card issuer for more information. If you ordered a special delivery product, you will be charged once a delivery time is confirmed. For digitally delivered orders, your credit or debit card will be charged at the time that you initiate the download of the product.

All purchases made through the Site are made pursuant to a shipment contract. As a result, risk of loss and title for products purchased through the Site pass to you upon delivery of the products to the carrier. You are responsible for filing any claims with carriers for damaged and/or lost shipments. Please note that all shipping addresses must be compliant with the shipping restrictions contained on the Site.

Products, services and specifications

All products and services described or depicted on the Site, and all related features, content, specifications and prices, are subject to change at any time without notice. Certain weights, measures and similar descriptions are approximate and are provided for convenience purposes only. Packaging may vary from that shown. We make reasonable efforts to accurately display the attributes of our products, including the applicable colors; however, the actual color you see will depend on your computer system, and we cannot guarantee that your computer will accurately display such colors. The inclusion of any product or service on the Site at a particular time does not imply or warrant that such product or service will be available at any time. Occasionally, the manufacture or distribution of a certain product or service may be delayed for a number of reasons. In such event, we will make reasonable efforts to notify you of the delay and keep you informed of the revised delivery schedule. By placing an order, you represent that the products and services ordered will be used only in a lawful manner. All DVDs and similar products are sold for private, non-commercial home use (where no admission fee is charged), non-public performance, or classroom or instructional use only, and may not be duplicated.

Return and exchange policy

Unless otherwise specified in the terms associated with a particular product, you may return or exchange any product purchased through the Site within fourteen (14) days of receipt, by calling our customer service hotline, 1–800–823–1969, in the event that the purchased product is defective or you received the wrong product. Except for the foregoing, you may not return, cancel or exchange any product or service. Certain jurisdictions may provide additional statutory rights. Nothing herein is meant to limit your return or cancellation rights under local law. In the event that a return or exchange is due to an incorrect order or faulty product, we will be responsible for the shipping costs associated with such return. We will ship a replacement product upon receiving your defective or incorrect product and verifying the reason for the return or exchange.

Accuracy of information

We attempt to ensure that information on the Site is complete, accurate and current. Despite our efforts, the information on the Site may occasionally be inaccurate, incomplete or out of date. We make no representation as to the completeness, accuracy or currency of any information on the Site. For example, products or services included on the Site may be unavailable, may have different attributes than those listed, or may carry a different price than that stated on the Site. If an item’s correct price is higher than our stated price, we will, at our discretion, either contact you for instructions before shipping or cancel your order and notify you of such cancellation. Items in your “Shopping Bag” reflect the current price displayed on the item’s product detail page. Please note that this price may differ from the price displayed when the item was first placed in your Shopping Bag. In addition, we may make changes in information about price and availability without notice.

Chemicals, agricultural materials, and other hazardous materials

Certain products made available through the Site may include chemicals, agricultural materials or other material that may be subject to regulations or restrictions with respect to import or export, or to whom we may sell such material or where or how such material may be used. It is your responsibility to read and abide by all warning notices that accompany any products that you purchase. In addition, we reserve the right to request additional information from you, verify your identity, limit sales to certified educational or research institutions, or cancel or delay your order if required by law or if we believe it is necessary or advisable. Due to special shipping and handling requirements, freight companies routinely impose a surcharge on each package of hazardous material shipped. In such event, we will add such surcharge to your order.

Registration and account security

You may have the ability to create an account on or through the Site (an “Account”). If you submit registration information to create an Account, you represent and warrant that all information submitted to Company in connection with such registration is complete and accurate, and that you will update such information if it changes. If you create an Account, you are responsible for all use of your Account, and for maintaining the confidentiality of the information used to access your Account (including user name and password). You agree not to share your user name or password with anyone, or use anyone else’s Account at any time. You agree to notify Company immediately if you suspect any unauthorized use of, or access to, your Account (including your user name and password). You acknowledge that the reuse of your password in connection with accounts on other websites increases the risk that the security of your Account may be compromised.

The Site may make available, or third parties may provide, links to other websites, applications, resources, advertisements, Content or other products or services created, hosted or made available by third parties (“Third Party Services”), and such third party may use other third parties to provide portions of the Third Party Service to you, such as technology, development or payment services. When you access or use a Third Party Service, you are interacting with the applicable third party, not with Company, and you do so at your own risk. Company is not responsible for and makes no warranties, express or implied, as to the Third Party Services or the providers of such Third Party Services (including the accuracy or completeness of the information provided by such Third Party Service or the privacy practices of any third party). Inclusion of any Third Party Service or a link thereto on the Site does not imply approval or endorsement of such Third Party Service. Company is not responsible or liable for the content or practices of any Third Party Service or third party, even if such Third Party Service links to or is linked by the Site, and even if such Third Party Service is operated by an affiliate of Company or a company otherwise connected with us or the Site

Feedback

Unless we expressly agree otherwise in writing, if you provide us with any ideas, proposals, suggestions or materials (“Feedback”), whether related to the Site or otherwise, you hereby acknowledge and agree that (a) your provision of any Input is gratuitous, unsolicited and without restriction and does not place Company under any fiduciary or other obligation; and (b) any Feedback is not confidential and Company has no confidentiality obligations with respect to such Feedback.. You hereby grant to us a world-wide, royalty-free, fully paid-up, exclusive, perpetual, irrevocable, transferable and fully sublicensable (through multiple tiers) license, without additional consideration to you or any third party, to reproduce, distribute, perform and display (publicly or otherwise), adapt, modify and otherwise use and exploit such Feedback, in any format or media now known or hereafter developed, and you hereby represent and warrant that you have all necessary rights to grant the foregoing license. We may use Feedback for any purpose whatsoever without permission or notice, compensation or attribution to you or any third party. You are and remain responsible and liable for the content of any Feedback.

Privacy

Please review the Privacy Policy for the Site, available at http://www.amplify.com/privacy, to learn about our information collection, usage and disclosures practices with respect to information collected by us through the Site. Please note that certain products or services made available by us, other than the Site, may be subject to different privacy policies. In addition, the Site’s Privacy Policy does not address, and we are not responsible or liable for, the information collection, usage and disclosures practices of any third party or Third Party Service.

Disclaimers

THE SITE, USER CONTENT, THIRD PARTY SERVICES, AND ALL PRODUCTS AND SERVICES SOLD THROUGH THE SITE (COLLECTIVELY, THE “SITE PRODUCTS”) ARE MADE AVAILABLE “AS-IS” AND “AS AVAILABLE” AND COMPANY DOES NOT GUARANTEE OR PROMISE ANY SPECIFIC RESULTS FROM USE OF THE SITE PRODUCTS. COMPANY AND ITS AFFILIATES EXPRESSLY DISCLAIM ANY WARRANTIES AND CONDITIONS OF ANY KIND, WHETHER EXPRESS OR IMPLIED, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN PARTICULAR, COMPANY AND ITS AFFILIATES MAKE NO WARRANTY THAT THE SITE OR USER CONTENT OR THIRD PARTY SERVICES, OR YOUR ACCESS TO OR USE THEREOF, WILL BE UNINTERRUPTED, TIMELY, SECURE, ERROR-FREE, ACCURATE OR RELIABLE. UNDER NO CIRCUMSTANCES SHALL WE BE LIABLE FOR ANY CONSEQUENCES OF ANY UNAUTHORIZED USE OF THE SITE PRODUCTS THAT VIOLATES ANY APPLICABLE LAW OR REGULATION. CERTAIN STATE LAWS DO NOT ALLOW LIMITATIONS ON IMPLIED WARRANTIES OR THE EXCLUSION OR LIMITATION OF CERTAIN DAMAGES. IF THESE LAWS APPLY TO YOU, SOME OR ALL OF THE ABOVE DISCLAIMERS, EXCLUSIONS, OR LIMITATIONS MAY NOT APPLY TO YOU, AND YOU MIGHT HAVE ADDITIONAL RIGHTS.

Under no circumstances will Company or its affiliates be responsible for any loss or damage, including property damage, personal injury or death, resulting from use of the Site, Products, problems or technical malfunction in connection with use of the Site, Products, attendance at any Company event or the conduct of any Site users, whether online or offline. Your use of the Site, Products is solely your responsibility and at your own risk. The User Content and Third Party Services do not necessarily reflect the opinions or policies of Company or its affiliates.

Limitations on liability

IN NO EVENT WILL COMPANY OR ITS AFFILIATES BE LIABLE TO YOU OR ANY THIRD PARTY FOR ANY INDIRECT, CONSEQUENTIAL, EXEMPLARY, INCIDENTAL, SPECIAL OR PUNITIVE DAMAGES, INCLUDING LOST PROFIT DAMAGES, ARISING FROM YOUR USE OF THE SITE PRODUCTS, EVEN IF COMPANY OR ONE OF ITS AFFILIATES HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. NOTWITHSTANDING ANYTHING TO THE CONTRARY CONTAINED HEREIN, THE TOTAL LIABILITY OF COMPANY AND ITS AFFILIATES TO YOU FOR ANY CAUSE WHATSOEVER AND REGARDLESS OF THE FORM OF THE ACTION, WILL AT ALL TIMES BE LIMITED TO THE AMOUNT PAID, IF ANY, BY YOU TO COMPANY FOR THE SITE PRODUCTS.

Indemnity

You agree to indemnify and hold harmless Company, its affiliates, subcontractors and other partners, and each of their respective officers, agents, partners and employees, from any losses, costs, expenses (including reasonable attorneys’ fees), liabilities, claims or demands, due to or arising out of your use of the Site, your breach or alleged breach of this Agreement, your violation or alleged violation of any rights of another, or any Content that you post or otherwise submit on, through or in connection with the Site.

Termination

This Agreement remains in full force and effect while you access or use the Site. If you create an Account, you may terminate your Account at any time, for any reason, by contacting us at general@amplify.com. Company may terminate or suspend your Account and/or your access to or use of the Site at any time, for any or no reason, with or without prior notice or explanation, and without liability. Upon any such suspension or termination, your right to access and use the Site will immediately cease, and Company may immediately deactivate or delete your Account and all files and other information associated with it, and/or bar any further access to such files and other information. Company shall not be liable to you or any third party for any suspension or termination of your Account or of access to or use of the Site or any such files or other information, and shall not be required to make such files and other information available to you after any such suspension or termination. Sections 2, 5, 13, 17, 18, 19, 22, and 26 shall survive any expiration or termination of this Agreement.

U.S. export controls

All software made available in connection with the Site (“Software”) may be subject to United States export controls. No Software may be downloaded from or through the Site or otherwise exported or re-exported in violation of U.S. export laws.

Governing law

The terms of this Agreement are governed by the laws of the State of New York, U.S.A., without regard to its conflicts of law provisions, and regardless of your location.

Arbitration

EXCEPT FOR DISPUTES THAT QUALIFY FOR SMALL CLAIMS COURT, ALL DISPUTES ARISING OUT OF OR RELATED TO THIS AGREEMENT, WHETHER BASED IN CONTRACT, TORT, STATUTE, FRAUD, MISREPRESENTATION OR ANY OTHER LEGAL THEORY, WILL BE RESOLVED THROUGH FINAL AND BINDING ARBITRATION BEFORE A NEUTRAL ARBITRATOR INSTEAD OF IN A COURT BY A JUDGE OR JURY, AND YOU AGREE THAT COMPANY AND YOU ARE EACH WAIVING THE RIGHT TO TRIAL BY A JURY. YOU AGREE THAT ANY ARBITRATION UNDER THIS AGREEMENT WILL TAKE PLACE ON AN INDIVIDUAL BASIS; CLASS ARBITRATIONS AND CLASS ACTIONS ARE NOT PERMITTED AND YOU ARE AGREEING TO GIVE UP THE ABILITY TO PARTICIPATE IN A CLASS ACTION.

Arbitration procedure

Any arbitration under Section 23 above will be administered by the American Arbitration Association under its Commercial Arbitration Rules and Supplementary Procedures for Consumer-Related Disputes (“Supplementary Procedures”), as amended by this Agreement. The Supplementary Procedures are available online at http://www.adr.org/aaa/ShowPDF?doc=ADRSTG_015820. The arbitrator will conduct hearings, if any, by teleconference or videoconference, rather than by personal appearances, unless the arbitrator determines upon request by you or by us that an in-person hearing is appropriate. Any in-person appearances will be held at a location which is reasonably convenient to both parties with due consideration of their ability to travel and other pertinent circumstances. If the parties are unable to agree on a location, such determination should be made by the AAA or by the arbitrator. The arbitrator’s decision will follow the terms of this Agreement and will be final and binding. The arbitrator will have authority to award temporary, interim or permanent injunctive relief or relief providing for specific performance of this Agreement, but only to the extent necessary to provide relief warranted by the individual claim before the arbitrator. The award rendered by the arbitrator may be confirmed and enforced in any court having jurisdiction thereof. Notwithstanding any of the foregoing, nothing in this Agreement will preclude you from bringing issues to the attention of federal, state, or local agencies, and, if the law allows, they can seek relief against us for you.

Employment opportunities

Company may, from time to time, post Company employment opportunities on the Site and/or invite users to submit resumes to Company. If you choose to submit your name, contact information, resume and/or other personal information to Company in response to such employment listings, you are authorizing Company to use this information for all lawful and legitimate hiring, employment and other business purposes. Company also reserves the right, at its discretion, to forward such information to Company’s affiliates for their legitimate business purposes. Nothing in this Agreement or contained on the Site will constitute a promise by Company to review any such information, or to contact, interview, hire or employ any individual who submits such information.

The Digital Millennium Copyright Act of 1998 (“DMCA”) provides recourse for copyright owners who believe that material appearing on the Internet infringes their rights under U.S. copyright law. If you believe that any material residing on or linked to from the Site infringes your copyright, please send (or have your agent send) to Company’s Copyright Agent a notification of claimed infringement with all of the following information: (a) identification of the copyrighted work claimed to have been infringed, or, if multiple copyrighted works are covered by a single notification, a representative list of such works; (b) identification of the claimed infringing material and information reasonably sufficient to permit us to locate the material on the Site (such as the URL(s) of the claimed infringing material); (c) information reasonably sufficient to permit us to contact you, such as an address, telephone number, and, if available, an e-mail address; (d) a statement by you that you have a good-faith belief that the disputed use is not authorized by the copyright owner, the copyright owner’s agent or the law; (e) a statement by you that the above information in your notification is accurate and a statement by you, made under penalty of perjury, that you are the owner of an exclusive right that is allegedly infringed or are authorized to act on such owner’s behalf; and (f) your physical or electronic signature. Company’s Copyright Agent for notification of claimed infringement can be reached as follows: Copyright Agent, Amplify Education, Inc., 55 Washington Street, Brooklyn, NY 11201; Facsimile: 212-796-2311; Attn: Legal. Company’s Copyright Agent for notification of claimed infringement can also be reached electronically at: legal@amplify.com. Company reserves the right to terminate infringers’ and suspected infringers’ Accounts or their access to or use of the Site.

Notice for California residents

Under California Civil Code Section 1789.3, California users are entitled to the following consumer rights notice: If you have a question or complaint regarding the Site, please contact us by writing to Amplify Education, Inc., 55 Washington Street, Brooklyn, NY 11201 or by calling us at 212–213–8177 or sending a fax to 212–796–2311. California residents may reach the Complaint Assistance Unit of the Division of Consumer Services of the California Department of Consumer Affairs by mail at 1625 North Market Blvd., Sacramento, CA 95834, or by telephone at (916) 445–1254 or (800) 952–5210.

Other terms

This Agreement does not, and shall not be construed to, create any partnership, joint venture, employer-employee, agency or franchisor-franchisee relationship between you and Company. You may not assign, transfer or sublicense any or all of your rights or obligations under this Agreement without our express prior written consent. We may assign, transfer or sublicense any or all of our rights or obligations under this Agreement without restriction. The failure of Company to exercise or enforce any right or provision of this Agreement will not operate as a waiver of such right or provision. The Section titles in this Agreement are for convenience only and have no legal or contractual effect. References to and mentions of the word “include,” “includes,” “including,” or “e.g.” will mean “including, without limitation.” References to “discretion” will mean “sole discretion.” This Agreement operates to the fullest extent permissible by law. If any provision of this Agreement is unlawful, void or unenforceable, that provision is deemed severable from this Agreement and does not affect the validity or enforceability of any remaining provisions. Without limitation, you agree that a printed version of this Agreement and of any notice given in electronic form shall be admissible in judicial or administrative proceedings based upon or relating to this Agreement to the same extent and subject to the same conditions as other business documents and records originally generated and maintained in printed form. Company will not be responsible for failures to fulfill any obligations due to causes beyond its control.

Please contact us at legal@amplify.com with any questions regarding this Agreement.

S3-05: Thinking is power

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

Join us as we sit down with Melanie Trecek-King, college professor and creator of Thinking is Power, to explore how much of an asset science can truly be in developing the skills students need to navigate the real world. You’ll learn about “fooling” students and the importance of developing critical thinking, information literacy, and science literacy in the classroom. We’ll also share real strategies and lesson examples that help build these essential skills and engage students in learning.

And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Melanie Trecek-King (00:00):

We say knowledge is power, but it’s not enough to know things. And there’s too much to know. So being able to think and not fall for someone’s bunk is my goal for my students.

Eric Cross (00:12):

Welcome to Science Connections. I’m your host, Eric Cross. On this third season, we’ve been talking about science’s underdog status. And just this past March at the NSTA conference in Atlanta, I had the chance to speak with science educators from around the country about this very topic.

Hermia Simanu (00:28):

Right now, there’s only two teachers in our high school teaching science.

Shane Dongilli (00:32):

I have 45 minutes once a week with each class. The focus is reading and math.

Alexis Tharpe (00:38):

Oftentimes science gets put by the wayside. And you know, I love math and I love my language arts, but I also think science needs to place be placed on that high pedestal as well.

Askia Little (00:46):

In fifth grade, oh, they teach science, because that’s the only grade that it’s tested.

Eric Cross (00:50):

That was Hermia Simanu from American Samoa. Her team flew for three days to make it to the conference. You also heard from Shane Dongilli from North Carolina, Alexis Tharpe from Virginia, and Askia Little from Texas. All of these teachers were excited to be at the conference and had a lot to say about the state of science education in their local schools. Throughout this season, we’ve been trying to make the case for science, showing how science can be utilized more effectively in the classroom. We’ve explored the evidence showing that science supports literacy instruction. We’ve talked about science and the responsible use of technology like AI. My hope is that all of you listeners out there can use some of this evidence to feel empowered to make the case for science in your own communities. And on this episode, we’re going to examine how science can help develop what might be the most important skill that we try to develop in our students: Good thinking. On this episode, I’m joined by a biologist who actually advocated for eliminating the Intro to Bio course at her college. Instead, Professor Trecek-King created a new course focused on critical thinking, information literacy, and science literacy skills. In this conversation, we discuss why the science classroom is such a good environment for helping students become better thinkers. Now, I don’t think that you can make a much stronger argument for science than using it to develop the skills that Melanie describes in this conversation. So, without further ado, I’m thrilled to bring you this conversation with Melanie Trecek-King, Associate Professor of Biology at Massasoit Community College, and creator of Thinking Is Power. Here’s Melanie.

Eric Cross (02:29):

Well, Melanie, thank you for joining us on the show. It’s so good to have you.

Melanie Trecek-King (02:34):

I am so happy to be here.

Eric Cross (02:35):

Now, I went to your session at NSTA in Chicago … I think it was two years ago. A couple years ago. And I was listening to your session, and as I was listening to you, I started Reverse Engineering in my mind what you were doing with your college students. I started reverse engineering the K–8. I was like, “This is amazing.” Where has what you’ve been doing been hiding? We need this not just in the college, higher ed. We need this all the way up and down. Because I hadn’t seen it before. So I think a good place for us to start is gonna be like the story of how and why you as a biologist wound up making the case to actually eliminate the Intro to Biology course at your college. So can you start off and tell us a little bit about that story?

Melanie Trecek-King (03:20):

Sure. So I started teaching at a community college in Massachusetts. And I absolutely love teaching at a community college. And I was teaching the courses that people who don’t wanna be scientists when they grow up have to take to fulfill their science requirement. And that course was Intro Bio. And I tried every way I could figure out to make that class be useful,] relevant to students. I mean, the thing is, our world is based on science and you have to understand science to be a good consumer of information, to make good decisions. And I’m a biologist, so it pains me to say this, but you know, somewhere in the middle of teaching students about the stages of mitosis and protein synthesis, I thought, “Is this really — like, if I have one semester that’s gonna be the last chance that someone’s gonna get a science education, is this really what they need?” And I just decided, “No.” So, to my college’s credit, they were very supportive. I went to them and said, “You know, I think we should assess the non-majors courses. Like, why do we teach non-majors science?” And we all agreed, well, it was for science literacy. OK, great. Do our existing non-majors courses do that? And so we evaluated each of the courses. I made a case that Intro Bio was not doing it. And so we actually replaced it with a course that I call Science for Life. And the whole course is designed to teach science literacy, critical thinking, and information literacy skills.

Eric Cross (04:48):

And so you did this while you were looking at mitosis. And you’re looking at students who may or may not be science majors. And then kind of asking that question. I know every educator asks this, and whether or not it’s welcomed or supported is a different question: “Is what I’m teaching actually gonna be relevant and useful later on down the road for this group of students?” And you actually got to run with it and then create this course, this new course. So, what were the skills that you were hoping to achieve with the new course you developed, and and why were those skills so important?

Melanie Trecek-King (05:21):

Well, if I just go back for a second to what you said, ’cause it, really hit me: I remember the actual moment — it had been building up to that point, but the actual moment that it hit me — I was teaching students the stages of mitosis. And I was applying it to cancer, because the thought is that if we use issues that are relevant to students to teach concepts, that it will be more meaningful to them. They’ll learn it better; they’ll be able to apply it. And they just looked absolutely deflated. They didn’t wanna be there. And I had this moment where I thought, “You know, if, if these students ever have cancer somewhere in their lives, is what I taught them going to be something that they remember? Is it going to be useful to them?” And quite frankly, like, no. <Laugh> They’re not gonna remember proto-oncogenes. And quite frankly, is that really what they need to know at that moment? What they need to know is, “What does this mean? Who is a reliable source of information here? If these treatments are recommended, what is the evidence for them? What are the cost-benefit analyses? Where do I go to find reliable information?” And in that space, cancer in particular, we have this whole field of — I wanna say charlatans, ’cause they may not actually be lying, but they’re pedaling false cures, false hopes. And people need that kind of hope, and so in their time of need, they’re more likely to fall for that kind of thing. Which leads me to the skills that I teach students. I call them this tree of skills. And the order is important. I start — and there’s a lot of overlap to be fair — but critical thinking, and then information literacy, and science literacy. The idea is that students carry in their pockets access to basically all of human’s knowledge at this moment in time. And if they needed to access it, they could. The question is, do they know what they’re looking for? Are they aware of their own biases that are leading them to certain sources, or certain false hopes? Are there certain things that are making them more vulnerable to the people that might prey on them? Are they able to use that information to make good decisions? There’s a great Carl Sagan quote, and it’s something like, “If we teach people only the findings of science, no matter how useful or even inspiring they may be, without communicating the method, then how is anyone to be able to tell the difference between science and pseudoscience?” So yes, the process of science is a process of critical thinking. However, we do tend to present science most of the time. Like, here’s what science has learned. And to be fair, those things that we’ve learned from science are really useful and inspiring. But if we don’t teach the process, so you’ve got somebody now who let’s say has been diagnosed with cancer and is on their phone and they’re scrolling through social media and everything looks the same. And of course the algorithms learn who you are. Next thing you know, there’s all of these like pseudo-treatments popping up. It all looks the same. Somebody who says that acupuncture can be used to cure cancer can feel the same, from someone who doesn’t understand the process of science, as a medical fact. And so the process is the process of critical thinking. My class everything is open note. The quizzes are open note. The exams — and I say open note, they’re also open online, because I know for the rest of their life they’re gonna have resources available to them; I want them to be good consumers with that information, which to me requires metacognition and critical thinking and information literacy and all those skills that I’m trying to teach them.

Eric Cross (08:58):

You’re basically taking what … we’ve taught science for so long. And more recently, it’s changed to more focusing on skills. At least in K through 12. But a lot of it was just memorization of a ton of different things that now we can pull up our phone, go on the internet. You can pull up a lot of those facts. But those facts don’t necessarily translate to actual real-world skills. When I listen to… I kind of make this analogy sometimes: students say … it’s funny, I have 12-year-olds that say this. They go, “How come they don’t teach us how to do our taxes?” And you know they’re regurgitating what they hear from adults, right? “Teach us real-world skills!” And I was like, really, if we taught you right now how to do your taxes, how many of you would really be like, “Oh, this is an awesome lesson! We’re really engaged!” But their point is that “I wanna learn something that I could actually use later on, that’s that I’m gonna carry on.” And in your course, you’re talking about these skills that actually can apply. Like you said, if I had cancer and I’m looking at different types of medical procedures, do I have the skills to really be able to evaluate and make informed decisions on that? And that’s, that’s not something that I’ve seen explicitly taught really anywhere. And I hadn’t heard anybody talk about it, really, until I heard your session, where you’ve kind of unpacked this, and over the last couple of years, have created some programs or resources for educators, where they can take this into their classroom. So what were some of those skills, again? What were were some of the skills that you thought, “I wanna make sure that my students can walk out and they know how to do this and apply it to maybe several different fields”?

Melanie Trecek-King (10:35):

Oh, that’s a really good question. Because the whole thing was a process for me. Like, when I finally let go of Intro Bio, I was so glad to see that class go, by the way. ‘Cause I just felt like I was beating a dead horse. So when I let go of it, I thought, “What do they need instead?” And for me, what I realized was I was trying to make the class I would’ve wanted to take. I realized the things that I personally didn’t know, that my own education maybe let me down a bit. But things that I thought were important. So then I took all of those, synthesized them, tried to figure out the best order. The class is currently in its third iteration. And I hope every iteration is an improvement. But I’m thinking about the students that I taught before the pandemic. It was Intro Bio. Up to just maybe the couple years before the pandemic, and during the pandemic, we had a new virus and we had a new vaccine and we had new treatments. There was hydroxychloroquine and there was ivermectin and then there’s masks. Are masks effective? Well, you know, in what circumstances? What kind of mask? There are all of these questions. And that whole thing was we saw science playing out in real time.

Eric Cross (11:50):

Absolutely.

Melanie Trecek-King (11:51):

And so were my students able to follow that? And then what happened in that process is that science became politicized. And in a time where things are uncertain and we need answers, ’cause it’s scary, people want certainty and science doesn’t tend to provide that. Especially when it’s just starting out. And then when it becomes politicized, people decide that they’re going to — it’s not necessarily a conscious decision — but they retreat into what people in their camps are saying or their groups are saying. Which actually leads me to one of the more important parts of information literacy skills in there, which is most of our knowledge is shared. We tend to have overinflated senses of what we individually know. And studies actually show that with Google, if you have access to Google, you think you’re smarter than if you don’t have access to Google. But we all have access to knowledge in our communities, and that’s one of the reasons humans are so successful, is that we can each specialize in different things and share our expertise and become greater than the sum of our parts. The problem with that, of course, is that we forget what we don’t know, and we assume that we know what the community knows. And so recognizing the limits of your own knowledge and how different communities produce knowledge, like the different epistemic processes that communities use to come to knowledge. When it comes down to it, an important part of knowing is knowing who to trust, right? Knowing where the source of knowledge lives. And in order to do that, you have to understand the processes that they’re using to come to that knowledge and the limits of your own knowledge. And then how to find who has that knowledge so that you can use that to make better decisions.

Eric Cross (13:38):

So, when I hear what you’re doing with your college students, and I think about what I’m doing in the classroom, in the middle school, we are really focusing on literacy as skills. Reading, writing, speaking, listening. And then when I think of the next step of the journey, your information literacy and the literacy you’re teaching is really the application of those things in the real world. And the examples that you gave are very critical examples. Evaluating claims about Covid. Making informed decisions about a medical procedure that you might need. And we all get that applied to us. We’re scrolling through social media and somehow social media is listening. It’s figuring out exactly what I’m doing, because all of a sudden the ads are telling me … how did you know I was alking about KitchenAid mixers now? I just said KitchenAid mixers and it’s gonna show up in my feed! But <laugh> I take that in the same way from the same place that I take in maybe an oncologist. So it’s it’s coming through the same channels. So now I kind of wanna pivot. So we’ve talked about what you’re doing, why you’re doing it, the connection between “am I really teaching the skills that my students need in the science class? Is it really critical thinking explicitly or is it just kind of implied?” Now I wanna ask you how you do it. What’s the annotated, abbreviated kind of syllabus of your course?

Melanie Trecek-King (15:03):

So the course is called Science for Life. And the premise behind it is the kinds of skills and understanding of the process of science that they would need to make good decisions to be empowered in a world based on science. And so the very first lecture, I say, “OK, I’m gonna tell you a story and I just want you to listen to the story. And at the end I’m gonna ask you why I told the story.” And the story that I tell them is some of the history of the witchcraft trials in Europe. And I start with the Malleus Maleficarum, or the Hammer of Witches, from the Pope, and about how people would accuse witches of causing birth defects or storms or crops dying. And, the best evidence that they had to absolutely know somebody was a witch was if somebody accused them, and then if they were accused, if they confessed. OK? But the problem is, to get them to confess, they would torture them. Roasting over coals, or splitting until somebody broke. And so I tell my students, “OK, this was absolute proof that someone was guilty of witchcraft. I don’t know about you; I would confess to anything, right? Make it stop!” So this is where I get to ask students, “Why would I ask you this? Why would I tell you this story? And traumatize you on the very first day of lecture?” And they see the reasoning, right? They thought they had evidence. The question was, is that good evidence? And so, you know, I’m getting students to have a basic understanding of epistemology, right? Without calling it that, or without going into all of the philosophical background of epistemology. Apply this to your own reasoning. What are you wrong about? Well, you probably wouldn’t know. OK, how would you know if you were wrong? Like what kinds of things do you feel that you’re so right about? How good is your evidence for that? So what I want them to do is internalize the thinking about thinking, and analyzing how they come to conclusions, and proportioning how strongly they believe. Their confidence in how right they are. So I think starting with that kind of misinformation, and getting students to internalize that process is important. But I think the example is really useful, because most of my students don’t believe in witchcraft. Right? So it’s not an issue that would immediately threaten them in some way. So when, when a belief is tied to identity or how we see ourselves or is really important to us, then it’s very difficult to be objective about that belief. And so by starting with witchcraft, it’s not triggering. I get them to think about thinking and practice that muscle so that when we get to those more important issues, they have the skills they need to evaluate them.

Eric Cross (17:55):

So would it be fair to say that your Science for Life class is really applied scientific thinking for the real world?

Melanie Trecek-King (18:01):

Absolutely. That’s the idea. I mean, science is too good to keep to ourselves, right? And it’s everywhere. So how can you understand the world through a scientific lens?

Eric Cross (18:10):

What are the nuts and bolts of how you teach your students these strategies? What do you do? What are some strategies and techniques that we can maybe share with listeners? And then where I want to go after that is I wanna ask you, how early do you think this can be started? So lemme start off first with, what do you do?

Melanie Trecek-King (18:28):

So I use three different strategies. One is, I provide students with a toolkit. And the toolkit is one that I created and it is like my one toolkit to rule them all. It is trying to apply critical thinking and science reasoning all together in one place. So that if students are met with a claim, they’ve got the toolkit with an acronym. They can now start and have somewhere to go. In that if I gave you a claim and said, “Just critically think through this claim,” I mean, that’s a mighty task. But if you have a structured toolkit, then it’s hopefully a systemic way that’s helpful. The toolkit is summarized by FLOATER. I have published it on Skeptical Inquirer. It’s free. So it’s Falsifiability, Logical, Objectivity, Alternative Explanations, Tentative Conclusions, Evidence, and Reproducibility. So I provide students with a toolkit. The next thing I do is I use a lot of misinformation in class. Back to what Carl Sagan says: What I heard was we should use pseudoscience to teach students the difference between a pseudo-scientific process and a scientific process. So, I use science denial, conspiracy theories, and give my students a lot of opportunities to practice evaluating claims with the toolkit. And the other thing I do is, I use inoculation activities. So inoculation theory is based on William McGuire’s original research in the ’60s, which is basically like a vaccine analogy. Where you can inject a small amount of a virus or bacterium into the body, so that it creates an immune response, so that it can learn the real thing. And so in the real world, it can fight it off. Inoculation theory does the same thing, but with misinformation. So, what we can do is, in controlled environments, expose students to little bits of misinformation so that they can recognize it in the real world. There’s different kinds of inoculation, but I’m a big fan of what’s called active and technique-based inoculation. So technique-based means that students are learning not the facts of misinformation, not factually why this thing is wrong, but about the technique used to deceive. So maybe the use of fake experts. Or maybe the use of anecdotes. Or the use of logical fallacies. The other part of that is active, which is where students create the misinformation. So for example, my students, just now, we finished covering pseudoscience. And I teach students the characteristics of pseudoscience. And basically we have fun with it. Where they pretend to be grifters and they sell a pseudoscience product. And so they have to make an ad like they’d see on social media, using the different techniques. And the point there is that it’s supposed to be funny, right? And lighthearted. But in a real way, by using the techniques used to sell something like pseudoscience, it’s opening their eyes. You can’t unsee how every alternative product has, “it’s an all-natural and used for centuries and millions use it and look at this person who says, ‘Wow, it worked for me!’ And it’s certified by some society that doesn’t exist, but this doctor behind it says that it’s really great!” I mean, it’s all the same stuff. So they create the misinformation using their own techniques.

Eric Cross (22:02):

That’s one of my favorite things that you’ve talked about, and I want to dive in that a little bit more. But when you’re teaching the toolkit, FLOATER, what does that look like in the classroom, when you’re actually breaking all of those things down? What does it look like as you’re walking your students through this, and you’re kind of coaching them on all of those different things? ‘Cause I feel like some things might be like, “Oh yeah, I got that.” And then some of them might be, “Oh, what is that?”

Melanie Trecek-King (22:24):

Yeah, it takes me probably a good solid lecture to get through the basis of the toolkit. But then over the rest of the semester, I’ll spend more time going into different parts, different rules, a bit more in-depth. So, for example, logical fallacies and objectivity. So the rule of objectivity basically states that you need to be honest with yourself. I’m gonna quote Feynman here, so: “The first principle is that you must not fool yourself — and you are the easiest person to fool.” We don’t tend to think that we can be fooled. But of course we can. So actually, if you wanna talk about it, I start class by fooling my students.

Eric Cross (23:03):

Wait, what do you do? What do you do for that?

Melanie Trecek-King (23:05):

Oh, so this is really fun. Day 1 of class, after the syllabus, I tell my … so you’re in my class now, Eric. “So I have a friend, and she’s a psychic. She’s an astrologer and she’s pretty good at what she does. I mean, she’s got books and she’s been on TV and stuff. She knows I teach this course about skepticism. And so she’s agreed to test how effective she is by providing personality assessments to students in class. So if you wanna participate, what I need from you is your birthday, your full name, answer a few questions. Like, if your house was on fire and you could take one thing, what would it be? Or if you could get paid for anything to do anything for a living, what would it be? Um, there’s a third one. Oh! If you could have any superpower, what would it be?” So the next class, it’s usually over a weekend. The next class I say, “OK, I’ve got your personality assessments back, but remember, we wanna test how effective she is. So in order to do that, I need you to read your profile as quietly as possible. And then I’m gonna have you rate her accuracy on a scale of 1 to 5. OK? So close your eyes; rate her.” Over the years doing this, it’s about a 4.3 to 4.5 out of 5. They think she’s pretty accurate. OK? “So now, if you feel comfortable, get with a person next to you. And I want you to talk about what parts of the personality assessment really spoke to you and, and why, and why you thought she was accurate or not.” And it takes them 5, 10 minutes before they realize they all got the same one. So, this is not my original experiment. It was first done by Bertram Forer in … I think it was the ’50s. And it’s done in psychology classrooms. James Randi made it famous. But the personality assessment itself is full of what are called Barnum statements. So, named after P.T. Barnum. These are statements that are very generic. So, “You have a need to be liked and admired by people. You are often quiet and reserved, but there are times where you can be the life of the party.”

Eric Cross (25:13):

How do you know this about me, by the way? This is a — I feel like you know me right now.

Melanie Trecek-King (25:17):

“There are times where you’ve wondered whether you’ve done the right thing.”

Eric Cross (25:19):

This is getting weird.

Melanie Trecek-King (25:21):

I’m just on fire, right? So these are Barnum statements. They’re the basis of personality assessment.

Eric Cross (25:29):

Mel, can I pause you right there? You said Barnum. Is that the same Barnum, like Barnum & Bailey Circus?

Melanie Trecek-King (25:34):

Yeah. P.T. Barnum, who didn’t actually say “There’s a sucker born every minute,” but we attribute him with that kind of ethos. These statements though, if you read a horoscope or even like personality indicators, like the MBTI, it is basically pseudo-scientific. And it ends up with lots of these Barnum statements. They produce what’s called the Barnum Effect, which is, “Wow, that’s so me! How did you know me?” I could even do more. Like, you have a box of photos in your house that need to be sorted. Or unused prescriptions. And these can apply to nearly everyone, but they produce this effect where we go, “Wow, that is so me!” Right? So by fooling them this way, I get to … well, so the next thing is, “Yes, I lied to you. And I’d like to tell you I won’t do that again. But I’m not going to, ’cause I might. So be on your guard.” But I did it for free. And why did I do it? “I did it because I could tell you ‘I could fool you,’ but you wouldn’t necessarily believe me. So I fooled you, so that you would learn what it feels like to be fooled.” It’s not fun. But we’re gonna make a joke outta this. And students are almost never upset about this ’cause it’s a fun process and they’re all fooled. And again, the point is, I didn’t disprove psychic powers. I didn’t just disprove psychics with this exercise. But I did show you how easy it was to fake. So if somebody is gonna tell you that they can know these things about you through some way, hopefully the evidence they provide should be stronger than something that’s easily faked. Right? Extraordinary claims require extraordinary evidence. If you claim to be able to read my personality based on my birthdate, then I need more than something that you can be taught to do in 15 minutes. So, I fool them to convince them that they could be fooled.

Eric Cross (27:27):

You’re giving them a practice scenario for thinking. And I was thinking about basketball. I grew up playing basketball. And my coach would have our own team be the defenders of the next team we were gonna play, so that we can be prepared for the defense. We were gonna see. Now, when I’m thinking about education, and what you just said reminded me of this, it’s like we’re often just teaching offense. We’re always teaching the plays. We’re always teaching what to do. But we rarely teach defense. What happens when someone comes towards you and, and they challenge you or they come at you with claims? How do we evaluate this? And I think in pockets we do it. We do claim-evidence-reasoning. We present claims and evidence and reasoning. But we don’t always have practice defending them. And I think there’s great resources. There’s Argumentation Toolkit and there’s all these awesome resources that do this. But does that fit? You’re kind of having them practice defense?

Melanie Trecek-King (28:26):

Yeah. You know, that’s brilliant. I never considered that analogy. But, yeah, in the real world, you don’t just get to always try to score all the time. Someone’s gonna challenge you and give you a claim that maybe you haven’t heard before. So how do you think through it?

Eric Cross (28:41):

Yeah. And you become better. So now I’m thinking about how early could we start doing this? For one, I love the idea of lying to your students, because I do that. And it’s just such a fun scenario. How early could we start implementing these strategies or these ideas or these toolkits? In your mind, what do you imagine? How early could we start this with young people?

Melanie Trecek-King (29:07):

Yeah. I’m so glad you asked that question, ’cause honestly, by the time they get to me, it’s almost too late. And I don’t wanna say it’s too late, ’cause it’s never too late. But, oh, we need to start so much earlier! That example that I gave about the selling pseudoscience argument? I have a wonderful colleague, Bertha Vasquez, who’s a middle school teacher in Miami and the director of TIES at CFI. She did this with her middle school students. And quite frankly, their examples were just as good, or in some cases better, than my college students. And they had so much fun with it, too. And she just said that, you know, <laugh>, they actually are more savvy with the kinds of things that they see online than we — I don’t wanna say give them credit for. But almost that we want to believe. My students give me examples of things that are from corners of the internet that I didn’t know existed. And quite frankly, that’s probably a good thing for my own mental health. But students are on there too, like middle school students, and we need to prepare them for the kinds of things that they see in the wild.

Eric Cross (30:13):

So in middle school, definitely. Now, you’ve also done some work in high school as well, right? In Oklahoma? Did you do some. …?

Melanie Trecek-King (30:17):

Yeah.

Eric Cross (30:18):

…some work with high schoolers? What was that like? Did you see any impact there?

Melanie Trecek-King (30:21):

So I didn’t actually do it in Oklahoma. I have taught the course … actually, you were talking about younger kids. I’ve taught the course to high schoolers in my area that are parts of dual enrollment. And they absolutely ate up the curriculum. And they were wonderful, wonderful students. And it was completely appropriate for … they were juniors, actually. But the course has also been taught in Oklahoma, through a dual enrollment program as well. And it was a small sample size. But we have pre-post testing that showed that it improved their critical thinking, their acceptance of science. But anecdotally the head of the program there said that in his years doing this, he’d never seen a course that helped them improve in their other courses so well. So, I felt very rewarded by hearing this. But apparently their critical thinking skills and information literacy skills helped them succeed in their other courses that they were taking. And I love that the students were transferring those skills to other classes. That’s the whole point.

Eric Cross (31:23):

And that’s a big … I think that what you just said is really the core, especially of what we’ve been talking about this season: What you’re talking about and what you’re teaching can transfer and supports literacy. And this is an example of science doing that across all other content areas. So I think that that’s huge, that that was said. What do people say about this course? I know I went on your website, and I looked at some of the comments that some folks were saying, and I know it’s just a snippet, but what do you hear from the education world about this? Because I don’t see it in many places. I see it kind of embedded, sprinkled into different content areas. But you’re actually teaching it explicitly. Do you tend to find positive feedback, overwhelmingly? Or do you get pushback on on some of this? What’s it been like for you?

Melanie Trecek-King (32:16):

I think the biggest pushback — and it’s good pushback, and I would agree entirely — is with inoculation activities, you do need to be careful to, when you debrief students, you wanna tell them why you did what you did and to use their powers for good and not for fooling other people. And I think importantly, for not putting misinformation out into the wild without having context around it. So if you do these kinds of inoculation activities, like if you have your students create pseudoscience ads, don’t just let them put them on social media. Obviously, you can’t control everything that they’re doing. But explain to them why you wouldn’t wanna do that. As far as everything else, I’ve heard really great feedback. You’re referencing my website. So, when I put together the course, I was trying to find resources for students to read. Textbooks are ridiculously expensive and I couldn’t find anything that I really wanted students to buy. So I just started writing, and I put it on my site. I have a site that’s basically the core of the curriculum. More in progress. And then I’ve got some of the topics that we explore and those are all assigned readings. My students are captive, in that I know they want a grade, and for four months they have to sit with me for the entire semester, in that I’ve specifically ordered the content in a way that would be most conducive to them learning these things. On the internet, though, and on social media, ’cause I post on there as well, people come in from all kinds of entry points, and so the goal would be to have them start at the beginning and go to the end. But people … I’m pleasantly surprised that there is an audience for critical thinking and science literacy content out there. And so that really warms my heart. But I am doing more and more for educators. And so I have a section for educators. I put content on there. I put assignments, the assignments that we’ve talked about and more, are on there. And the educators that I’ve had use it have just been really wonderful. Like, I hear great things. If I might, the biggest issue that I’m having is actually reaching educators. I’ve gone to — I met you at NSCA, actually, that was only last summer.

Eric Cross (34:30):

Oh, wow. Wow.

Melanie Trecek-King (34:32):

Right?

Eric Cross (34:32):

Yeah, you’re right. It wasn’t even a year.

Melanie Trecek-King (34:35):

Yeah, I think it was like July last year. So, um, you’ve been to the conferences. And I just went to the last one as well. But I have yet to figure out a way to really get in front of enough educators to share the content. So if anybody’s listening and is interested in learning more, please let me know! <Laugh>

Eric Cross (34:52):

Yes. And we talked about your website, but I didn’t say what the website was. So it’s ThinkingIsPower.com.

Melanie Trecek-King (34:57):

Yes.

Eric Cross (34:58):

And on there, there’s tons of resources. There is the toolkit. And it’s all free.

Melanie Trecek-King (35:06):

Yes.

Eric Cross (35:07):

And there’s a dope t-shirt on there that I just bought today, that Melanie’s actually wearing right now. It says, “Be curious, be skeptical, and be humble.” And I love that. Because I think one of the things that we can’t forget about teaching people how to think and critically evaluating information, sometimes those conversations can become very dehumanizing. And what I mean by that is it sometimes can become, like, intellectual sport, where we forget that there’s a human being on the other other side. And we lose that empathy and compassion. We can kind of see that. It just becomes this intellectual jousting and arguing. And one of the things I know about you, and when you talk about this or you talk about the work that you do, and even the shirt that you’re wearing, there’s this, “be humble.” There’s this human that is never lost in this. And you said it, too: When you’re teaching your students and you’re equipping them with all of these intellectual skills and all of these tools, to use it for good. So to maintain your humanity, to maintain your character, and then to use it to edify and lift people up, not to go out and do harm. That balance, I think, is so, so important. So it’s something that I really appreciate about you and how you teach.

Melanie Trecek-King (36:19):

I appreciate those kind words. Actually—

Eric Cross (36:21):

Oh, of course!

Melanie Trecek-King (36:22):

—and if I might, I sometimes see people using critical thinking like a weapon. It’s like, “I have learned fallacies and I’m just gonna use the tools of critical thinking to tell you why you’re stupid, or why you’re wrong, and why my position is right!” But real critical thinking involves applying those same standards to your own thought processes. And even something like argumentation: the goal of our argumentation is not to BE right; it’s to GET it right. And so we’re on the same team. If we’re arguing about something, if the idea is in scientific argumentation we’re trying to find the truth, which one of us is making a better argument based on the evidence? Can your perspective help me see my own blind spots and vice versa? And the more different perspectives that we have, the more able we are to find whatever reality is. But we are in this together. And so, yeah, I think … I’m glad to hear that that’s coming through. But if you don’t have the kind of humility that says, “You know, I could be wrong,” then you’re never gonna change your mind anyway. So having the humility to say, I’m wrong. <Laugh>

Eric Cross (37:33):

Yeah. You end up just seeing people just defend turf, as opposed to support “look for truth.” And I know for me, my own education journey, I end up with more questions than answers anyways. So I go in trying to find an answer for something and I end up with 10 more questions. And I go, “OK, this is kind of how it is.” You go down this rabbit hole and you just end up with all these different questions. And it forces the humility, because you’re like, “I don’t know! I think this is what it could be, but it could also be these other answers or explanations. So this is just where I’m at, based on what we know right now, at this present time, which might shift.”

Melanie Trecek-King (38:07):

And that sounds reasonable. Yes. Which might shift. Yes.

Eric Cross (38:11):

And especially for us as life-science biology teachers, our content is something that definitely shifts. I know some of the things I teach now are not things that I learned when I was even in middle school. Just because things evolve. They change. We learn, we get new data. That’s just the way it is.

Melanie Trecek-King (38:24):

<Sighs> And Pluto is no longer a planet.

Eric Cross (38:26):

I know. Rest in — well, no, Pluto’s still there. Yeah. It’s no longer a planet. But that was one part of my kindergarten memorizations <laugh> is Pluto being in there.

Melanie Trecek-King (38:36):

Gotta change your mind.

Eric Cross (38:38):

I know. Any words of advice for science educators out there who want to focus more on honing these critical thinking skills and strategies with their own students, but they don’t know where to start? Where would you point them? Or what advice would you give them?

Melanie Trecek-King (38:52):

I think start with what you want the students to know. And not necessarily the FACTS that you want students to know, but start with the skills that you want them to know. And then really be honest with your process. When I designed Science for Life, I started with, “these are the skills that I want students to know.” And everything was in service of that. So this sort of backwards design, I think, helped me follow a path that was more likely to be useful, if that makes any sense. But it really required doing it all over again. So don’t be afraid to question the things that you’re currently doing, even if that’s all you’ve been taught or all you know.

Eric Cross (39:41):

What I’m hearing is, don’t be afraid to question your own assumptions about what you’re doing. And don’t be afraid to adapt or change or modify. Kinda, pivot. Be flexible.

Melanie Trecek-King (39:51):

Yes, be flexible and pivot. And this is where I’m in a different position than middle school and high school educators. Because I have complete freedom over what I teach in my class.

Eric Cross (40:01):

Sure.

Melanie Trecek-King (40:01):

At the end of the semester, I always joke with non-majors that there’s nothing they have to know, which actually gives me a lot of flexibility, because I could teach ’em a lot of different things. So if there are things that you have to teach students, obviously that’s one thing. But I personally think that the way that we’ve been teaching science needs a refresher. A rethinking. And so I would say, “If you want your students to learn science literacy, honestly ask, what does that mean to you? And what would that look like to get to that point?” For me, though, it was also keeping in mind that maybe I didn’t already know the best way to do that.

Eric Cross (40:43):

One of the things you mentioned earlier is trying to reach out to educators. And I know that when we work together, it’s a force multiplier. And what you’re doing is developing skills. And there’s these skills that are happening right now in academia that you’re doing. And then how do we transfer that into middle and high school. Or, I’m sorry, middle and elementary school, high school. We need to get more people into this conversation to kind of brainstorm and figure that out. We have a Facebook group, Science Connections: The Community, where we have educators that gather. That can be one place we start the conversation. And again, I know on your website you’ve been super active on social media; you’ve grown your presence on Twitter and all these different places, engaging with folks. Which is awesome. ‘Cause I know I see your posts and I’m saving the things that you’re posting and I’m thinking of ways that I can do it in my classroom. I’m gonna take that product. By the way, is that on your website, the lesson that you do with the product?

Melanie Trecek-King (41:43):

No, actually. So the article, “How to Sell Pseudoscience” is … I know Bertha Vasquez wrote up a version of it.

Eric Cross (41:50):

Maybe we can grab that. ‘Cause we might be able to put that into the show notes for folks, because she’s a middle school educator. If there’s already something that’s been done for teachers like us, we’re like, “Yeah, let me get that and let me remix it and make it my own!” if there’s already a exemplar out there.

Melanie Trecek-King (42:04):

Yeah, she’s done it. And so I will absolutely share that with you.

Eric Cross (42:08):

So, all season long, we’ve been talking about science as the underdog. We kind of framed it, you know, science oftentimes takes a back seat to math and English. It’s kinda the first thing to go. Or the first area where time can get cut. Because of what gets tested gets focused on, oftentimes. And then in addition to that, when you’re a multi-subject teacher, elementary science isn’t just one thing — it’s every field. You know, you’re a biologist, which is different than a geologist. And when you’re teaching every subject, that’s a lot. And you might not have had a science class for years. And the realities that we’re seeing over and over with different researchers and practitioners is that science could actually enhance literacy, and building those skills. And I think you really talked about it with the critical thinking skills. Those can transfer. Or the administrator that said, “This is one of the only courses I’ve seen where it transfers to other areas.” Could you share maybe with our listeners, just any advice for advocating for science in their own world?

Melanie Trecek-King (43:13):

Wow, I’m not sure I’m qualified to answer that question! One of the things that comes to mind though — because I was listening to your last episode and educators … I honestly didn’t realize how little time they had for science. And how often science was then the first to go, to allow room for other subjects. But science overlaps with a lot of other issues. And so I feel like there could be a way to bring in science when teaching these other subjects. So, for example, argumentation and logical fallacies are easy to apply to reading and writing. Information literacy, and being able to find good information online, teaching students how to laterally read, to be able to check a source, or how to use Google effectively, to put in neutral search terms to find sources, or teaching students how to recognize the characteristics of conspiratorial thinking: All of these things can overlap with so many other subjects. So the scientist in me is a little biased towards science being important enough to do this. But try to bring it into the other subjects. It doesn’t have to be completely separate.

Eric Cross (44:43):

So integrating science into other things. And I … big believer. And a hundred percent agree with you. Now I’m gonna ask a question that kinda like takes us backwards. You shared an app with me when we first met that I thought was really cool. And I know it’s a friend or colleague of yours. But as a middle school teacher, I thought it was great, because it was something that my students could download and practice some of the skills that you’re talking about. Would you talk a little bit about the cranky uncle? Is it the Cranky Uncle app?

Melanie Trecek-King (45:17):

Cranky Uncle.

Eric Cross (45:18):

Could you share a little bit about that?

Melanie Trecek-King (45:20):

Yeah. Cranky Uncle is awesome. So, Cranky Uncle is the brainchild of John Cook, who is the founder of Skeptical Science and the author of the 97% Consensus study on climate change. Cranky Uncle … so he’s also a cartoonist. And Cranky Uncle is a cartoon game where … I don’t even have to explain who Cranky Uncle is to my students. Everybody inherently gets the, the character, right? So he’s like the guy at Thanksgiving that you don’t wanna talk to because he denies climate change and he’s just really cranky. But Cranky Uncle uses the techniques of science denial, which are summarized by the acronym FLICC: So it’s Fake experts, Logical fallacies, Impossible expectations, Cherry-picking, and Conspiratorial thinking. So he uses those techniques. Again, this is technique-based inoculation. So they recognize the techniques in the game, and you earn cranky points. And as you make Cranky crankier and crankier because you’re recognizing his techniques, you learn the techniques of science denial, and level up and open up other techniques. This is another one of those examples where climate change has a lot of science behind it, right? And if you wanted to get to the science behind climate change for any particular issue … so let’s say it’s cold today, so I’m gonna say there’s no climate change. OK? If I’m gonna unpack that at a factual level, and with science, we could be here for a while. But if I told you, “That’s like saying, ‘I just ate a sandwich so there’s no global hunger.’” OK? So that’s a parallel argument. Humorous. Love to use this kind of argumentation, ’cause it makes for some … I mean, it’s funny, but you get the point. It’s an anecdote. And anecdotes aren’t good evidence. So just like that, you could teach the technique of using an anecdotal fallacy for climate-change denial. So, I have my students play this game. You could do it when you’re studying argumentation. You could do it for science denial. I use an inoculation extension with that, where I have my students pretend that … um, actually, back up for a second. So I teach a class on critical thinking. And at the end of semesters I would get emails from students on, well, they’re failing the class, but they really shouldn’t, for all of these reasons. And reading these emails, I’m like, “If you think that’s a good argument, you clearly didn’t learn what I was hoping you would learn.” So I now have my students, early in the semester, after they play Cranky, pretend that it is the end of the semester and you’re failing the class and you’re failing because you didn’t do the work. Use at least four of the fallacies from class to argue for why you should pass. So they have to put it on a discussion forum, and they’ll say things like, “Well, if you fail me, then I won’t get into graduate school and then people will die and it will all be your fault.” Or, “My dog died, and so I was really sad.” Or, um, “You’re just a terrible teacher. And you’re short. So I don’t like you.” Or that kind of thing. So, oh, they love to attack my character. It’s really funny. But it’s supposed to be funny. And the point is, the students are using those arguments, they’re using the fallacies, to argue for something. And so by creating that misinformation themselves, they learn how those fallacies work. But taken together, I mean, everything that we just talked about there, Cranky Uncle, and the fallacy assignment, or whatever iteration you want that to be in, that doesn’t have to be in a purely science unit. Right? That could be sociology. It could be argumentation. It could be English.

Eric Cross (49:01):

Absolutely. That could be totally a prompt in an English class. And practiced in there. And then this could be an interdisciplinary thing, going back and forth between English and and science. Just having these discussions and looking at it from different angles. And you’re practicing the skills in two different contexts. So you get into argumentation. And then that app, I know I had fun with it. And the questions on there definitely resonate with people in my own family. I’m like, “I feel like I’m talking to exactly somebody that I’m related to right now.” <Laugh> Melanie, anything else that you wanna share, or discuss or highlight, before we wrap up?

Melanie Trecek-King (49:39):

So we could talk about lateral reading, if you like. ‘Cause I know a lot of educators use the crap test.

Eric Cross (49:45):

Please, please, please talk about that.

Melanie Trecek-King (49:47):

So, when evaluating sources, a lot of educators teach what’s called the CRAP test. And I wish I remembered what it stood for. But basically what you do, a lot of us have been taught when you go to a website, to figure out if it’s reliable, you wanna go to the about page. Read the mission; see who they are; maybe read some of the content; evaluate the language. So is it inflammatory? Are they making logical arguments? Are the links to reputable sources as well? And the problem is that if a site wants to mislead you, they’re not going to tell you that it’s a bunk site, right? They’re just gonna do a good job of misleading you. And so, what you wanna do instead … the CRAP test basically is an evaluation of a site. And that’s what’s called vertical reading. So you’re looking through a site to determine if it’s reliable. Uh, I think his name’s Sam Wineberg at Stanford, proposed something called lateral reading. Where, instead of on the site, what you wanna do is literally open a new tab and into the search engine type the source. You could do the claim, too. And then something like Reliability or FactCheck or whatever it’s that you’re checking, and then see what other reputable sites have to say about it. So, in their study, actually, they did a really interesting study where they compared professional fact checkers to PhD historians to Stanford undergrads. And they evaluated — I wish you could … um, there’s two pediatrician organizations. One’s like the American Association of Pediatrics and the American Academy of Pediatricians, something like that. They’re very similar sounding. So you give them to students. I do this with my students as well, the same study. So I give my students those two websites. And I say, “Which one of these is more reliable?” And they do exactly what most of us do, which is spend time on the site looking around. And most of the time, if not nearly all the time, they come to the wrong conclusion. And so then I tell them what lateral reading is: “OK, instead of looking through the site, open a new tab, search the organization and reliability.” Something like that. And it takes probably 30 seconds before they realize one of them has been dubbed by the Southern Poverty Law Center as a hate group. As opposed to the other one, which is like a hundred year old huge pediatrician organization that produces their own journals and so on. But nearly all my students are fooled. And in the study, none of the fact checkers were fooled. I’m gonna get the number right. It’s something like 50% of the historians and 20% of the Stanford undergraduates got the correct answer. And they spent a lot more time on it. So it’s a great way to teach students how to use the power of the internet to evaluate sources much more quickly and, effectively. And yes, use Wikipedia, right? Wikipedia is not a final answer, but Wikipedia is actually pretty accurate. So if Wikipedia is the first place you stop, then yes, go there, see what Wikipedia says, and then follow some of their sources.

Eric Cross (52:47):

What popped in my head was like, Yelp reviews for websites. That almost sounds like what it was. It’s like when I search for a product, I don’t go and read the product description marketing. ‘Cause that’s all designed to sell me on something. But I’ll go and look in Reliability, if it’s like a car, or just other sites to cross-reference. And that sounds like what you were talking about is like cross-referencing. Seeing what FactChecker [sic] said about this site, versus seeing what a site says about itself.

Melanie Trecek-King (53:14):

Well, that’s a great analogy. Because if I wanted to know if a product was effective, what the manufacturer says about the product, clearly there’s a strong chance of bias. Right? They’re going to be on their best, um, put their best foot forward. Versus, what do independent reviewers say about this product?

Eric Cross (53:35):

Yep. And I am known to research something to death. And I get something called “paralysis by analysis.”

Melanie Trecek-King (53:42):

Ohhhh, yeah.

Eric Cross (53:44):

And it’s so bad that even if I’m trying to buy, like, towels, I need to find the best-bang-for-the-buck towel. I have to defer some of these decisions out, because I’m on the internet for three hours now. I’ll be a pseudo-expert in towels, and thread count, and all of that stuff. But yeah, that maybe that’s just the science person.

Melanie Trecek-King (54:03):

I mean, I feel your pain. I do the same thing. <Laugh> It’s annoying. Like, it’s just towels. What does it really matter? But yeah.

Eric Cross (54:10):

Coffee! It doesn’t matter what it is. I just need to go, “OK, I have to use these powers for good. Otherwise I’m gonna be researching forever.”

Melanie Trecek-King (54:16):

I wanna say one other thing. So, again, this is a college class and I have a lot of freedom. But one of the driving philosophies behind the class is a wonderful quote in a book, Schick and Vaughn, How to Think about Weird Things. And they said, “The quality of your life is determined by the quality of your decisions, and the quality of your decisions is determined by the quality of your thinking.” And I know my students want a grade. But I’m really trying to teach them how to be empowered through better thinking. That’s where the name “Thinking is Power” came from. I mean, we say “Knowledge is Power,” but it’s not enough to know things. And there’s too much to know. So being able to think and be empowered to have your own agency and not fall for someone’s bunk is my goal for my students.

Eric Cross (55:07):

And doing that is gonna help them through the rest of their lives. Not be swindled, not be taken advantage of, be able to make better decisions. There’s so many benefits to building that skill. And I know your students have definitely grown and benefited. I’m sure you’ve heard, long after you’ve taught them, heard back from them and how they’ve applied that course to their lives. Melanie, thank you so much for being here. For a few things. One, for providing and filling this space where there’s such a need. Again, the critical thinking resources, the tools that you used, are so, so important. If we ever lived in a time where they were critical, it was really what we experienced during the pandemic in the last few years. We watched people’s information literacy and science literacy play out in real time. And we literally saw life-and-death decisions being made based off those skills. That highlighted, I think how important this is. And then, taking the time to generate resources for educators like myself, that we can take and adapt and put into our classroom and start teaching our students. ‘Cause like you said, by the time they get to you, they’re, they’re so far downstream or so far in a system that, depending on the teachers that they’ve had and the education system they’ve been in, may or may not have even touched on these things. They might have learned a lot of facts, but they may not have built their muscle to be able to critically analyze and interpret the world around them. And you’ve just — even the last year, it hasn’t even been a year since we talked the first time — I’ve watched your resources continue to grow, and you share them. And so I, on behalf of those of us in K–12, thank you. And thank you for being here.

Melanie Trecek-King (56:49):

Oh, well, thank you so much for this opportunity. Thank you for everything that you do, reaching out to other educators and for giving me a platform to hopefully reach other educators.

Eric Cross (57:00):

Thanks so much for listening to my conversation with Melanie Trecek-King, Associate Professor of Biology at Massasoit Community College and creator of Thinking Is Power. Make sure you don’t miss any new episodes of Science Connections by subscribing to the show, wherever you get podcasts. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. You can find more information on all of Amplify shows at our podcast hub, Amplify.com/Hub. Thanks again for listening.

Stay connected!

Join our community and get new episodes every other Wednesday!

We’ll also share new and exciting free resources for your classroom every month!

What Melanie Trecek-King says about science

“Students carry in their pocket access to basically all of humanity’s knowledge at this moment in time. The question is: do they know what they’re looking for?”

– Melanie Trecek-King

Associate Professor of Biology at Massasoit Community College and creator of Thinking is Power

Meet the guest

Melanie Trecek-King is the creator of Thinking is Power, an online resource that provides critical thinking education to the general public. She is currently an associate professor of biology at Massasoit Community College, where she teaches a general-education science course designed to equip students with empowering critical thinking, information literacy, and science literacy skills. An active speaker and consultant, Trecek-King loves to share her “teach skills, not facts” approach with other science educators, and help schools and organizations meet their goals through better thinking. Trecek-King is also the education director for the Mental Immunity Project and CIRCE (Cognitive Immunology Research Collaborative), which aim to advance and apply the science of mental immunity to inoculate minds against misinformation.

A woman with long blonde hair and a black top is shown in front of a blue background, framed by a circular graphic with an illustrated flask in the corner.
A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

Winter Wrap-Up 02: Mathematizing Children’s Literature

Promotional graphic for Math Teacher Lounge podcast, episode 2, featuring Allison Hintz and Antony Smith, discussing how mathematizing children's literature can build math fluency.

While we’re hard at work producing the exciting fifth season of Math Teacher Lounge: The Podcast, we’re continuing to share some of our favorite conversations from our first four seasons. This time around, we’re revisiting our popular episode that connected literacy and math!

In this episode, we sit down with Allison Hintz and Antony Smith, authors of Mathematizing Children’s Literature, to talk about what would happen if we were to approach children’s literature, and life, through a math lens–and how we can apply those same techniques to classroom teaching!

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Bethany Lockhart Johnson (00:02):

Hi, I’m Bethany Lockhart Johnson.

Dan Meyer (00:04):

Hi, I’m Dan Meyer.

Bethany Lockhart Johnson (00:05):

And we are so excited for another episode of Math Teacher Lounge. And as you know, podcast format; you’re listening now. I think one beautiful thing about the podcast format is that it gives us a little bit more time to have these rich conversations. And I promise I won’t do it, but I could talk to our guests for hours, hours! Authors Allison Hintz and Tony Smith have just released Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion. And today we get to talk to the authors. Allison, Tony, welcome. Welcome to the lounge.

Allison Hintz (00:53):

Thank you. We’re so grateful to be here.

Bethany Lockhart Johnson (00:55):

We’re so excited to have you here. And I wanna say that my very first—was it my first math conference? Maybe it was my first math conference—up in Seattle, the CGI conference, and I’m all like, you know, wide-eyed and just like, “Can this be a place for me, this math community?” Re-envisioning my relationship with math and thinking about myself as a math teacher, what? And I went to your session on mathematizing children’s literature, and I was just so fired up. I was so wowed by your ideas, your energy, and your passion for students’ thinking. And I feel like as I read this book, I felt like I was hanging out with you. Like you were just so encouraging all the way through. Of educators, of other folks working with young people, and really guiding us how to listen with joy and with an open curious mind.

Dan Meyer (02:03):

Yeah. I would love to hear a bit about the genesis of this book for you folks. Like, I’m coming at this from a secondary educator lens. I’ve got small kids, so that’s also part of my interest here. But I love any book, any idea that seeks to merge what seems like two disparate worlds. Like it’s often the case that we feel like, well, there’s approaches for ELA and approaches for math, and they’re kind of separate disciplines. And these poor elementary teachers have to learn all of them and be experts at all of them. And here you both come along and say, “Hey, what if they are the same kind of technique?” Can you just speak to how this came about?

Allison Hintz (02:38):

Definitely. Tony, do you wanna take a try? Do you want me to start us off?

Antony Smith (02:42):

I can start. We oftentimes present and talk together and so we kinda switch back and forth. So that’s just how we are. So probably about eight or nine years ago, Allison and I, our offices were next to each other on our small campus. We’re both professors and we just happened to have a few children’s books that we looked at together and we were just thumbing through the pages. We really liked children’s literature. And we noticed that I would stop at certain points wondering about character motive or plot or sequence of events or language use. And Allison would stop at very different points in the book and notice number and concepts or something about mathematics. And that’s when we started to wonder, what would it be like if we were sharing a children’s book with a group of children and we put our ideas together? Where would we stop? What would we talk about? What would we ask children about in terms of their thinking and what they notice?

Allison Hintz (03:42):

And so we started playing with these questions that we had and started approaching stories with multiple lenses to see what kinds of things would children notice and what kinds of things might they say. And we were also on our own journey in trying to understand how to plan for and facilitate lively discussions and classrooms that surface really complex mathematics. And it felt like stories were a place where that might be a fruitful context for hearing children’s thinking. We’ve worked with a lot of teachers and students in our region. We live in the Seattle area and we’ve applied for some funding over time that’s really helped us be in a lot of community-based organizations and educational contexts and libraries and pediatricians’ offices and classrooms, various classrooms, and see what’s interesting about this and what might teachers and children do with stories that would surface complex mathematics to think about together.

Antony Smith (04:41):

Over time, we came to the realization that if we wanted to hear children’s ideas, we had to stop bombarding them with questions. <laugh> Yeah. And at first it made it worse that we were asking them math and literacy questions at the same time. And so we realized that what we needed to do was to back off and to ask children what they noticed and wondered.

Bethany Lockhart Johnson (05:01):

Can you say more about that and how that kind of evolved into mathematizing children’s literature?

Antony Smith (05:07):

We did work with a number of very thoughtful, talented classroom teachers and children’s librarians in public library systems who were just so masterful at asking open-ended prompts and questions, rather than kind of like the de facto reading quiz, that a read-aloud can become, which I’ve always disliked as a literacy educator. And we realized in our observing these read-alouds or interactive read-alouds or shared reading experiences that given the opportunity in the space and an adult who was actually listening, that children came up with all of the ideas we would have asked them about and more. So we didn’t have to be bombarding them with questions. They were already much more thoughtful than what would’ve been sufficient to answer our questions.

Allison Hintz (05:58):

And much like mathematics, it was really an iterative process. You know, we had some clunky read-aloud discussions where we were trying to accomplish so much and toggling multiple chart papers and different colored pens and all sorts of “how do we capture these ideas” and “do we separate ’em? do we keep ’em together?” And so it’s really been over time that with partners, we’ve learned these ways of having multiple reads of the same story that allow us to hear what children notice and wonder, and then to delve more deeply into their questions and their ideas through multiple reads where we might spotlight literary ideas that they notice; we might spotlight mathematical ideas that they notice. We might make purposeful integrations between those. But we found it to be most productive—and Kristin Gray really help us think about this—to have an open Notice and Wonder, get everything out much like an open-strategy share. We welcome here, record all the ideas, and it goes all over everywhere. You know, it can be a really not math-y noticing! And those are amazing! So there’s a lot of, um, yes, there is a ladybug on this page! The grandma is wearing green triangle earrings! Oh, your grandma wears green earrings! I mean, it all comes out.

Bethany Lockhart Johnson (07:27):

Wait, have you been in my classroom? ‘Cause that’s exactly— <laugh>

Allison Hintz (07:29):

<laugh> And then, you know, we think of it a lot like if math teachers might use the 5 Practices for selecting and sequencing, or if you might move from an open-strategy share to a targeted share, how can we get out all the questions that children are asking and then step back from them, take some time to really think about what they’re telling us they’re curious about, and plan some purposeful, intentional subsequent discussions that can delve more deeply into their ideas.

Dan Meyer (08:02):

I’d love to go into that a little bit more if that’s all right. Um, I’m gonna speak from someone who doesn’t have an elementary background and I’m gonna voice some worries that I had, some anxiety. One anxiety I have like in a classroom or a curriculum is when there’s no room for student ideas. Right? When it’s like, oh, there’s just room for the curriculum author or the teacher here. That is a sadness. But I when I see an instructional environment like you’re describing here, where there is openness to all kinds of different student ideas, of different levels of formality, from different kinds of cultural fonts of knowledge or wherever, I also get a little bit nervous because that, like, increases the risk that a student might come to understand that “my ideas are not good enough,” whereas in the class with no room for their ideas from their home or their language or their hobbies, like, they’re not gonna internalize the message that, “that wasn’t good enough.” And so I’m really curious as you move from the open Notice and Wonder where kids share all of themselves with you, and then you move to a targeted focus on some sort of disciplinary objective, how do you navigate that tension and help students feel like their contributions are valuable, even though we aren’t taking them up per se?

Allison Hintz (09:18):

That’s such an important question. I mean, I think we’ve grappled with this broadly in math education. I think any time we’re thinking about which ideas we choose to take up to pursue to consider, we have a responsibility to think carefully about whose ideas are being taken up and heard and considered. And so one of the tensions I hear you naming, I think, Dan, is when we engage in lively discussion where children’s thinking’s at the center, how do we make sure to upend and interrupt kinda status norms that run the risk of being deepened? Um, and I think by paying attention to whose ideas are taken up as much as which ideas are taken up, and what’s the mathematics we wanna explore is one tension. Um, another tension I might hear you naming is, you know, the complications that teachers face with time and pressure and coverage, and which mathematics ends up getting worked on. And, um, you know, it’s something we’ve really had to struggle with in mathematics education, where we move to more discussion-oriented classrooms that are really centered in sense-making to know that it takes a lot of time to do this thoughtful, thoughtful work. Um, does that begin to get at some of the tensions you’re raising? Is there, is there more you’re thinking about?

Dan Meyer (10:53):

I think it’s really helpful that you kind of broadened the scope of the question beyond your book to “this is an issue that we are, you know, really challenged by and focused on broadly in math education.” And, um, I appreciate you bringing the element in of whose idea—not just which idea is taken up, but whose idea is taken up—is an opportunity where, let’s say, multiple people raise an idea that is towards an objective the teacher has, they have the opportunity to disrupt certain kinds of status, like ideas about status, in that moment. From your perspective, like, are there techniques to say, I don’t know, parking-lot certain kinds of questions and say like, “Hey, like these are awesome”? I don’t know. I just know that I see kids at like ninth grade. They are very reticent, often. They’ve internalized totally this sense of like, “I’m not gonna just, like, share about the pants the grandma’s wearing, you know; that will not be received well.” And so I’m just kinda wondering how that happens and like, what are the ways we can disrupt that? That process?

Antony Smith (11:54):

So thinking about that, Dan, from the teacher’s perspective, in those kinds of scenarios where you wanna honor each child’s contribution, a couple of things that come to mind: One is that by, you know, initially by modeling what I as a teacher, something that I notice or wonder about, helps kind of set the expectation for what kind of response would be encouraged. And it’s broad, but it gives an example. And then also we really try to record or to chart all of the ideas that are shared so that we can revisit and honor those together. And then either later or on another day, if we choose one or two of those to explore in some way within a more focused read, then another thing that we do is have the idea investigation afterward that continues that thought, but goes back to being as open-ended as possible, so that those students or children who maybe didn’t have their idea as the one that was focused on by the group could go back to that or explore some other idea of their own, so that the idea investigation isn’t a lockstep extension activity, which is why we don’t call it that. So they could again bring in their own perspective. But I have to say from the teacher’s point of view, there is that moment of potential panic <laugh> because there is that power transfer when you’re asking children to help steer where this is going. And if you really mean it, you have to let them steer a little bit. And that can be terrifying. And, um, I always think of one teacher, Ashley, we worked with who read an adorable book, Stack the Cats, by Susie Ghahremani. And in that book, there’s a point where there are eight cats and they’re kind of trying to be a tower of cats and they fall and they’re sort of in the air on that page. And she asked her first graders—she stopped, and she asked, “How, do you think, how will the cats land?” And for about a minute and a half, the entire <laugh> class, was silent. They had their little papers; they had chart paper; they had clipboards; they had everything they needed. But that unusual phenomenon of a group of six- and seven-year-olds actually just sitting and thinking and not being peppered with activities was really stressful, but amazing. And then, after about the 90 seconds, they started out into their exploration of how the eight cats might land. They just needed a minute to think. And it’s so rare that we’re able to let children have that.

Allison Hintz (14:40):

In that same moment, Ashley, who’s a learning partner to us, she turned to us kind of quietly, like, “Should I pose a different question?” And <laugh>, we’re like, “No, let’s stick with it. Let’s see what happens.” So I think it creates this space too, this thinking culture, right? And this culture of “what does that mean to really pose a rich task?That’s open-ended, where there’s multiple access points?” Those eight cats could land in so many different ways. And there was broad access, there was a wide range of all the cats landing, and one’s on their feet, ’cause cats always land on their feet <laugh>, and there was every combination. And so, um, I think what’s really interesting—and to me, this brings back to your wonder, Dan—is, you know, “What’s the risk in openness?” And there’s always risk in openness. Um, it’s scary as a teacher, right? If I’m not the authority of knowledge and I don’t have control over where we’re gonna go, it might get into places that I didn’t anticipate. Or I don’t really feel as solid in the math as I want to. Or I don’t know what it sounds like to stick with silence and wait time, to know if my students are really in productive struggle or if that question was a flop. And so, um, I think this is some practice space for young mathematicians and teachers of mathematics, and just teachers, to explore with that openness and kind of the risk of the openness required for complex thinking to emerge.

Bethany Lockhart Johnson (16:12):

You know, it feels like the way you’re both describing this, it really is a culture shift, right? I kept feeling like I was given permission to be a beginner as I read this book. Like I was really…I loved how you said, I believe it was you, Allison, when you were in the class, you had a couple index card that you kept on your clipboard and that as you walked around, you were like, “Hey, if I don’t know what to ask, I ask one of these questions.” You know? And just this idea that, that, like Dan was saying, there is that loss of control, but that’s also a way to create this culture where students ideas are valued and we are allowing students to really generate the questions, which I thought was such an important idea to explore.

Allison Hintz (17:00):

We started this work long ago, super-excited about math-y books. And we saw a lot of potential in them and we still do. But the limitation we saw is that math-y books, they, they put forth a certain mathematics to be curious about. In some ways they tell you what mathematics to think about. So we started asking ourselves what would happen if we considered any story a chance to engage as mathematical sense-makers. And we started playing with non-math-y books and we got to a place where we could consider every story an opportunity to engage in mathematical thinking. And so we started noticing things over times, oh, these books tend to be really math-y. We call those text-dependent. We’d have to pay attention to the mathematics to understand the story. Whereas this pile of stories, these, they’re not overtly math-y. You could really enjoy the story and not pay attention to mathematics and have an amazing conversation. But what would happen if we thought of about this story as mathematical sense-makers and how might it deepen our understanding of the story? And then this other teetering pile of books, these are books where, you know, children didn’t tend to engage as overtly as mathematicians in it, but there’s opportunities in this story to go back to something—to a moment, to an illustration, to a comment—and think as mathematicians. And those were more about illustration exploring. And so, as we notice these different kinds of books, we really broaden what we thought about. And I think one of the things we really wanna think about in community through this book is what happens if we approach any story, every story, as mathematical sense-makers, because stories are alive in children’s lives, in homes and communities and in schools. And it’s a broad opportunity that we wanna take up. I was thinking, as I stay in this strait for just a moment about book selection, before we move into that process, um, Bethany in a previous MTL, you talked about representation.

Bethany Lockhart Johnson (19:12):

Mm, yeah.

Allison Hintz (19:14):

And do you remember when you shared the image of hair braiding?

Bethany Lockhart Johnson (19:19):

Yes. Vividly, yes. <laugh>.

Allison Hintz (19:22):

Yeah. And can you say just what that meant to you? What that….

Bethany Lockhart Johnson (19:27):

Yeah. Well, it was from a conference; Sunil Singh had used it and was talking about the artistry in mathematics and beauty in hair braiding. And, um, particularly, he was showing this particular image of this Black woman with her hair braided in profile and looking at the angles and the symmetry. And I shared that, you know, I spent so many hours in the beauty shop with my aunties and my mom and my grandma and continue to, to this day, that it just, it struck me immediately as familiar. And it struck me immediately as seeing an image that was reflective of my lived reality, projected as valuable and worthwhile for consideration in the world of mathematics. Which is not what I felt as a student of mathematics as a young adult or child. So it was this beautiful moment of, for me, the power of when we see images and we allow opportunities for re-envisioning what may be a common practice for that student, or may be something that they see every day.

Allison Hintz (20:44):

And in that same way, that image that was put up, we wanna think really carefully about representation in the stories that we select. And when we think of stories as mirrors or windows, we really wanna be mindful in story selection of whose stories are told and whose stories are heard. And when you said that you would sit down to listen to a story and you felt at ease or that you saw an image and you saw yourself that can be and should be something we really think carefully about when we select the stories that we select.

Dan Meyer (21:21):

It’s a wider path for representation of different kinds of people in literature, because people’s stories seem so much more present and towards the surface of their lives, versus, say, the abstractions and numbers and shapes in mathematics. It feels like more of a struggle to find ways to show people, hey, like you’re here, this, this place belongs to you. So in all these reasons, I think it’s really great you folks are using literature, which has this history of humanities, literally humanities, as a vehicle for mathematics. That seems pretty special here.

Antony Smith (21:56):

We both go to libraries and bookstores and look through books as often as we can, but also our partner, a children’s librarian, Mie-Mie Wu, helped us go through—when we would meet, she would bring three or four hundred books at a time.

Bethany Lockhart Johnson (22:13):

When you described her wheeling in the cart, oh, I wish I been in that room! <Laugh>

Antony Smith (22:18):

And the cart was, you know, probably three or four times bigger than she was sometimes. And we would go through hundreds of books and look at them and listen to her thoughts as a skilled librarian sharing with families, diverse families, and what catches the attention of a three-year-old sitting with her grandfather. And that was really a valuable, helpful experience. And it’s a partnership that continues. So in Last Stop on Market Street—and this is in the book; we talk about this, this children’s book quite a bit—in this story, CJ with his Nana, his grandmother, are riding the bus to the last stop on Market Street in San Francisco, to go, as we will find out, to help serve in a soup kitchen to help the community. And the teacher, Susan Hadreas, had the children record their ideas. She charted them in an open Notice and Wonder read. And one of the ideas that a young boy noticed was that CJ on the bus…a man with a guitar starts playing the guitar on the bus and CJ closes his eyes and it says CJ’s chest grew full. And he was lost in the sound and the sound gave him the feeling of magic. So this boy said, “I wonder, what does that feel like if you’re feeling the magic? What’s that?” And that was one of many ideas in the open Notice and Wonder, and Allison will talk about the math lens read, but first Susan went back and read with them. She had that idea, she circled it on the chart paper, and another day that week, she said, let’s go back and visit this story we really liked. And remember, we wondered what feeling the magic was like. Let’s go back through and let’s keep track of all the feelings and emotions that CJ had across the journey to the soup kitchen in this book. And so they did another read of the story; they were very familiar with it, of course, but they noticed new things and they also, every few pages, stopped and she helped chart all of the emotions that CJ experienced from envy to excitement to sadness. There’s a huge range in this book. And it was fascinating.

Allison Hintz (24:36):

I think one of the things that the children noticed was that CJ’s feelings were shaped by community. And that he shaped and shaped…he was shaped by and helped shape his community. And so the ways that he felt across the story were impacted by the other characters that he comes across. The guitar man on the bus. The bus driver who can pull a coin out from behind someone’s ear. The lady with the butterflies in the jar. Nana helping him to see the rainbow. And the students started, you know, being curious about that. How do we shape and how are we shaped by community? What communities are we a part of? This class is one community. I’m in many communities across my life. And they started to quantify the number of people in the story. So Mrs. Hedreas went back for a math lens read, and she said, let’s just keep track of and pay attention to how many people are in CJ’s life in this day. Because I can hear you starting to think about quantity. This class at the same time in other areas of the day had been working on counting collections, how to keep track, so they got out their tools. Some people pulled out ten frames, some people pulled out clipboards. They had a wide range of things they could use to help them keep track. They developed their own strategy, keep track however you want. She did a quicker read through it, flipping the pages, and then they get into these debates: <laugh> “We already counted that person!” “But they took their hat off and put it down to collect money!

Antony Smith (26:10):

“What about the dog?”

Allison Hintz (26:11):

“That’s the same person!” “Yeah, there’s a dog pound in his community!” <laugh> “Do animals count in our community?”

Bethany Lockhart Johnson (26:17):

I love it!

Allison Hintz (26:17):

“Yes, they count!” Uh, and so we went through and quantified and there was really this understanding as you saw these people throughout the story that communities can be of different sizes, but community has impact. And you have responsibility in your community to show up and to lean in and to know that bringing your full, authentic, vulnerable self, you shape people and they shape you. And what communities are people a part of. And it turned into this really interesting discussion about quantity and helped us think more about quantity and community. I think a really important moment for us and for that class was the transition from being people who almost did mathematics to a story, like counted things on a page, um, count acorns on a page in an autumn book, to being mathematicians who thought within the story.

Antony Smith (27:17):

And then two idea investigations that came from that —not at the same time, of course, but with the same group of children—one was they identified an emotion of their own and wrote and drew about that. And also, who helped them address or get out of or acknowledge that emotion. And then the other idea investigation was that all of the children drew or kind of mapped out a community that they were part of. Whether it was their neighborhood or their classroom or their soccer team or whatever it was. And so then those investigations strengthened the connections of those concepts to the lives of those children.

Bethany Lockhart Johnson (28:05):

Well, I, actually wanted to ask you about idea investigations. Because I feel like that was such an important invitation in your book. And the way I understood the idea investigation is you’re really paying attention to what’s coming up in your other reads. Right? And then these are opportunities to extend the thinking, or like you said, to extend a particular aspect: What’s your community? Can we map your community? Or what’s a particular emotion? And it was in such contrast to what I think I have probably done in my classroom more than once, which was like, “Oh, we read this story about seals. So now my story problem is gonna be about seals, right? <laugh> Like in the story, you know, Jojo, the seal had five balls. <laugh> So if Jojo still had five balls and two of them bounced away…” You know, or whatever. Right? But that’s not what an idea investigation is. Right?

Allison Hintz (29:03):

Yeah. I think this is where we also had some stumbles and can totally relate to what you’re saying as previous classroom teachers as well. We have come to a place where we are pretty in favor of a super open-ended idea investigation that takes up the things that have surfaced in the multiple reads and making sure it’s a rich task with many, many ways children can engage with that. There’s many, many, many right answers or ways to engage. Less is more there. So we moved way away from, like, even a worksheet that might have an idea from it to blank paper and math tools and places to get into some productive struggle around some of the complex things that were raised.

Antony Smith (29:59):

A challenge with worksheets is that they put a frame around children’s ideas. So either there are only three lines to write on, or there’s only a small box to draw in. Whereas a blank page really opens up the possibility. Um, and so—is it Ann Jonas who wrote Splash!? sorry, I don’t have it in front of me—the book Splash!, about animals that end up in and out of the pond, including a cat that is not happy about ending up in the pond, an idea investigation after that for very young children was, with the list of the different creatures displayed at the front of the room: On blank paper, hey, draw your own pond and decide how many of which and each type of animal you want in your pond and then write about it. Just on blank paper. And so that allowed some children to draw, like, three giant goldfish. But other children drew 17 frogs and three cats. And, and just, it lets children follow—

Bethany Lockhart Johnson (31:02):

It was theirs, right? It was theirs.

Antony Smith (31:04):

Their idea. <laugh> And that comes partly from, I think, as Allison mentioned, we both were classroom teachers before moving into academia. And I remember giving children worksheets, particularly math worksheets, where they weren’t necessarily bad, but right at the bottom, it says like, explain your strategy. And it gives two lines.

Bethany Lockhart Johnson (31:23):

Right! <laugh>

Antony Smith (31:25):

The only thing a seven-year-old can write there is “I thought.” Or “I solved it.” <laugh> And that’s not where we need to go.

Dan Meyer (31:34):

Yeah. If I could just ask the indulgence of the primary crowd here, like, I’m trying to make sense of all this. And I just wanna like, offer my perspective. My summary statement of what’s going on here. I’m trying to—I love how you both came here—

Bethany Lockhart Johnson (31:45):

<laughs> How ya doin’, Dan? How ya doin’?

Dan Meyer (31:47):

<laughs> I’m, ah, A, I’m loving this a lot. Um, B, I came in here loving how you folks are broadening the work of primary education to kind of find commonalities between these sometimes seemingly disparate kinds of teaching in ELA and math. Love that, I wanna say. But I think you folks are describing, with all these teachers you observed and your own work, is the work of attaching meaning to what students might not realize yet has meaning. Or they might think it only has one kind of meaning. But you, the teacher, with their knowledge, realizes that there are many more dimensions of meaning that can be attached to those thoughts. And I’m hearing that from you folks, when you describe A, what math is and the power of a teacher to name a thing as mathematical. Like, “Oh, you didn’t think math was that, but math is noticing; math is wondering; math is asking questions,” for one. But also this work you’re describing of how, like, first the task has to invite lots of student thoughts and then to say like, “Oh, I see that there’s a similarity to these two.” And to raise those up for a conversation or to ask a question like to extend one person’s, one student’s question a little bit more. But it’s always…I’m just hearing you folks attaching more meaning than the student might have originally thought. I appreciate the conversation. That’s really interesting.

Bethany Lockhart Johnson (33:03):

Well, and now that the book is out, I think it’s gonna keep evolving, right? Now that it’s gonna be in the hands of teachers and librarians and educators and caregivers, it’s exciting to see kind of where it goes next. Which actually brings us to our MTL challenge. Dan Meyer, do you wanna share?

Dan Meyer (33:22):

Math Teacher Lounge, we have a challenge for the folks who listen and we’d love for them to hop into the Facebook group Math Teacher Lounge, or hit us up on Twitter at @MTLShow and just, like, kind of exercise beyond listening, exercise the ideas you folks are talking about, some kind of a challenge that can help us dive deeper into your ideas. So what would you folks suggest for our crowd, for our listeners?

Allison Hintz (33:42):

I would love to invite people to playfully experiment with a favorite story, with a story that’s new to you. I would love to invite listeners to sit with a story maybe on your own, and just ask yourself as a mathematician: What do you notice and wonder in this story? Don’t feel any pressure. Maybe sit with a child or some children and listen to what they notice and wonder. Like, really listen! Don’t ask questions! But hear their questions and place children at the center and consider multiple reads. Consider continuing to pursue their questions. And we have a planning template that might support people in kind of sketching out some ideas if you’re open to playing with that too.

Bethany Lockhart Johnson (34:34):

And we will post—

Dan Meyer (34:36):

That’s awesome.

Bethany Lockhart Johnson (34:36):

—a link for that planning template in our Facebook group and on Twitter as well. So thank you so much for that resource, because I think it’ll definitely help. It could help you, like you said, it could help you kind of organize your thoughts or help you think about this work in a new way. So thank you for that resource and thank you for the amazing resource that is Mathematizing Children’s Literature. I am so excited to continue to engage with you both and with listeners as they dive into this book. If folks want to engage with you more, where can they find you? How can they reach you?

Allison Hintz (35:12):

Well, we’re on Twitter.

Bethany Lockhart Johnson (35:14):

Great.

Dan Meyer (35:15):

What’s your home address? <laugh>

Bethany Lockhart Johnson (35:24):

Wait, let me try that again. <laugh> ‘Cause it does sound like I’m like, <fake ominous voice> “Where can they find you?”

Allison Hintz (35:29):

4-2-5…. <laughs>

Antony Smith (35:32):

At the bookstore!

Bethany Lockhart Johnson (35:34):

Y’all, if folks want to continue this conversation or share these ideas or the math challenge, how can they tag you? How can they, they reach you on the World Wide Web, besides the Math Teacher Lounge Facebook group?

Antony Smith (35:50):

Yeah. Well, we are both on Twitter, and we’ve been trying to promote the hashtag #MathematizingChildrensLiterature. It’s very long, but once you type it once, your phone or computer…

Bethany Lockhart Johnson (36:01):

Easy. Yeah, those click, right? Is that what it is now?

Antony Smith (36:03):

<laugh> The other is that we do for our project, we have an Instagram account that is @MathematizeChildren’sLiterature.

Allison Hintz (36:11):

We care really deeply about hearing from people. You know, we think our ideas are constantly evolving and that there’s such exciting room to grow. And we just felt compelled to share what we were learning now so that together we could learn and build vibrant experiences for young children and teachers and families through stories. So we want to hear from people! We wanna learn about stories that are important in your lives and what children say, and grow these ideas together.

Bethany Lockhart Johnson (36:42):

And credit to Dan, you told me you went and ordered a bunch of the books they have on the suggested read list.

Dan Meyer (36:48):

Oh my gosh.

Bethany Lockhart Johnson (36:49):

You read ’em to your son.

Dan Meyer (36:50):

I got such a side-eye from my significant others around here for what I dropped on Amazon in one night! <laugh> Uh, all these books I didn’t have. Some of them I did. We are not fully illiterate around here! We do love the written word at the Meyer household! But there were a bunch that that I grabbed. I’m morseling them out day by day.

Bethany Lockhart Johnson (37:09):

Wait, at bedtime I read my one-year-old One Is a Snail, Ten Is a Crab. <laugh> And let me tell you, he had vigorous pointing and “Da? Da da da da?”

Allison Hintz (37:22):

<laugh> Aww, da da!

Bethany Lockhart Johnson (37:22):

So hey, we’re on the road. <laugh> <music> Deeply grateful, not only for your work and your beautiful book and your work, but also for the invitation to dive into the world of children’s literature in a way that many of us have not before. And it’s fun! Thank you, Tony. And thank you, Allison. And thanks for hanging out in the lounge.

Allison Hintz (37:48):

Thanks for having the lounge!

Antony Smith (37:49):

It’s been fun!

Allison Hintz (37:52):

Thank you both.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Allison Hintz says about math

“We started asking ourselves, “what would happen if we considered any story a chance to engage as mathematical sensemakers”.”

– Allison Hintz

Author and Associate Professor, University of Washington Bothell

Meet the guest

Allison B. Hintz: Dr. Hintz’s research and teaching are in the area of mathematics education. Her focus on mathematics came about during her years as a fifth grade teacher – it was alongside her students that she developed her own positive identity as a mathematician! Today she studies teaching and learning, specifically facilitating engaging discussion. Her research and teaching happen in partnership with educators and children in formal and informal settings and focuses on beliefs and practices that support all children in lively mathematics learning. She is a co-author, with Elham Kazemi, of Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Twitter: @allisonhintz124

Antony T. Smith: Antony T. Smith is an associate professor of literacy education at the University of Washington, Bothell. He works alongside teachers to create engaging literacy-mathematics learning experiences through exploring and discussing children’s literature. He is committed to the concepts of motivation, engagement, challenge, and creativity in literacy teaching and learning.

 Twitter: @smithant  Instagram: mathematizechildrensliterature

Two people appear in separate circular frames; the woman is smiling and wearing headphones, while the man stands in front of bookshelves, perhaps discussing Mathematizing Children’s Literature.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

S3-03: Instructional strategies for integrating science and literacy

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

We’re continuing our investigations around science and literacy with Doug Fisher, Ph.D., professor and chair of educational leadership at San Diego State University. We talk about the importance of integrating science and literacy, as well as practical guidance for teachers who want to unite the two disciplines in their own classrooms.

Listen as we discuss how science and literacy can be powerful allies and specific strategy areas to focus on when integrating the two disciplines. And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Douglas Fisher (00:00):

It’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. This season, we’re making the case for our favorite underdog, which of course is science. Each episode we’re showing how science can be better utilized in the classroom, and making the case for why it’s so important to do so. In our last episode, we examined the evidence showing that science and English instruction can support each other. And now on this episode, we want to give you some more strategies for really making that a reality in your own home or classroom or community. So to help me, I’m joined on this episode by Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Dr. Fisher is actually someone who has conducted literacy training at my own school, so I’m excited to be able to share some of his wisdom with all of you. Oh, and just a heads up, Dr. Fisher dropped some gems about the ways teachers can integrate literacy and science in their classrooms. So you may want to have a notepad. Ready. And now here’s my conversation with Dr. Douglas Fisher.

Eric Cross (01:12):

Well, Doug, thank you for your time and for being willing to come and talk about literacy and science. I know you’re busy, all over the place, and so I was super-excited that we were able to lock you in and talk about this. And, on this episode, we’re gonna talk about the ways that science and literacy can support each other. And one of the reasons why I’m really excited for you is because you said some really key things for me as a science teacher, when you talked about literacy and supporting students. That just resonated so deeply in me. And I was like, “I need more Doug!” Because we’re on that same frequency. And I know it’s a subject that you’ve spent a lot of time writing about. So can you tell us a little bit about how this became an area of interest or a passion for you? Just literacy, and all of the work that you’ve put into it?

Douglas Fisher (01:54):

Yeah. So I’ve wanted to be a teacher for a really long time. And I went to San Diego State as an undergraduate, and I was taking English class and we were assigned topics. You know, like, you’ll do an assignment, you’ll write a paper for this English class. And I got the topic “illiteracy,” and I was a freshman at San Diego State reading all of these things about adults who don’t read very well or not at all. And I ended up writing my very first college essay on illiteracy — at the time, you know, called illiteracy, at the time. And so I got super interested in this. And so as I moved through college and into my teaching career, literacy became a really important thing for me to think about, because it’s the gatekeeper. You know, you can be taken advantage of, if you’re not very literate. People can use vocabulary against you, if you’re not very literate. We know that people who have higher levels of literacy have better health outcomes. They have better lifespans, longer lifespans. I mean, there’s just — literacy impacts so much more than “Are you reading your fourth-grade textbook?” It really has lifelong implications.

Eric Cross (03:01):

That part that you said about being taken advantage of … I just got a flyer in the mail yesterday. It was one of these mailers that looked like it was an authentic debt-reduction type of thing, but it was really just like a marketing email. If you read the fine print at the very bottom, it had all of this jargon about “This is a paid, you know, for-profit company.” But when you look at it, it had official stamps all over it. And I could imagine if someone’s receiving that, that probably fools a lot of people. Is that kinda like what you’re talking about, like being taken advantage of?

Douglas Fisher (03:28):

Yes. I had a student turn 18, got a letter from a “credit card company” that was offering her daily compounding interest. And if you don’t know what that means — at 23 percent! — if you dunno what that means, you are gonna be a victim. Literacy really influences a lot of our life. It’s also how our brain works. We have a language-based system in our brain. We read, write, speak, listen, and view. And the things we learn, we learn through speaking, reading, writing, listening, and viewing. From what we know, we are the only species that has an external storage mechanism. Like, we have the ability to store complex information outside of our body, in the form of notes. We can type them. We can write them. And we can then go back and retrieve that information, that complex orthographic information later. And it means the same thing. We can say we have a storage system and we’ve been doing this for a really long time. Way back to, you know, hieroglyphics and messages on cave walls. And throughout the ages of humans learning, how to store information that they can re-access again later. That’s become a super-complicated system. It’s how computers operate. And we send messages to each other and we text each other and we write things down, and we’re really good at putting ideas, information out there. Now, if it’s just speaking and listening, then we can forget it. We can say, “No, you said this,” or “I said that.” But when it’s written, and it’s print literacy, you know, it’s the orthographics there, you can go back to the same message and over and over again. Now, you might change the interpretation of it, but the message is still there.

Eric Cross (05:16):

Right. And that is such a key element, at least of modern education, is this written element of it. It’s what many schools live and die by. They’re quantitatively and qualitatively analyzed by it. It’s public. They can see it. And so there’s this heavy emphasis. And why do you think science and literacy can be powerful allies together?

Douglas Fisher (05:38):

Awesome. Well, it’s hard to learn science if you’re not literate.

Eric Cross (05:42):

This is true.

Douglas Fisher (05:42):

But that’s a one-way direction. And yes, science teachers and scientists do a lot of reading, writing, speaking, and listening and viewing. They use the five literacy processes all the time. When we interview scientists, they spend a lot of their time reading the work of other scientists and writing their findings, writing grant proposals, presenting at conferences, you know. So a huge part of the work of a scientist is not just at a bench conducting experiments. But even if you’re conducting experiments, you’re using your literacy processes to think about what you’re seeing in your experiment. So that’s a one-way direction. And I do think literacy has an influence on science. But since science goes the other way, it influences literacy. As you learn more and you understand more about the world, your background knowledge grows, your vocabulary grows, you become more literate in those different areas. And how you think. So if I’m learning about life science; I’m learning how the world works in a more, biologic physical world. And that knowledge helps me think about when I’m reading a novel, and there’s an appeal to some science knowledge or a concept that gets played with, you know, perhaps time-space continuums … well, if I don’t have the science knowledge of how I think the world works, it’s hard for me to understand what this author is doing. So it does go both ways. They feed each other. And the more literate we become, the more complex science information we can understand. ‘Cause our background knowledge and our vocabulary influence how much we understand about what we read. And as we access more complex science information, it starts to change the way we think about other things in our world.

Eric Cross (07:23):

There was a couple of things that you said in that, but one of the first things that kind of perked my ears is when you said grant proposals. Because I have friends that are scientists — and this is one of the things that when I was in school, they don’t talk about — but how much of their research is reliant upon getting funding —

Douglas Fisher (07:37):

Mm-hmm. <affirmative>,

Eric Cross (07:38):

— which you don’t think about if you’re becoming a chemist or a physicist or a biologist or working in the field, is that that funding, coming from the NSF or anywhere else. And sometimes students ask in class like, “Why am I writing so much? Like, I want to go into science!” Or “I wanna do this!” And this is a real-life example of how the writing could actually apply, in addition to all of the things of collecting data and conclusions and results. But that grant proposal thing just really perked my ears, yeah.

Douglas Fisher (08:01):

And if you can’t write a grant proposal, your ideas and experiments are not gonna get funded. And if you can’t write a strong proposal, that compellingly convinces your readers to fund you, you’re not gonna get funded. But then once you get the grant, you have to write publications. You have to share your work with other people. Make PowerPoint presentations and write journal articles or books or whatever. So it’s a cycle that literacy influences the things we do, including the things we do in science.

Eric Cross (08:31):

Now to get in maybe some data, if you were trying to convince someone that like this happy marriage can exist, what would be like your number one piece of evidence to support this, this back and forth of supporting each other?

Douglas Fisher (08:44):

Awesome. So the quote I’ll often say — and this is from studies from more than two decades ago now — but in general, in high school science, students are introduced to 3000 unfamiliar words, 3000. Each year! Because there are words that are used in a scientific way that are used commonly in other places. And there are discipline-specific words. So 3000 words a year in high school science. The Spanish 1 textbook only has 1500 words in it. So science teachers have double the academic-language vocabulary demand that a typical introductory world-language class has. So just the vocabulary alone should say to us, literacy is gonna be important if you’re gonna learn science. And if you don’t understand these technical words, and you don’t understand the way science uses this particular word in this particular way… . When you say the word “process,” it means something very specific In science. “Division” — cellular division is not the way we think about it in mathematics; there’s a similar concept, but cellular division is different than dividing numbers. And those are words that get used in multiple areas. Then you have all these technical terms that you have to be able to use, to understand the concepts. To share the concepts. To talk to other people. Whether you’re in, you know, fifth grade and talking science, or you’re a university professor, there’s a shared language, appropriate for our grade level, that we have shared meanings of.

Eric Cross (10:22):

And we’re essentially … what I’m hearing you say is … most of the people that are listening to this are science teachers. We’re we’re also language teachers. In a sense.

Douglas Fisher (10:29):

So my frustration is when people say, “Every teacher’s a teacher of reading.” And I don’t like that. I’ve written against that phrase. I don’t think all teachers are teachers of reading, any more than all teachers are teachers of chemistry. Or all teachers are teachers of algebra. But what I will say is the human brain learns through language. And all of us — every teacher that I’ve ever met understands that language is important in my class. If my students don’t have strong listening skills and speaking skills; reading, writing, and viewing skills; I’m gonna have a hard time getting them to learn things. If I can help them grow their speaking, listening, reading, writing, and viewing in my content area, I’m gonna do a service for my learning of my subject and also their more broad literacy development.

Eric Cross (11:16):

  1. So, at a high level, what does it look like to integrate science and literacy? We’ve done education for the last, what, hundred years?

Douglas Fisher (11:24):

Mm-hmm. <affirmative>

Eric Cross (11:25):

—kind of pretty similarly, right? Kind of siloed way. What does this look like at the 30,000-foot level? You’re a professor, department chair. Run schools. Speak everywhere. Like, when you think about this from that high level, what does it look like?

Douglas Fisher (11:39):

A high level? Every time I meet with students in a science class, you know, biology or fifth grade or whatever? They should be reading, they should be writing, they should be speaking and listening. Every class. So what print do you want them to access? And it can be a primary source document, it can be an article, it can be from a textbook. Are they reading something? Are they writing to you? Because writing is thinking. If they are writing, they are thinking. As soon as their brain goes somewhere else, they stop writing. The pen won’t move or the fingers don’t type. And then speaking and listening, of course, is the dynamic of our classes. So every day we should see some amount of reading, writing, speaking, and listening, viewing in our classes. That’s at a high level. There are some generic things that seem to work across the literacy. So, learning how to take notes. Focusing on vocabulary. Using graphic organizers. These are generic things that as educators we can use in our classes. Then there’s more specialized things. So, scientists and science teachers think differently than historians and literary critics and art critics. So scientists, if you look at the disciplinary literacy work, there’s a whole body of research where they interview and study high-end experts in their field: chemistry, physics, biology, et cetera. And there are some characteristics that were more disciplined, specific. Scientists like cause and effect relationships. They look for them when they’re reading. They like sourcing information. “Where this come from?” “What’s the history of this idea?” Scientists have a long view in terms of time. Historians have a shorter view of time. English teachers have even shorter view of time. Scientists tend to think in long periods of time. And so all of that influences how a scientist reads and how we should apprentice young people after they get past the generic “I know how to take notes. I know how to study my vocabulary. I know how to do summary writing for my teacher in my notebooks and things,” there’s some generic tools. Once we get past those, we need to be looking at specifically how do people in science use literacy.

Eric Cross (13:52):

I’ve never had my thought process of reading deconstructed just now, but we just described how scientists read. I was like, “Yeah, that’s pretty much how I read, right there.” I also like how you said how we should apprentice young people. And I feel like you as the literacy guy, you chose that word very specifically, as far as apprenticing young people. That is a view, I think, that’s really important to hold. ‘Cause that’s what we’re doing essentially … is, if we’re doing what we should be doing, we are apprenticing these young people.

Douglas Fisher (14:18):

Yes.

Eric Cross (14:18):

And helping them develop. Now, let’s imagine there’s a listener out there and they’re interested in getting better at integrating science and literacy instruction. They want to start somewhere. Before we dive in, do you have any initial words of encouragement for the person who’s like, “Everything is like a priority right now,” in their classroom or in their world?

Douglas Fisher (14:37):

Yeah. So I’ll talk about elementary for just a moment. When we’re reading informational texts in our literacy block, we should be reading information that is aligned to what kids need to learn in science and history in, in that grade level. Why are we reading things that are gonna be in conflict with what they’re gonna learn in science later that day in fourth grade, for example? So when we look at our standards, our expectations, what is it that third graders need to know in history, science, mathematics, language arts? And when we’re reading text and we’re learning to apply our reading strategies during our literacy block, why aren’t we reading topics that build our background knowledge for our science time? So we’re seeing some synergy there. We should be looking at life cycles in grades that are appropriate for life cycles and knowing there’s more to life cycles than the frog and the plant or the seed. There are all kinds of life cycles. And we call ’em life cycles for a reason. That’s a general concept. Now in science, we’re looking at this particular lifecycle right now. And so that’s a high level. If we could get more connection to the content standards during our literacy blocks, it would be very good. When we talk about the time at which we call “science” in the day, in more of the K–8 continuum, the science needs to include some primary source documents. Some real things that students are reading. Read about a scientist; read about a scientist’s discovery; read about what they discovered. So that we’re building our background knowledge. So when we go to do things, activities, labs, simulations, we have background knowledge and we understand what we’re experiencing. It can’t be like—I watched this awesome lesson on lenses and the teacher had all these different lenses in the room and the students came in and they were brand new. They don’t know anything. They were picking ’em up. They’re exploring them. They’re trying to figure out, and they’re trying to come up with theories about what this is and how it works. And then the teacher gave them a reading, a short reading, on refraction of light. And they read this thing. And the clarity that they had about what these lenses must do, well! All of a sudden they’re putting them up to the lights! They’re asking if they can go get the lights out of the storage unit! ‘Cause there’s — and they’re shining different lights through the lenses to see what happens to the light. Because that little bit of reading turned some focus on for the students. And it allowed them to take what I’m thinking about, what I’m trying to figure out, how this thing works in another direction. That’s the power of using literacy in our classes.

Eric Cross (17:20):

And what I’m hearing essentially is transfer across disciplines, across content areas, ultimately. And in an elementary school classroom, would it be fair to say, probably the teacher has more autonomy to be able to do that, since they’re teaching all the subjects? But secondary, logistically, planning and those types of things … from what you’ve seen, is it fair to say this kind of needs to be like a top-down, full vertical alignment, to teach like this?

Douglas Fisher (17:45):

I think that would be awesome to do that. But if I’m a sixth grade English Language Arts teacher and I’m working with my sixth grade science teacher, the conversation should be, “What units are you teaching?” Because I’m choosing informational text. My job is to teach them how to find central ideas. My job is to teach them how to find the details in the text. My job is to have them make a claim and support that claim with evidence. The stuff I use is generic. Yes, we do read some literature and some narratives, but we also read about 50% of the text in English around informational text. So if I can help you and accomplish my standards as well, fantastic. So let’s have this conversation and say, “Oh, this is what you’re teaching in science in the next three weeks? I’m gonna choose some texts and we’re gonna analyze ’em for central idea. We’re gonna analyze ’em for details. We’re gonna, for mood or tone or whatever that we’re teaching. And by the way, I’m building background knowledge. So when they come to you, they know some stuff about what you’re going to be teaching next.” So I don’t think it’s impossible to say teams of teachers could come together and say, “What do we believe that our students need to know and learn and be able to do? And then how do we choose things that are gonna help them accomplish exactly that?”

Eric Cross (19:01):

And that’s empowering. Because that’s one thing that we can control maybe is this East-West, peer-to-peer, different content areas. A system may not be able to change as quickly, but I can definitely go talk to my English team or math team and check in and kind of see, “Hey, where do we have overlap in that?” And I know the times that I’ve accidentally had overlap with the teams, it’s super-exciting. And the students have been more bought in! Because it’s like, we’ve done something on the human microbiome and we’ve talked about genetics and all these different things, and then when they read The Giver, or they read some book about genetics, they have all this knowledge. And they’re excited. And they talk about colorblindness or they come to my class and they’re like, “Hey, we read about this!” It’s almost like they saw a magic trick, the fact that these things linked up. And the engagement has been so much higher when it’s the same content in different classes, but through different lenses. At least, that’s what I’ve seen in my years of teaching.

Douglas Fisher (19:54):

I saw a lesson on space junk that was so cool. Middle-school students learning space junk. And the history teacher had a part of it, science teacher had a part of it, English Language Arts teacher had a part of it. And these students, I mean, you watch them look up all the time, ’cause there’s space junk up there. Where’d it come from? Why is it there? What are the politics of this? How do we clean it up? I mean, it was just so interesting to watch them when the teachers came together. And the teachers met their standards in this couple-week-long space-junk exploration. Investigation was met. Politics was met. All these different things. Economy. You know, how much does it cost to clean up this problem? So there’s really cool opportunities when teachers come together and realize we can work together and improve the literacy and learning of our students.

Eric Cross (20:50):

Absolutely. So before this recording, we picked your brain a bit. And I know that there were three specific strategy areas that you wanted to touch on. And one of those — which is kind of coming back to the 3000-words language teachers — was vocabulary. So what are the opportunities that you see, as far as the way of educators to approach vocabulary? Because, you know, there’s a lot. We got a lot of it. The 3000 words.

Douglas Fisher (21:14):

Yeah. There’s a lot of it. So the worry is, we make a vocabulary list and have students look up the words in definitional kinds of things. That’s not really gonna help. Students need to be using the words. They need to be using the words in their conversations, in their writing, in how they think about your content in science. So vocabulary is a huge predictor of whether or not you understand things. Vocabulary is also a pretty good predictor if you can read on grade level. So when we think about vocabulary, there’s something called word solving. You show students a piece of text and you’re reading it, you’re sharing your thinking, and you say, “Oh, here’s a context clue!” Or “I know this prefix or suffix or root!” And in science, a lot of the words are prefixed, suffixed, or root words. We tend to add things together with a lot of prefixes and suffixes and have roots and bases in science. So we can help students think about, “Oh, what does geo- mean? We already know what geo- means here. It means the same thing in this word. Let’s apply that knowledge.” So word solving is part of it, showing students how we think about words that we might not know. The second is more direct instruction of vocabulary. As students encounter the words, we work on what it means, how we say it. We practice it a few times. The process is called orthographic mapping. It’s kind of a scientific idea here. But you have the sound and the recognition of by-the-word, by sight, and what it means. And your brain starts to automatically recognize that word in the future. So I don’t have to slow down, disrupt my fluency, and try to figure out what the word is saying. ‘Cause I’ve seen it enough. I’ve heard it pronounced enough, I’ve pronounced it enough, and I know what it means. So teachers should be saying, “What words in sixth grade science, what words in third grade science, do my students really need to know?” And I’m gonna have them encounter those words over and over. I’m gonna have them use the words. I’m gonna have them see the words. I’m gonna have them say the words. I’m gonna say the word and we’re gonna be over and over with these terms, so that students incorporate them into their normal view of, “These are the things I know about the world.” By the way, when they go to read that next thing, and they understand “geology,” you know, for sixth graders, for example, they know how to say it. They don’t stumble on it. And it activates a whole bunch of memories in their brains. “This is what geology is.” There are branches of geology, there’s physical geology, there’s all this thinking that activates as they read.

Eric Cross (23:35):

There was a practice that I participated in and am trying to incorporate — I don’t know what the name of it is. But essentially what happened was we were dissecting a flower. And the instructor had us name parts of the flower. But we got to come up with our own names for it.

Douglas Fisher (23:49):

Ah.

Eric Cross (23:50):

So, for instance, the stamen we call “the fuzzy Cheeto.” And we all used our own words and then everything was legitimized. And so we went through and learned the whole activity using our own vocab words. But then, in the end, after we presented and talked about it, then the words, the actual academic language was attached to our word. And we were able to say, “OK, the fuzzy Cheeto is the stamen,” and this, this, this, and this. But it was such an interesting practice, because it kind of legitimized all of our definitions. But we weren’t stumbling on these long Latin terms and things like that. Is there a name for that? Or. … ?

Douglas Fisher (24:29):

Yes. I don’t know the name for that. I think it’s really smart. So here’s what I would say about that, is: we don’t learn words, we learn concepts. Words are labels for our concepts. So what that teacher did for you was allow you to develop concept, a concept knowledge. “There’s a part of this plant, it goes like this, we’re gonna call it fuzzy Cheeto. Now I have this concept. And look, it occurred in all these plants. And those people called it that and that other group called it that. We called it a fuzzy Cheeto. Here’s the part of it.” And then the concept is in your brains. And the teacher said, “It’s really called stamen.” And it’s an instant transfer, because you already had the concept. What we often see is students are trying to learn a really hard academic word and the concept for the word at the same time. And so it slows down the whole process. And there’s higher levels of forgetting. Because human beings, we don’t learn words; we learn concepts. If you don’t have the concept, if I gave you a word out of the blue that you’ve never seen, never heard, and a week from now I asked you to remember it, you probably would not, because it didn’t register. It wasn’t part of your schema. You didn’t have a way to organize the information. You don’t have a concept. So that teacher? It’s a great idea. Got you to develop concept knowledge. And then said, “Here’s a real label for it: What some other people called it when they had the chance to come up with their own names.”

Eric Cross (25:50):

Shout out to my teacher, who was—

Douglas Fisher (25:51):

Right.

Eric Cross (25:52):

It was learned then. It was a great practice. And the fact that you’re right, like, I just mean from my own personal experience, I agree that learning concepts versus complicated words. And it’s interesting that you said higher levels of forgetfulness, you know. And you often hear that complaint about it: “Students forget! Students forget!” But this complex topic and this complex word that’s new to me, and I have to remember both of those things.

Douglas Fisher (26:12):

That’s right.

Eric Cross (26:13):

And the other neat thing that it did, is it actually honored the background and like the founts of knowledge of all the different groups in the classroom. You just said something about “this group called it this and this group called it this,” and so by letting different groups share all of those names, now we’re starting to build these kind of interesting connections. That’s at least what I remember experiencing. And so this, even this practice of this approach is very layered, beyond just kind of generating new knowledge of things. So I appreciate that aspect of it. Now another area that you mentioned was complex text.

Douglas Fisher (26:41):

Yeah.

Eric Cross (26:42):

And how we can get students into complex text. So what can we do there?

Douglas Fisher (26:46):

I think science is an ideal place to get students reading things that are hard for them. And I do believe that some parts of school should be a struggle. Not all day, every day. But there should be doses of struggle, which are good for our brains. And these complex pieces of texts that don’t give up their meanings easily allow students to go back and reread the text and maybe mark the text and talk to peers about the text and answer questions with their groups. And the whole point of complex text is to say, “We persevere through it. We may not understand it fully on our first read. But we go back and we might underline, we might highlight. We might write some margin notes. Our teacher might say, ‘What did this author mean here?’ And we go back and look at that part and we take it apart. What do we think about that? And we talk to each other. It’s showing that when we read things, we work to understand. We work through our thinking, often in the presence of other people. And our understanding grows as we go into the text over and over and over again.” So I said geology earlier. There’s about a two-page article on “what is geology” that sixth graders often read. And some kids find it super boring. It’s a once-read, “OK, geology, I don’t really understand it. There’s a bunch of words in here that I don’t understand.” But if you go back to it a few times and you start taking apart, “What are the branches of geology? Oh, I’m gonna go reread that.” How are these two branches related to each other?” “What are the subtypes of each branch of geology?” “How do geologists do their work?” You start asking questions where students are going back into the text. You spend a little bit of time. Now, the introduction to geology, the students know so much more. So whatever you do next— video experiments, whatever—they have a frame of reference, because of that deep, complex read. It’s probably better than simply telling them, “Here’s the information.”

Eric Cross (28:45):

Right. And I even feel like as an educator, when I reflect on my own learning in the classroom, and then looking at it through the perspective of an educator <laugh>, you find this difference between how you were taught and then what the data says good teaching is.

Douglas Fisher (28:59):

Mm-hmm. <affirmative> mm-hmm. <affirmative>.

Eric Cross (29:00):

It’s so easy to slide back into how you were taught!

Douglas Fisher (29:02):

Yeah.

Eric Cross (29:02):

Even though, you know, you mentally assent to, “This is the best way. This is the data shows.” And you find yourself kind of sliding back at times.

Douglas Fisher (29:10):

Yep. And there’s good evidence to support what you just said, that most people teach the way they experienced school. And it is very hard to change that. And people have studied this. And it’s very hard to change that. Because it worked for us. And we have an n of 1, and it worked for us. Now, remember, there were a whole bunch of other kids in the class that it may not have worked for. And we chose to be in school the rest of our lives, and some of your peers did not choose to be in school the rest of their lives. In fact, some of them hated school and found no redeeming qualities of their experience. So just because it worked for us in a case of one, n of 1, doesn’t mean it worked for all of the kids, or even the majority of them.

Eric Cross (29:57):

Very well said. It’s that, what is that, the survivor bias? Survivorship bias? Where you were the one that made it. But you don’t think about all the other folks. ‘Cause we’re thinking about ourselves.

Douglas Fisher (30:05):

That’s right.

Eric Cross (30:06):

Great case for empathy too, is thinking about the people left and right. Because my friends are like, “I hated science.” And I say, “Who hurt you? Like, what did they do? It’s so amazing, so much fun!”

Douglas Fisher (30:16):

“What happened to you? Science is the coolest. Right? It’s so amazing!”

Eric Cross (30:21):

But I also had a unique experience in seventh grade with my teacher who did some of these things, and made it accessible for so many of us, in opening opportunities that I wouldn’t have had otherwise. But you’re absolutely right. That was my story. That wasn’t the story of everybody that was around me. And I think that’s really important. Now, I know this is also a big one for you, but I wanna talk about writing. What are the opportunities that you see in terms of writing specifically?

Douglas Fisher (30:51):

So would love it if science teachers had short and longer writing tasks in the science time. Of course, you can integrate some of the science writing, the longer ones, in the English language arts time, especially if you’re the elementary teacher and you can have control of the whole day. But I said this earlier; I’ll say it again. Writing is thinking. While you are writing, there’s nothing else you can do but think about what you are writing. Your brain cannot do something else. So if a science teacher wants to know, do their students really understand the concepts? Have them write. Now some of the shorter ones, I like something called “given word” or “generative sentences”: “I’m gonna give you a word: CELL. C-e-l-l. We’re in science. I want you to write the word ‘cell,’ c-e-l-l, in the third position of a sentence. So it’s gonna go word, word, cell, and then more words.” You could also say, “I want the sentence longer than seven words,” or whatever. But the key is, I’m telling you where I want the word. You will know instantly if your students have a sense of what the word “cell” means in the context of science. If they write “my cell phone,” they don’t get it. If they write about spreadsheet cells or jail cells or whatever, they didn’t get it. But if they talk to you about plant cells and animal cells and the components of those cells, and then once they have that sentence down, you can say to them, “Now write three or four more sentences that connect to that sentence.” It’s super simple. So whatever concepts you’re teaching, put ’em in a specific position. Now you don’t have to only put it in the third position. You can say the first position, the fifth position, the fourth position. But it forces them to think about what they know about the word and then how to construct a sentence for you. That’s a very simple way to get some writing from your students that helps you think about what they understand. Other kinds of writing, you can have quick writes, you can have exit-slip writes. There’s something in the research space called the muddiest part, where halfway through the lesson you have them write so far what has been the least understood or the most confusing part of this lesson. And they do a quick write, right there, at the muddiest part. And as a teacher, you flip through these and you start to say, “Oh, these are the points that are confusing to my students.” So if 80% of them all have the same thing, I gotta reteach that. If these five got, “This is the muddiest part,” If these five thought, “This is the muddiest part,” these seven, “I thought this was the muddiest part,” what do I need to do? Because it’s gonna be hard to move forward if this is their area of confusion. There are also all kinds of writing prompts that have a little bit longer. My favorite one is RAFT. What’s your Role? Who’s your Audience? What’s the Format? And what’s the Topic we’re writing about? Super flexible writing prompt. When you teach something, we don’t want students to only think they write to their teacher. So your role is an atom. You are writing to the other atoms. What do you wanna write about? What’s the topic? What’s the format of it? Is it a love letter? Is it a text message? Is it … so we, we mix it up with students in saying, how do they show some knowledge through a prompt that we give them? And then of course, longer pieces as they get older. More opinion pieces through fifth grade. More claims and arguments starting in sixth grade. So that they’re starting to see, “I have to use the evidence from things I’ve learned, read, listened to, watched, and construct something: an opinion, an argument where I back it up with reasons or evidence.” And those longer pieces, you know, less frequently. The shorter pieces, pretty regularly. So the teacher sees the thinking of the students.

Eric Cross (34:29):

When you were speaking about these really creative writing prompts, there were specific students coming into mind, that were coming into mind … they’re, they’re great science students, but they also have this really strong artsy side drawing, creative writing, and things like that. And when you said something about atoms talking to each other, it elicited, in my brain, certain students that would really love this aspect of creativity in the sciences. And it’s not how we’re typically trained as science teachers, to kind of incorporate this, like you said. A book of props. But I’m imagining, like, as a science teacher, if I took this, this would be a great way to reach more students to be able to show what they know, in a way that might resonate with their own intrinsic “Oh, I get to write creatively!” So I was kind of writing furiously as you were sharing all that information there.

Douglas Fisher (35:12):

So here, I’ll give you another example for elementary people. Again, with RAFT. There’s a book called Water Dance. It’s a pretty popular book for elementary teachers. It’s really about the life cycle of water. For example, you are a single drop of water. You are writing to the land. The format is a letter. And you’re explaining your journey. Now, if they can do this, they’re essentially explaining to you the cycle of water. But you got it in a way that people are now, “Oh, I’m a drop of water. So it’s me. My perspective. Where do I go from? Where do I start?” Because you can start anywhere in the cycle, right? My drop could have started in the clouds. My drop could have started in the ground. My drop could have started in the lake. But it has to show you the journey. So there are many ways of showing you the right answers.

Eric Cross (36:02):

And that’s using the RAFT protocol.

Douglas Fisher (36:04):

That’s RAFT: Role, Audience, Format, Topic. It’s been around 20 or 30 years.

Eric Cross (36:09):

You just gave the name to something a teacher shared in our podcast community, Science Connections: The Community, on Facebook. Teacher shared a Google slide deck and on it were just three slides. And the role that the student had to have is they had to show, then tell, the story of a journey of a piece of salmon being eaten, a piece of starch from pasta being eaten, and then an air molecule in a child’s bedroom. And they had to give the path of travel and the experience from the mouth and then breaking down into protein and all those kinds of things. And this teacher shared it and I wish I knew the teacher’s name because I wanna give ’em credit, but they shared it. And so I used it with my students and then had ’em read aloud their stories and dramatize it. And they were so into it!

Douglas Fisher (36:49):

So cool.

Eric Cross (36:50):

But through it, I was able to see that they understood different parts of the body. They understood cell respiration. The whole thing. And it was fun! To watch them get so into this creative writing. And now I know the name of it. That’s been 30 years they were using RAFT. So you just talked a bit about complex texts and writing. And before we go, I wanted to circle back to something that you said, because I think it’s important, and if you could elaborate on it a little bit, about the value of struggle. Can you talk more about that?

Douglas Fisher (37:21):

Sure. I do believe in a lot of the U.S. we’re in an anti-struggle era of education. And it predates Covid. I think it made it worse during Covid. We front load too much. We pre-teach too much. We reduce struggle. We quote, “over-differentiate” for students. And there’s value in struggle. The phrase, “productive struggle” — if you haven’t heard it, Google productive struggle — it’s an interesting concept, that we actually learn more when we engage in this productive struggle. Now, productive struggle originally came from the math world, and it was this idea that it’s worth struggling through things to learn from it, that you’re likely to get it wrong, and then there was productive success. And there are times when we want students to experience success and we make sure we put things in place for productive success. But there are times where we want them to struggle through a concept. ‘Cause it feels pretty amazing when you get on the other side, when you know you struggled and you get to the other side. If you think about the things, listeners, think about the things in your life where you struggled through it and you are most proud of what you accomplished. I want students to have that. I don’t wanna eliminate scaffolding, eliminate differentiation. But I do want some regular doses of struggle. So if you look at the scaffolding, we have a couple choices. We have front-end scaffolds, distributed scaffolds, and back-end scaffolds. Right now we mostly use front-end scaffolds: We pre-teach, we tell students words in advance, that kind of stuff. But what if we refrained from only using front-end scaffolds, and we use more distributed scaffolds, when they encounter. So there’s a difference between “just in case” and “just in time” support for students. So we tend to plan on the “in advance, here are all the things we’re gonna do to remove the struggle before students encounter the struggle.” What if instead we said, “Let them encounter some struggle. Here’s the supports we’re gonna provide. We’re gonna watch; we’re gonna remove those scaffolds, and allow them to have an experience of success, where they realize, ‘I did it. I got it.’” Every science teacher I’ve ever worked with, when they do an experiment or a lab or simulation, they are looking for productive struggle. They don’t tell the answers in advance. They don’t tell if the answers are right. That’s your data. What does your data tell you? I mean, this is what you do. But then the other part of your day when you move into, like, reading, you don’t do that. You fall into the trap of removing struggle. And so allow them to grapple with ideas. Allow them to wonder what words mean. Allow them to say, “I’m not getting this, teacher! It’s really frustrating!” And you say, “Yeah, this is really hard. This is why we’re doing it at school. ‘Cause it’s really hard. If it was easy, I’d have you do it at home. But we’re doing it here, ’cause it’s really hard and it’s OK not to get it at first.” And create a place where errors are seen as opportunities to learn, and struggling through ideas and clarifying your own thinking and arguing with other people to reach an agreement or reach a place where we agree to disagree is part of the power of learning.

Eric Cross (40:38):

There’s a teacher, who I took this from. My master teacher when I was student teaching. And she said that there’s no such thing as failure in science, just data. And I took that same mantra. And I resonate with what you said about how science teachers, all of us, hold onto that productive struggle, because it’s part of being a scientist. It’s part of the experiments. That genuine “aha” moment. Or it didn’t work out? That’s great! That’s totally fine! Let’s write about it and let’s take photos and let’s publish it and let’s be scientists. That’s totally true. As we wrap up, Dr. Fisher, is there any final message that you have to listeners about bringing science and literacy together? I know you speak everywhere, but for everyone that’s listening, if you can put out your encouragement or message or suggestion … you’ve given so many great tips and practical applications. But, any final thoughts on the subject?

Douglas Fisher (41:32):

I think many science teachers are intimidated because they think they have to be reading teachers. And there’s a knowledge base to reading. And some teachers are reading teachers and science teachers, and I don’t wanna dismiss that. But it’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work. And so as you think about the way in which you are learning and the ways in which you want your students to learn, what role does language play? What role does speaking, listening, reading, writing, viewing, play in your class? And then provide opportunities for students to do those five things each time you meet with them.

Eric Cross (42:12):

Dr. Fisher, thank you so much for being here and for your encouragement, and sharing your wisdom and experience. And then personally serving my city, here in San Diego, and my students, when they make it to your high school and ultimately the alma mater of San Diego State University.

Douglas Fisher (42:30):

That’s right.

Eric Cross (42:31):

Yeah. We really, really appreciate you in serving all kids and lifting the bar and making things more equitable for all students. And encouraging teachers. So thank you.

Douglas Fisher (42:39):

Thank you very much.

Eric Cross (42:42):

Thanks so much for listening to my conversation with Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Check out the show notes for links to some of Doug’s work, including the book he co-authored titled Reading and Writing in Science: Tools to Develop Disciplinary Literacy. Please remember to subscribe to Science Connections so that you can catch every episode in this exciting third season. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. Also, if you haven’t already, please be sure to join our Facebook group, Science Connections: The Community. Next time on the show, we’re going to continue exploring the happy marriage between science and literacy instruction.

Speaker  (43:26):

I had this moment of realization I felt a few months ago: I’m like, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that.

Eric Cross (43:39):

That’s next time on Science Connections. Thanks so much for listening.

Stay connected!

Join our community and get new episodes every other Wednesday!

We’ll also share new and exciting free resources for your classroom every month!

What Dr. Douglas Fisher says about science

“There are really cool opportunities when teachers come together and realize we can work together to improve the literacy and learning of all our students.”

– Dr. Doug Fisher

Professor and Chair of Educational Leadership, San Diego State University

Meet the guest

Douglas Fisher, Ph.D., is professor and chair of Educational Leadership at San Diego State University and a leader at Health Sciences High & Middle College having been an early intervention teacher and elementary school educator. He is the recipient of an International Reading Association William S. Grey citation of merit, an Exemplary Leader award from the Conference on English Leadership of NCTE, as well as a Christa McAuliffe award for excellence in teacher education. He has published numerous articles on reading and literacy, differentiated instruction, and curriculum design as well as books, such as The Restorative Practices PlaybookPLC+: Better Decisions and Greater Impact by DesignBuilding Equity, and Better Learning Through Structured Teaching.

A middle-aged man with short light brown hair and glasses, wearing a white shirt and dark blazer, in a circular frame with a green accent and simple graphic elements.
A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Promotional image for "Math Teacher Lounge" Season 3, Episode 4 titled "Ideas to Build Math Fluency," featuring Valerie Henry, Tracy J. Zager, and Graham Fletcher.

Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guests

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.

Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.

A collage of three headshots: an older woman with glasses, a man with a beard in a blue shirt, and a woman with dark hair smiling in front of greenery.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

NO PURCHASE NECESSARY. A PURCHASE DOES NOT INCREASE YOUR CHANCES OF WINNING. VOID WHERE RESTRICTED OR PROHIBITED BY LAW.

These Terms and Conditions (the “T&Cs”) apply to each sweepstakes offered by Amplify Education, Inc. (the “Sponsor”) on a webpage, email, or other document that links to these T&Cs (the “Entry Page”). For detailed rules for each sweepstakes, please review the sweepstakes rules on the Entry Page (such rules, the “Sweepstakes Rules”). These Terms and Conditions, together with the Sweepstakes Rules, will comprise the “Official Rules” for the sweepstakes.

To enter

Fill out the entry form on the Entry Page. Limit of one (1) entry per person using only one (1) email address for each drawing conducted during the sweepstakes period. Eligibility of individual entries will be at the sole discretion of the Sponsor, for any reason or for no reason, though specific reasons for disqualification may include use of inappropriate language. Entries generated by script, macro, mechanical or other automated means and entries by any means which subvert the entry process are void. Multiple entries received from any person in excess of the stated limitation will be void. Sponsor is not responsible for incomplete, lost, late, stolen, misdirected, damaged, illegible entries, for address changes of entrants, or for malfunctions of electronic or telephone equipment, computer hardware or software, failure of any entry to be received on account of technical problems or traffic congestion on the Internet, or any combination thereof, including any injury or damage to any entrant’s or any other person’s computer or other property related to or resulting from participation in the sweepstakes, or for other problems related to electronic entries. All entries become the property of Sponsor and will not be returned.

Eligibility

In addition to any eligibility restrictions contained in the Sweepstakes Rules, each sweepstakes is open only to individual legal residents of the states of the United States or the District of Columbia, except for residents of Rhode Island, who are at least 13 years of age or older as of the time of entry.

  • Minors – Parents and Guardians: An eligible person under the age of majority in such person’s jurisdiction must have his/her parent’s or legal guardian’s consent to enter this sweepstakes. The parent(s) or legal guardian(s) of an entrant under the legal age of majority in his/her jurisdiction of residence (a) will ensure that the entrant in respect of whom they agree to the Official Rules will comply with the Official Rules; and (b) warrants that he/she agrees to the Official Rules and gives the consents contained herein, including permission for his/her child/ward to participate in this sweepstakes. The parents(s) or legal guardian(s) of each such entrant agrees to indemnify the Released Parties (as defined below) for and against: (i) any claims made by the entrant, his or her legal guardian(s), or any member of his or her family against the Released Parties in connection with this sweepstakes; and (ii) any losses (including any liability) caused by any conduct of the entrant that is inconsistent with the Official Rules.
  • Teachers/School Personnel: By entering this sweepstakes, you represent and warrant that your participation in this sweepstakes complies with your school, institution, school board and school district policies. Any entry submitted in violation of such policies may result in disqualification. Verification: Amplify reserves the right to verify an individual’s eligibility, compliance with applicable policies in the case of teachers and school personnel and, if applicable, a parent’s or legal guardian’s consent to enter the sweepstakes by requesting proof of identity, compliance, or eligibility in the form acceptable to Amplify. Failure to provide such proof may result in disqualification, such that entrant will no longer be eligible to participate in the sweepstakes and will have no recourse or other opportunity to submit an entry.
  • Entrant: In the event of a dispute regarding any entry, the entry will be deemed made by the authorized account holder of the e-mail address submitted at the time of entry (i.e., the natural person who is assigned to an email address by an Internet access provider, online service provider or other organization responsible for assigning email addresses for the domain associated with the submitted e-mail address).
  • Ineligibility: Employees of Amplify, its advertising and promotion agencies, its contest administration agents, and each of Amplify’s and such agencies’ respective parent companies, subsidiaries and affiliates (all of the foregoing, the “Sweepstakes Entities”), and such employees’ immediate family and household members, are not eligible.

Drawing

Winners will be selected on the date(s) specified in the Sweepstakes Rules (the “Drawing Dates”). Each winner be selected in a random drawing, from all eligible entries received since the beginning of the sweepstakes period or the prior Drawing Date, as applicable. Winner does not need to be present to win. The drawing(s) will be conducted by Sponsor or its designee, the judge of the sweepstakes, whose decisions are final and binding on all matters relating to the sweepstakes. Winner will be required to sign and return an affidavit of eligibility/liability and publicity release, or the prize will be forfeited and an alternate winner selected.

Prize and odds of winning

The Prizes and number to be awarded are specified in the Sweepstakes Rules. Odds of winning depend on the number of eligible entries received. Prizes will be awarded. No prize substitutions, upgrades or cash equivalents, except at the sole discretion of the Sponsor if an advertised prize becomes unavailable. Prizes are non-transferable. All taxes, if any, associated with the prize are the winner’s sole responsibility.

General

By entering, entrants agree to: (1) release the Sponsor, its agents, and any platforms used to conduct the sweepstakes, such as Facebook, Twitter, or others (each, a “Platform” and together with Sponsor and its agents, the “Released Parties”), from all liability, injuries, loss and/or damage of any kind arising from their participation in the sweepstakes and the acceptance, possession and use/misuse of any prize; (2) to be bound by the Official Rules and the decisions of the judge; and (3) to be contacted by Sponsor by mail, telephone and/or email regarding the sweepstakes. The sweepstakes is in no way sponsored, endorsed or administered by, or associated with, any Platforms used to promote it. By accepting a prize, winner consents to the use of his/her name and likeness for advertising and promotional purposes without additional compensation in all media worldwide (except where prohibited by law). The sweepstakes is subject to all applicable federal, state and local laws and regulations. If for any reason the sweepstakes is not capable of running as planned, including due to an infection by computer virus, bugs, tampering, unauthorized intervention, fraud, technical failures, or any other causes which corrupt or affect the administration, security, fairness, integrity, or proper conduct of this sweepstakes, Sponsor and its agents reserve the right, at their sole discretion, to modify, suspend or terminate the sweepstakes, and select the winner from all eligible entries received prior to the termination and/or to disqualify any individual who is responsible or who tampers with the entry process. This sweepstakes is governed by the laws of the State of New York, with venue in New York County, New York, and all claims must be resolved in the state or federal courts in New York County, New York.

Removal for future mailings

To have your name and address removed from Sponsor’s future mailings, please select the unsubscribe link in any email you receive from Sponsor. Sponsor will process your request within 60 days.

Winner’s name

For the name of the winner, email mail@amplify.com or send a stamped, self-addressed envelope to be postmarked within 15 days and received within 30 days of the relevant Drawing Date to: Amplify, Marketing Department, Winner’s Name, 55 Washington Street, Suite 800, Brooklyn, NY 11201.

Sponsor

Amplify Education, Inc., 55 Washington Street, Suite 800, Brooklyn, New York 11201.

Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!