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Shifting to problem-based learning in K–5 math

Illustration of a sun, a clock, a die showing six, and a multiplication equation next to a green leafy plant on soil, all on a light yellow background—perfect for introducing fun math activities for kindergarten.

Math is all about getting the right answer. Right?

Wrong! Getting the correct answer matters, of course—accuracy is part of proficiency—but when math instruction focuses primarily on correctness, students can miss something essential: the opportunity to think deeply, share ideas, and make sense of problems for themselves.

Many K–5 math classrooms follow a familiar and well-established rhythm: The teacher demonstrates a strategy, students practice it, and the class moves on. This approach is widely used for good reason—it can feel clear, efficient, and reassuring. But over time, it can leave fewer opportunities for students to reason, deepen problem-solving skills, explore different approaches, and develop understanding that lasts.

This is where problem-based learning comes in.

What problem-based learning means in K–5 math

Problem-based learning places rich mathematical problems at the center of instruction. Instead of starting with a demonstrated method, students encounter a problem first, then draw on what they already know, try strategies, and make sense of the math through discussion and reflection.

As students tackle complex problems, they explain their thought processes, compare approaches, and revise ideas. The right answer still matters, but it emerges through critical thinking and sense-making, not just following steps. The result is learning that feels purposeful, engaging, and durable.

This approach reflects how math works beyond the classroom. People begin by understanding a situation, not by choosing a procedure. Problem-based learning helps students build that habit early.

Why shifting to problem-based learning matters

When student thinking stays private, happening only in heads or notebooks, it’s hard to assess understanding or guide learning in the moment. Problem-based learning brings thinking into the open.

As students share strategies, representations, and explanations, teachers gain insight into how they’re reasoning. Instruction can respond to real understanding rather than relying solely on correct or incorrect answers. And students benefit, too, by seeing that their ideas matter and math is something they can actively participate in.

Over time, this approach supports deeper understanding, stronger engagement, and lasting mathematical proficiency.

Three practices that support problem-based learning

Shifting to problem-based learning doesn’t require a complete overhaul all at once. A few core practices can help math teachers support the transition in K–5 classrooms.

  • Establish norms for learning math together. Productive problem-solving depends on a classroom culture where students feel comfortable sharing ideas, even when those ideas are unfinished. Norms that emphasize listening, explaining reasoning, and revising thinking help create a collaborative learning community.
  • Use tasks that invite curiosity and access. Effective problems allow all students to get started while still offering opportunities to extend thinking. Open prompts such as “What do you notice?” or “What do you wonder?” encourage students to connect prior knowledge to new situations and engage meaningfully with the math at hand.
  • Make learning goals explicit at the right moments. Problem-based learning includes purposeful instructional moments. Synthesizing student ideas near the end of a lesson helps students see how their thinking connects to the mathematical goal, bringing clarity without cutting short exploration.

Rethinking the teacher’s role

Problem-based learning also involves a shift in how teachers support instruction.

In classrooms grounded in problem-based learning, teachers guide learning by selecting meaningful problems, monitoring student thinking, and facilitating discussion. Strategic questioning helps students clarify ideas and make connections. Well-timed synthesis highlights important mathematical relationships and supports accurate understanding.

This approach allows teachers to focus less on delivering steps and more on supporting sense-making—while gaining clearer insight into where students are in their learning.

A gradual, supported shift

Shifting to problem-based learning is a process. Many classrooms begin by adjusting how lessons start, increasing opportunities for discussion, or rethinking how students share their thinking.

Over time, these changes add up. Instruction becomes more student-centered. Students engage more deeply. Fluency develops alongside understanding, and productive struggle becomes part of everyday learning.

When classrooms shift toward problem-based learning, math becomes more than getting the right answer. It becomes a way for students to reason, collaborate, and make sense of the world.

The power of productive struggle in K–5 math

A cartoon pizza cut into slices with a serving spatula in the center, flanked by colorful shapes and a cartoon animal on the right—an engaging way to spark curiosity about procedural fluency and fluency in math.

Struggling is not necessarily fun. It can be uncomfortable and frustrating. It can even feel like a great reason to give up.

But struggling and learning often go hand in hand. The key is for that struggle to be productive—for it to feel like something you worked through until you were successful, providing the confidence you need to tackle the next hard task.

That’s especially true—and essential—in math learning.

The key is productive struggle: the kind of effort that stretches students’ thinking without shutting them down. When designed intentionally, math activities for elementary students can challenge learners while still supporting confidence, curiosity, and persistence.

Here’s more about how productive struggle helps math students succeed.

What is productive struggle?

Productive struggle refers to students grappling with challenging problems that are not immediately solvable, but still within reach. It’s the space where students test ideas, make mistakes, revise strategies, and slowly build understanding.

Research shows that productive struggle helps learners move beyond surface-level memorization and toward deeper, more durable learning.

Rather than being told exactly what to do, students are encouraged to reason, explain, and persevere.

This doesn’t mean leaving students to flounder. Productive struggle requires clear goals, thoughtful scaffolds, and meaningful tasks so students know what they’re working toward and believe they can get there.

The role of growth mindset in math learning

Productive struggle is closely tied to another key idea: growth mindset.

A growth mindset is the belief that ability comes not from innate, baked-in talent, but through effort, strategies, and learning from mistakes. In the math classroom, this mindset helps students see challenges not as threats, but as opportunities.

When teachers communicate high expectations and normalize mistakes as part of learning, students are more willing to take risks. They begin to stop saying, “I can’t do this math problem,” and start saying, “I’m not there yet.”

This shift matters, especially in elementary grades. Students who develop a growth mindset early may be better equipped to avoid math anxiety and to handle increasingly complex math concepts, because they’ve learned that struggle is not a sign of failure, but part of the process.

Why struggle feels risky—and why it’s worth it

Supporting productive struggle can feel risky for teachers. Classrooms are busy. Time is limited. And no one wants students to feel frustrated or discouraged.

But avoiding struggle altogether creates its own problems. When math activities are too procedural or overly scaffolded, students may complete tasks without truly understanding them. Over time, students may come to believe that math is about following steps rather than making sense of ideas.

By contrast, well-designed struggle builds investment. Students engage more deeply when they’re asked to think, explain, and choose strategies. They develop problem-solving skills, perseverance, confidence, and a stronger sense of ownership over their learning.

What productive struggle looks like in practice

In classrooms that support productive struggle, students are actively involved, even when tasks are challenging. You might hear students explaining their reasoning, comparing strategies, or revising their thinking after a mistake.

Effective math activities for elementary students include:

  • Multiple entry points so all learners can begin.
  • Opportunities for students to explain why their strategy works.
  • Support for more than one correct approach.
  • Clear expectations paired with flexible pathways.

Even in kindergarten math activities, productive struggle for the youngest learners might look like counting, sorting, or representing numbers in different ways, paired with questions that prompt reasoning rather than quick answers.

Students need tasks that are mathematically meaningful, paired with structures that help them persist: opportunities to talk, visual representations, strategic questioning, and time to reflect.

In this way, struggle builds math muscle. Productive struggle helps students feel on top of their math game—and ready to learn more.

Why fluency matters in K–5 math education

An illustration showing a caterpillar, a hand matching shapes and colors on tiles, and another hand holding numbered cards—perfect for read-aloud math activities or exploring math in picture books with children.

If you’re fluent in Farsi, let’s say, you don’t search for every word or stop to translate every sentence in your head. You understand, process, and respond automatically, in real time.

Math fluency works the same way. This kind of fluency is something you can use naturally to understand what’s presented and respond to it meaningfully.

In K–5 math, fluency allows students to move beyond getting through the problem toward real mathematical thinking. Without it, even confident students can get stuck. With it, students gain access to deeper understanding, flexibility, and confidence.

What is math fluency?

Fluency in math is sometimes misunderstood as speed or memorization—but research and classroom experience tell a fuller story.

The National Council of Teachers of Mathematics defines procedural fluency as the ability to: “…apply procedures efficiently, flexibly, and accurately; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.”

In other words, the skills often referred to as computational fluency and math fact fluency tell only part of the story. Full mathematical fluency means knowing how and why strategies work, and being able to choose among them.

Memorization does have a role in math learning, but it alone does not lead to fluency. A student who has memorized facts but doesn’t understand relationships between numbers may still struggle when problems change slightly or require reasoning.

By contrast, a fluent student can adapt. They can explain their thinking, check whether an answer makes sense, and shift strategies when needed.

This is why fluency acts as a bridge between conceptual understanding and procedural application. It connects what students know to what they can do, and helps them do it with confidence.

Why procedural fluency matters in K–5 math

In the elementary grades, students are building the foundational math skills they’ll rely on for years to come. When procedural fluency is weak, students can feel overwhelmed by basic calculations, leaving little mental energy for problem-solving or new concepts.

Students without strong procedural fluency often feel stuck. For them, math can start to feel like an endless series of obstacles rather than a meaningful, engaging exploration—and that experience does not set anyone up to feel like a math person.

Fluency is what frees students up to focus on the heart of a problem. When they’re not bogged down by calculations, they’re able to reason, explore patterns, and tackle more complex tasks. Fluency opens doors—to higher-level math, to confidence, and to a more positive math identity.

In their paper, “Eight Unproductive Practices in Developing Fact Fluency,” Gina King and Jennifer Bay-Williams write: “Being fluent contributes to a productive disposition about mathematics, opens doors to a range of mathematics topics, and arms students with a skillset applicable to whatever they wish to pursue.”

What teaching math fluency looks like in the classroom

Effective K–5 math instruction treats fluency as something that develops over time, through meaningful practice, discussion, and reflection. Students need opportunities to explore number relationships, explain their thinking, and revisit strategies in different contexts.

In classrooms where math fluency is developing, instruction consistently supports flexible thinking, reflection, and revisiting ideas over time. You might see and hear the following:

  • Revisiting strategies across problems. Students are encouraged to solve the same problem in more than one way and to compare approaches. Classroom discussions focus on how strategies work and when one might be more efficient than another, helping students build strategic thinking and confidence.
  • Frequent, well-spaced opportunities for practice. Key facts and strategies reappear over time rather than being practiced once and set aside. This spacing helps students retain learning and apply it more accurately and efficiently when they encounter familiar ideas in new contexts.
  • Regular routines that emphasize reasoning. Short, consistent routines invite students to mentally compute, explain their thinking, and listen to others’ ideas. The focus is on understanding number relationships and reasoning through solutions rather than relying on memorized steps.
  • Thoughtful use of visual representations. Tools such as number lines, arrays, and other models help students see how numbers and operations relate. These representations support flexible thinking and make procedures more meaningful and accessible.

Across these experiences, fluency is something you can hear as well as see. Students explain their reasoning, reference strategies they’ve used before, and check whether their answers make sense, building accuracy, efficiency, and flexibility over time.

Math fluency helps students open their minds to the richness of math, and to their own power as math learners.

Introducing Amplify Classroom

Screenshot of the Amplify Classroom Discover page displaying subject filters, grade levels, a search bar, and a list of educational activities with descriptions and tags to support family engagement.

Feeling crunched for lesson-planning time? You’re not imagining it. A recent EdSurge report found that teachers get, on average, just 266 minutes of dedicated planning time a week—under an hour a day. And that’s before the meetings, paperwork, and “Got a minute?” queries start rolling in.

When teachers have so little space to craft high-quality interactive lessons, any tool that streamlines planning or teaching can make a huge difference.

Enter Amplify Classroom (formerly Desmos Classroom), launched for the 2025–26 school year and available for free! Already used by more than 300,000 teachers, this all-in-one platform brings together free resources for K–12 students; teacher guides and real-time teaching tools; and interactive lessons across math, literacy, and science—helping educators focus less on logistics and lesson plans and more on student engagement.

Interactive lessons that stick

Amplify Classroom’s free teaching resources go far beyond static worksheets or “entertaining” electronics. The platform’s library of more than 1,000 lessons features a wide range of free K–12 resources, including K–5 activities, middle school science explorations, and high school math challenges. Highlights include:

  • A grade 1 math activity called Leaping Lily Pads!, in which students help a purple frog hop toward a golden crown while making connections between subtracting 1 and subtracting 2—and practicing subtracting 2 and adding 2.
  • A grade 4 science activity called Food Chains, in which students create their own sequences of organisms, then line up those organisms to model how energy flows through an ecosystem, tracing that energy from start to finish.
  • Literacy practice that explores how the letter “y” sounds in words like myth.
  • Classic Desmos math challenges, like balancing raccoons on a seesaw against a 21-pound weight.
  • Hands-on Polypad manipulatives that let students experiment with tangrams, grids, and colorful geometric shapes.

These types of activities are not just engaging in the moment. They can also set the stage for lifelong math enjoyment. “I’ve been wary about making my kids not hate math,” says kindergarten teacher Martin Joyce. “No ‘drill-n-kill.’ [Now] they’re asking if they can do math on the computer before bed!”

What you can do with these free resources

Once you create a free teacher account, you can:

  • Teach more than 1,000 free interactive lessons across math, literacy, and science.
  • Customize any premade lesson or build your own with the drag-and-drop editor.
  • Monitor student thinking in real time with intuitive dashboards.
  • Share snapshots of student work—names optional—to prompt discussion and highlight ideas.
  • Control the pacing of lessons, pausing to dive deeper into a concept or syncing everyone to the same spot.

Here’s how it works in practice:

  1. Find a lesson. Browse by subject, grade level, or topic until you land on one that fits your plan for the day.
  2. Share it with your class. Assign the activity so students can join from their own devices.
  3. Teach and adapt in the moment. Use the dashboard to see student thinking in real time, highlight responses, and pace the lesson as you go.

Grade 5 teacher Traci Jackson saw how these K–5 activities boosted collaboration and learning in her class: “After an audible groan when the activity was paused, students made sense of ordered pairs through a purposeful Amplify Classroom experience. One student pair wrote without any prompting!”

More to explore

  • Explore Amplify Classroom, the free platform for grades K–12.
  • Learn how Amplify Classroom is supporting teachers across math, literacy, and science.
  • Find free professional learning resources for educators and free activities for students in our Problem-Based Learning Starter Pack.

How asset-based assessments can revolutionize math instruction

A student writes in a notebook at a desk with a laptop, as her awesome teacher stands beside her. Both appear engaged in conversation about her academic struggles during ELA class.

Many of today’s math classrooms are facing a perfect storm: declining scores, widening learning gaps, and growing pressure on teachers to deliver solutions. According to the National Assessment of Educational Progress, students are experiencing the steepest drop in math scores since 1990. EdWeek Research Center reports that a persistent gap between educational theory and day-to-day practice is putting added stress on teachers, often leaving them to navigate complex pedagogical demands without adequate support.

So how can we provide both students and teachers with the tools they need to succeed? How can math assessments and math intervention programs provide real help and drive student progress—without piling on more work?

One promising answer lies in rethinking how we assess what students know.

Rethinking the role of math assessments

Traditional assessments tend to focus on correctness alone. Did the student get it right or wrong? How many points did they earn?

But this binary approach misses a lot. A skipped question could mean a tech hiccup or a moment of confusion—not a lack of understanding. A wrong answer might come at the end of otherwise solid problem-solving.

An asset-based assessment approach shifts the focus from mistakes to meaning. It looks beyond outcomes to understanding how students think—their strategies, reasoning, and partial understandings. And when teachers can see that thinking, they gain far more useful data to guide instruction and inform their math intervention program.

This approach doesn’t lower expectations—it raises the quality of insight and gives struggling students (and really all students) a better shot at meeting standards with instruction that’s tailored to their actual needs.

Honoring students’ thinking and teachers’ time

Every student thinks differently. Asset-based assessments help reveal individual thinking, often through short-answer or open-response formats that ask students to explain how they solved a problem.

But this shift isn’t just for students. Teachers can benefit enormously when assessments are designed to surface trends in student thinking. If 30% of a class misinterprets the same concept, that result reveals a teaching opportunity. Rather than reteach an entire unit, teachers can adjust with focused, targeted support. That means less time spent diagnosing, and more time actually helping.

And when technology in the math classroom makes this data easy to collect, analyze, and act on, teachers get a level of consistent insight that is not only helpful, but actionable.

From student performance to student performance + thinking

The ultimate goal of asset-based assessments isn’t to replace performance data—it’s to enhance it. Knowing how a student got to an answer (or why they didn’t) can make all the difference in determining what to do next.

Here’s an example involving a division problem:

A wooden table with four chairs is shown. Text explains each table seats 4, the art class has 33 students, and asks how many tables are needed—an example of using technology in the math classroom to boost student engagement.

When real students were given this problem, they responded with answers like:

  • 33/4 = 8.25, round up to 9 so all kids can sit!
  • 33/4 = 8 with a remainder of 1. She needs 8 tables.
  • 8 x 4 = 32, but 9 x 4 = 36. I don’t know if we can leave one student sitting lonely on the floor, though.

Traditional grading might stop at “correct” or “incorrect” for these responses. But when students are asked to explain their thinking, teachers can uncover a range of reasoning—from successful multiplication strategies to misunderstandings about remainders.

These glimpses into student thinking aren’t just informative—they’re transformative. They can illuminate the performance of students in a deeper, more actionable way. They can help teachers take smarter next steps, and they can help students feel understood, capable, and more like “math people” every day.

More to explore

How problem-based learning can transform the math classroom

With test scores and student engagement on the decline, it’s clear that traditional teaching methods aren’t meeting the needs of all of today’s math learners.

One solution that’s gaining momentum is problem-based learning. By focusing on real-world problems and structured approaches, this approach develops critical thinking, reasoning, and application—skills that are essential for math success.

But making this shift isn’t easy. For math teachers and educators, it requires careful planning, a clear strategy, and community commitment.

That’s why we’re here to help.

The decline in test scores and engagement

The latest National Assessment of Educational Progress (NAEP) results show a sharp decline in math proficiency across grade levels. Only 26% of eighth graders performed at or above the NAEP Proficient level in 2022. These results represent the largest score declines in NAEP mathematics at grades 4 and 8 since initial assessments in 1990. The pandemic didn’t help, but it’s not the only factor.

This downward trend is compounded by a sense of disengagement. According to YouthTruth’s report Making Sense of Learning Math: Insights from the Student Experience, only half of students feel that what they’re learning in math connects to the real world. Recent survey data also shows that less than half of U.S. students feel that they “often” or “always” work on interesting problems in math class.

When math feels irrelevant or intimidating, students disengage—and the learning gaps that follow can be difficult to close.

An opportunity to grow

But the data also includes opportunities. According to NAEP research, more than 70% of students report that they enjoy activities that challenge their thinking and thinking about problems in new ways.

Problem-based learning helps give those students what they want.

And in a world that relies increasingly on data, analysis, and innovation, students need to learn not just how to follow steps and apply formulas, but how to think mathematically. In other words, problem-solving skills need to be part of student learning. This is particularly important in elementary and middle school math, where foundational concepts are built—and where students have the chance to forget their identities as “math people.”

That’s why working to infuse problem-based math learning into your district’s instruction can help reverse negative math and engagement trends.

What does problem-based learning in math look like?

Let’s go back and define this approach more fully. Research shows that math instruction is most effective when it encourages students—individually or grouped with peers—to grapple actively with math problems. When instruction gives students the opportunity and freedom to solve problems, rather than dictating solutions and then having them practice, students are more motivated.

For example, instead of memorizing the formula for calculating area and then practicing it in a series of disconnected problems, students might tackle a problem-solving challenge like:

How much paint is needed to cover our classroom walls?” Or they might work on a broader question such as: “How can we design a park, taking into account constraints like space, cost, and accessibility?

At its core, problem-based learning values mathematical thinking and reasoning. Rather than focusing on procedures and memorization, problem-based learning encourages students to:

  • Explore open-ended problems.
  • Ask questions and make connections.
  • Develop strategies to solve problems collaboratively.
  • Build curiosity and perseverance.
  • Reflect on their reasoning and process.

In the problem-based learning classroom, students are positioned as active participants in their math experiences, building a deeper understanding of concepts as they work through challenges. This is particularly critical for ensuring students don’t just learn math, but understand why it works and how to apply it. These approaches can transform math classrooms into spaces where students build both foundational and real-world math skills—and a healthy dose of math confidence, too.

Critical factors in making the shift

Integrating problem-based learning into traditional math teaching can feel like (and is!) a big change—in lesson-planning, mindset, and more.

To make it work for administrators, teachers, and students alike, schools do best when they focus on a few critical factors. These include:

  • Clear vision: Understand (and communicate) why the shift matters and what it looks like in action.
  • Leadership buy-in: Gain commitment from school leaders and administrators.
  • Teacher support: Offer professional development, resources, and ongoing guidance specific to math instruction.
  • Structured approaches: Establish a well-defined plan for implementing problem-based learning in math classrooms effectively.

What problem-based learning can look like in the classroom

While problem-based learning offers proven benefits, it can be difficult to integrate into the classroom without a clear structure. Teachers need tools and strategies to guide students through the process and ensure that learning goals are met.

A structured approach to problem-based learning in math should include:

  1. Defining the problem: Present a clear, engaging math challenge connected to real-world scenarios.
  2. Student inquiry: Encourage exploration, discussion, and different solution paths.
  3. Collaboration: Support teamwork to share ideas and reasoning.
  4. Reflection: Allow students to evaluate their process, solutions, and learning.

This structured approach not only improves students’ conceptual understanding, but also aligns with Amplify’s research findings, which show that students who engage in active learning outperform their peers in more traditional settings.

By embracing problem-based learning in math classrooms, educators can:

  • Boost student engagement and confidence.
  • Improve student problem-solving and mathematical reasoning skills.
  • Help reverse declines in math achievement over time.
  • Empower students to see the value and relevance of math in academics and in their lives.

Ready to learn more?

If you’re ready to explore how your school can make the shift to problem-based learning in math, our new change management ebook is the perfect place to start. It offers practical guidance, real-world examples, and a deeper look at the strategies highlighted above.

Download the ebook now to discover actionable insights and strategies to help make problem-based learning come alive in your math classrooms.

Learning mathematics through problem solving: Part 1

Productive struggle as a path to success

Many of us grew up with word problems as a part of math instruction, but we now know that students learn better when problems are more than just a part of learning. In fact, research shows that learning based on problem solving sets math students up for long-term success. 

Why problem-based learning matters 

What’s the problem with word problems? So-called “show-and-tell” pedagogies often rely on teachers demonstrating how to solve math problems, which doesn’t produce the kind of sticky learning that puts students on a path to long-term success. 

As a result, too few students are prepared for Algebra I. Even fewer go on to succeed in the high school math courses that are prerequisites for college and for careers that require quantitative skills.

Research published in Frank Lester’s 2003 book Research and Issues in Teaching Mathematics Through Problem Solving shows that instruction is more effective when the students themselves grapple actively with the math problems, working in groups or individually. This productive-struggle approach is often called problem-based learning. 

What problem-based learning looks like 

In a problem-based lesson, students are introduced to a handful of interesting and often real-world problems or tasks that can be understood and/or solved by referencing background knowledge, previously learned content, and newly provided information. 

These problems are designed to get students thinking about solutions they can then discuss with their peers. According to 2019 research conducted by Jack Dieckmann and Renae Skarin, this fosters both understanding of the content and math language development.

Over the course of the problem-based lesson, the teacher monitors student work, selects examples of that work to discuss with the class, and asks questions that propel the conversation and learning forward (as described by Margaret Schwan Smith and Mary Kay Stein in their 2011 book Five Practices for Orchestrating Productive Mathematics Discussions.

This synthesis incorporates students’ new insights and conceptions into their bigger-picture understanding of mathematics.

Problem-based math programs 

There are already high-quality curricula that call for this kind of pedagogy, but this approach can be hard to implement because it requires both a shift in practice for many teachers and more active engagement from students.

That’s why the highest-quality problem-based lessons embody all eight of the National Council of Teachers of Mathematics (NCTM) Teaching Practices. Amplify Math is one of them. 

Learning mathematics through problem solving: Part 2

Problem-based learning can put students on the path to math success. In this post, we’ll dig a little deeper into what it is, what it’s not, and teachers’ role in putting it into action. 

You can read the first post in this series here.

Tackling real-world questions

In our previous post, we established that a problem-based math curriculum sets math students up for long-term success. We showed that lessons in a problem-based learning model introduce students to interesting and often real-world problems or tasks that require them to draw on background knowledge, previously learned content, and/or new information. 

Problem-based learning vs. teaching as presenting

With traditional show-and-tell pedagogy, the teacher describes the procedures and formulas to answer problems and then gives students an opportunity to practice what they’ve been shown. This model is very common—most middle school and high school math teachers report using it as their primary mode of instruction.

With this approach, instruction is focused on getting answers through isolated skills and processes, so many students fail to develop the conceptual foundations required for the math to make sense. This often means students don’t know when a piece of knowledge is useful to a new, novel problem.

While teachers may be able to make a given lesson fun (for example, by turning it into a game), the math in the lesson is often uninspiring. Students may remember the game, but forget the math.

The limits of telling students how to do things

The occasional use of direct instruction is not always a bad option for teachers. Not all concepts and skills require substantial inquiry in order to stick or make sense.

But there are limits to deploying direct instruction as the primary mode of teaching. They include the following:

  1. For routine algorithmic problems such as calculating the sum of two multi-digit numbers, teaching has to involve a certain amount of telling—but just telling students how do something doesn’t set them up for success. Students remember algorithms better over the long term when those procedures are grounded in conceptual understanding. If students forget a procedure, conceptual understanding can help them recover it.
  2. Not every problem is routine or has an algorithm. Word problems are a big part of math, and word problems aren’t routine. No algorithm can make solving them a mechanical process. Instead, students have to comprehend the situation and create equations or models that reflect the relationships presented in the problem.
  3. In middle school math, algorithms become even less prevalent. As soon as rational numbers enter the scene, even a numerical calculation like -1(-1 – 1) has elements of strategy. 

Algebra often presents a student with choices, as when solving an equation like 3(x + 1) = 6. Will they begin by using the distributive property to rewrite the equation as 3x + 3 = 6? Or should they begin by dividing both sides of the original equation by 3 to obtain x + 1 = 2?

With problem-based pedagogy, choices about how to solve a word problem or which calculation strategy to pick can become learning moments. If some students do it one way while other students do it another way, both groups can learn by discussing how the two methods relate. 

How Amplify Math can help 

Amplify Math lessons help teachers cultivate and structure these student conversations. The program includes easy-to-follow instructional supports that make implementing a problem-based program more effective and enjoyable for both teachers and students. The lessons are designed to elicit creative thinking and get students collaborating. 

By working on problems that are intriguing, engaging, and relevant, students see how the math they are learning in class connects to their everyday lives. Students are placed into situations where they need to reason, collaborate, revise their thinking, and apply what they’ve learned.

Learning mathematics through problem solving: Part 3

A young girl solving a K-12 mathematics problem by pouring liquid into a container, surrounded by various lab equipment like a scale and measuring tape.

Tackling real-world questions as a path to math success

In previous posts, we’ve established that problem-based learning sets students up for long-term success. We’ve shown that problem-based lessons introduce students to interesting and often real-world problems or tasks, and described the key role teachers play in putting problem-based learning into action. 

In this post, we’ll look more closely at how teachers can support students engaging in problem-based learning, even when the students do much of their work together in groups. 

You can read the first post in this series here and the second post here. 

Teachers transfer learning responsibility to students

In a problem-based lesson, students are introduced to a handful of interesting and often real-world problems or tasks that can be worked out by referencing background knowledge, previously learned content, and newly provided information. 

With problem-based learning, teachers transfer the responsibility of the actual learning to students. Teachers set up the activities and lessons, then students are given the right information and scaffolds to make sense of math concepts and opportunities to practice and apply their learning. 

These problems are designed to get students thinking—and talking together—about solutions. This way, students begin to grapple with math content and grasp math language development.  

During class, the teacher’s role is to observe students, ask questions, select and share student work, and help students synthesize their learning at the end of the lesson. That’s where teachers help students apply new insights and conceptions to their bigger-picture understanding of the math at hand.

When students do need to be taught a process directly, teachers can shift from conceptual to procedural instruction. (For example, after making sense of adding signed rational numbers, students practice to gain fluency.) In these moments, the problem-based structure is focused more directly on producing answers and debugging procedures than on new sense-making.

Problem-based math teaching aligns with NCTM practices

The highest quality problem-based lessons embody all eight of the NCTM Teaching Practices. These are: 

  1. Establish mathematics goals to focus student learning.
  2. Implement tasks that promote reasoning and problem solving.
  1. Use and connect mathematical representations.
  2. Facilitate meaningful mathematical discourse.
  3. Pose purposeful questions.
  4. Build procedural fluency from conceptual understanding.
  5. Support productive struggle in learning mathematics.
  6. Elicit and use evidence of student thinking.

​​How Amplify Math can help teachers

We started with a world-class problem-based curriculum (Illustrative Mathematics’® IM K–12 Math™) and made changes to help educators implement engaging problem-based core curriculum for students. Amplify Math helps shift to planning and teaching problem-based lessons, tracking student progress, and differentiating instruction based on real-time data. We’ve made the math problems more exciting and relevant for all students, thus making it easier for all students to become active participants in their learning.

What does problem-based math learning unlock for students? Part 1

Webinar series recap, part 1 of 3

Problem-based math learning helps teachers set the stage for memorable learning experiences and transfer the responsibility for the learning to students, which has been shown to help develop students’ problem-solving and math reasoning skills.

Our webinar series explores how this type of instruction engages all students in grade-level math every day, and how instructors can go about implementing problem-based learning in the classroom. In part 1 of the webinar series, award-winning teacher Kristin Gray asks—and answers—the question: What does problem-based learning unlock for students?

Experience and explanation form a learning cycle

Imagine you’ve just gotten a new piece of technology: a phone, a TV, a computer. How do you learn to use it? Do you read the entire user guide first? Jump in and never touch the guide? Or turn it on and try some things, referencing the guide as needed? 

If the last option sounds like you, that’s very common—and it’s an example of learning through problem-solving. 

“It’s something we naturally do,” says Gray.  “We’ve had a phone before so we would pick up this new phone and try doing things that we know worked on our last phone, and then we would experiment: Does it work the same on this phone? This bouncing between experience and explanation is really the foundation of how we learn through problem-solving.”

What learning through problem-solving looks like in the math classroom

If we think of instructional methods in the math classroom along a spectrum, on one end we might have a classroom where students are left to solve a problem and discover the relevant math on their own. On the other end, the instructional method might be to show students how to get the answer and then practice doing similar problems. 

The methods at both extremes are challenging, and it’s hard for instructors to go from one to the other, says Gray. “We need to install a soft landing space in the middle of these extremes—and we can think of that space as learning through problem-solving, or problem-based learning.” 

What does that look like in the math classroom? 

Students will tackle interesting problems, raise questions about the math required, receive an explanation, and apply it back to the problem—as with the example of learning new technology. 

“When we show students how to get the answer, we send the message that math is solely about answer-getting and learning processes. Answers are important, but we want to use problems to teach the math, not just teach students to get the answer,” says Gray. 

Practice is also key, she adds: “This place in the middle pulls the best from both extremes and puts them into a structure that supports teachers in teaching and students in learning.”

Why students should learn through problem-solving

Learning through problem-solving has the potential to engage all learners in math, says Gray. It influences the way teachers and students think of themselves as mathematicians and what it means to know and do math. 

In the 2000 NAEP survey, 70 percent of fourth and eighth graders reported that they enjoy activities that challenge their thinking, and enjoy thinking about problems in new ways. 

“Students are already naturally curious and like solving challenges and trying things in new ways, so that’s a great start,” says Gray. 

“No matter how kindly, clearly, patiently, or slowly teachers explain, they cannot make students understand,” says Gray. “Understanding takes place in the student’s mind as they connect new information with previously developed ideas. Teachers can help, but understanding is a by-product of solving problems.” 

Add understanding is motivating. It inspires perseverance and confidence. It supports making connections, not learning concepts in isolation. 

When students are given a new problem and are able to use prior knowledge to help solve it, that “promotes the development of autonomous learners,” says Gray. 

How Amplify Math supports problem-based learning

Amplify Math supports teachers in the planning and delivery of problem-based lessons. It also enables teachers to monitor student progress and differentiate instruction based on real-time data. 

Lessons start with warm-ups that tap into prior knowledge and move into problems that require collaboration to solve. Teachers monitor, engage, and ultimately synthesize student work into the main idea. There are also ample opportunities for practice and reflection. 

Learn more about Amplify Desmos Math.

Register to watch the rest of the series here. 

Visit Gray’s site, Math Minds, here.

What does problem-based math learning unlock for students? Part 2

Webinar series recap, part 2 of 3

Our webinar series explores how problem-based learning engages all students in grade-level math every day, and how instructors can bring problem-based learning into their classrooms.

We reviewed part 1 of the series in this blog post. Now, in part 2, we dig deeper into this key aspect of problem-based learning: transferring responsibility for learning to the students.

So…now what? “If you watched Kristin Gray’s webinar,” says educator Kathleen Sheehy, “You may be thinking, ‘I learned so much about the power of problem-based learning. Where do I get started?’”

In this webinar, Sheehy joins fellow educator Ben Simon to explore how teachers can truly make that key shift toward student-centered instruction. “It is a journey. So we are going to talk about the small shifts that teachers and others can make that add up to something big,” Sheehy says.

The role of the teacher in student-centered learning

Most adults were not taught to do math this way as kids—and many teachers were not taught to teach math this way. When teachers have a lot of content to get across in limited time, it can feel risky to shift to a style that requires a bit of letting go.

“Student-centered instruction helps us embrace the idea that people can come at math ideas from different directions,” says Sheehy. “It’s collaborative and social. It focuses on problem-solving with an emphasis on multiple strategies and flexible thinking.”

Problem-based math learning may not be the sage-on-a-stage model, where the teacher stands up front and acts as the only math expert in the room—but it doesn’t mean the teacher relinquishes control, either. You can have both student-focused instruction and solid classroom management.

“It’s not a free-for-all. It’s very structured,” says Sheehy. “The teacher also plays a role in providing instruction and then guiding their students to the key takeaways they want for them.”

Building stakeholder investment

To be most effective, problem-based learning needs to be not only focused on the student but supported by the community as well. This means you aren’t the only one who needs to adjust to the new approach.

What actions can you take to build stakeholder investment? How can you get the principal, other teachers, parents, and kids (who are also accustomed to another style of learning) involved and excited?

Be able to articulate a really compelling reason why student-centered instruction is right for your students. The following are just a few research-backed examples:

  • It helps students develop deeper and longer-lasting mathematical understanding.
  • It helps students grow as problem-solvers, engaging them in productive struggle and collaboration and learning core life skills.
  • It helps students develop a growth mindset, which reduces math anxiety, boosts math confidence, and helps them relinquish the idea that someone either is or is not a math person.

When the teacher is the supporter of knowledge, not the gatekeeper, students lead the learning process and feel more confidence with and connection to math, says Sheehy.

How and where do you communicate these ideas? Sheehy and Dixon have found that providing a short hands-on math experience with problem-based learning examples can be very effective. This enables stakeholders to experience the difference themselves, especially when conducted in a low-stakes scenario like a parent math night or PD training.

Sheehy also suggests asking them what they think the impact of student-centered learning would have been for them when they were students. “We’ve heard people say things like, ‘I would have been way less anxious about math if I’d learned it this way,’” she says.

Making a plan to start the shift

“We’re not expecting to create a masterpiece overnight. It takes time to develop the teacher and student skills and to establish everything that needs to be in place,” Sheehy says, “You can’t get better at all the things all at once.”

Where to start? “Size up the shift,” she says, and make a plan.

“Using very clear look-fors can enable educators to decide where to focus,” says Sheehy. “‘What would I look for if I walked into a classroom that is beginning to engage in student-centered instruction?’”

Here are a few key elements to look for:

  1. Management of materials, routines, and classroom setup in a way that facilitates collaboration.
  2. Establishment of a classroom community (using norms charts, etc.) around the core idea that everybody belongs there and is a mathematician.
  3. A teachable structure that models the thinking process and creates predictability, allowing students to focus.

Sheehy and Dixon have found that a focus on these three areas helps teachers name what they are trying to improve in a systematic way.

“Once I tackle this first area and feel successful with that, I know what I’m going to tackle next, and after that,” says Sheehy. “These look-fors can help you make informed decisions that, little step by little step, can help you eventually get to where you want to be.”

How Amplify Math supports problem-based learning

Amplify Math is designed to support problem-based learning, so you’re making that shift every time you teach. The program specifically supports teachers in the planning and delivery of problem-based lessons, and enables them to monitor student progress and differentiate instruction based on real-time data.

Lessons start with warm-ups that tap into prior knowledge, then move into problems that require collaboration to solve. Teachers monitor, engage, and ultimately synthesize student work into the main idea. There are also ample opportunities for practice and reflection. 

Learn more about Amplify Desmos Math.

Register to watch the recording.

Subscribe to Math Teacher Lounge.

What does problem-based math learning unlock for students? Part 3

Webinar series recap, part 3 of 3

We hope you’ve enjoyed reading about—and watching—parts one and two of our three-part webinar series on student-centered learning. The earlier segments explored the thinking and framework behind student-centered instruction.

In this section—a sneak peek at a new lesson from Desmos Math 6–A1—we explore what it actually looks like in practice (and in a fish tank).

Read on for a look at how problem-based math instruction creates memorable learning experiences, and how you can find inspiration to do the same in your classrooms. (Impatient to find out? You can also just go straight to the full recording!)

Carlos’s fish: A different type of real-life problem

The idea for this lesson arose from the real-life experience of Desmos Classroom engineer Carlos Diaz, who found himself in possession of a “magic” toy aquarium. (For more of the entertaining backstory, watch the demo!)

The aquarium contained small fish that grow when you add water—by up to 400%, according to the package.

Takeaway 1: We are always surrounded with inspiration for student-driven math lessons, we just have to keep our eyes open.

Takeaway 2: Green did keep his eyes open, and they were drawn immediately to that 400%. He was skeptical—”At 400% larger, will they even fit?”—and then inspired. “We need to test this thing out,” he thought.

A stream of other questions came forth: Does the scale factor apply to lengths, volumes, something else? Would the growth be linear, or exponential? (Would Carlos ever have to clean the tank?)

The power of open-ended questions

We can’t tell you how large the fish grew (spoiler!) but we can tell you that they did (metaphorically) bust out of their tank and into a lively math lesson.

In the lesson, students look at the toy and are asked: What do you see? What do you notice? What do you wonder?

This type of question helps form the basis of student-centered learning. Here, students are not presented with a fixed set of variables and parameters and asked to solve strictly within them. Rather, they’re presented with a relevant or real-world problem and invited to reference background knowledge, previously learned content, new information, and even imagination.

Potential for exponential growth

From there, a teacher can guide students to make connections between a situation in context and the type of solution or equation that might be relevant. Students can explore collaboratively why one strategy might work better than another.

In this case, a teacher can help students determine that they’ll need to calculate exponential growth (mass), and support them in deciding the best way to do so. Then, having arrived thoughtfully at an approach, they can actually solve the problem and find an answer.

In other words, teachers leading student-driven learning transfer responsibility to those students. Teachers set up the lessons and activities and then provide just enough information and scaffolding to allow students to learn and reinforce math concepts, apply knowledge, and discover new approaches.

Let’s put it this way. Science has found that—contrary to popular belief—goldfish can remember things for not just weeks or months, but years. With student-focused learning, your students will, too.

Learn more.

Register for a free trial for access to this and other lessons. 

Learn more about Amplify Desmos Math. 

Watch the webinar.

Subscribe to Math Teacher Lounge.

Daily math routines that spark student curiosity

It’s the educator’s eternal question: How do I keep students engaged?

When designing daily math practice, teachers are always working to make real-world math problems fresh and relevant, find new entrance points for concepts, or simply come up with surprises. All of these approaches can be very effective.

And though it may seem counter-intuitive, so can routines.

The power of instructional routine

The word routine can connote a sense of doing something mechanically, even without thinking. But teachers know that well-placed classroom routines can open opportunities for creative thought.

Routines provide a way for you and your students to build and maintain a sense of familiarity and structure throughout the school year. They also free up time teachers would otherwise spend giving directions. When students know exactly how a certain activity should run, and understand all instructions and expectations, everything goes more smoothly.

That’s why a core set of shared routines can be a powerful, practical force for establishing an effective classroom learning community..

Bringing math routine into the classroom

We know routines can be effective in any classroom. Now, we also have research offering direct evidence that certain routines are particularly effective in math classrooms.

Think-pair-share

Do you want your students to have more time to think before solving and sharing about a problem? 

GOAL: Provides opportunities to identify, compare, and contrast multiple strategies

TIP: During partnered discussion, consider displaying sentence frames such as, “ First they… Next they…” “Their strategy was to…” or “I see a/an… in both strategies.”.

How to do it:

  • Invite students to solve a problem that can be solved with multiple strategies. Then, display two or more different responses representing different strategies.
  • Give students time to analyze the strategies on their own and then invite them to discuss them with a partner.
  • Facilitate a class discussion to describe, compare, contrast, and connect the different strategies. Utilize open-ended questions like, “Why did different strategies lead to the same outcome?” or, “What was helpful about each strategy?”

Where to learn more

We worked with our curriculum team to develop routine cards for math teachers, so you can implement routines that are part of our math program in your classroom. Most of the routines you’ll find throughout Amplify Desmos Math have been specifically proven effective in math classrooms. All of them have been adapted from established teaching practices.

We invite you to access a sample set of some of our most popular routines and decide which ones to try out in your classroom!

Resources

Download free math instructional routine cards.

Explore Desmos Classroom.

Learn more about Amplify Desmos Math.

Desmos Math 6–8 earns perfect scores from EdReports

It’s great news when a student who has worked hard to do their best gets a perfect score on an exacting test.

We’d like to take a brief moment to share some similar news of our own: Desmos Math 6–8 has earned perfect scores and an all-green rating from EdReports!

This is a powerful affirmation not only of our program, but also of every Desmos Math 6–8 student who benefits from the high-quality instructional materials, student-centered instruction, and thoughtful technology in the math classroom.

The power of math technology

Here’s a bit about the program. Based on Illustrative Mathematics’ IM 6–8 Math™ and Open Up Resources, Desmos Math 6–8 features interactive, standards-aligned lessons that are easy to use and fully customizable.

The program empowers teachers with an engaging curriculum that helps them:

  • Celebrate student brilliance.
  • Put student ideas at the center of instruction.
  • Drive student achievement every day.

The technology in the program is purposeful: students are empowered to explore new ideas, and our teacher dashboard helps teachers bridge those ideas together. Whether teachers are observing student learning on our lesson summary page or guiding productive discussions with our conversation toolkit, our facilitation tools make teaching more effective and more fun.

The rigorous EdReports review process

EdReports.org is an independent nonprofit designed to improve K–12 education. Among other things, its expert reviews help equip teachers with the highest-quality instructional materials.

Their review process is necessarily individualized and rigorous. Educator teams develop rubrics and evidence guides; recruit expert reviewers with a collective thousands of years of experience; then conduct rigorous, evidence-based reviews.

The reviews collect evidence about important characteristics of high-quality instructional materials. These include the presence of standards, how well they are sequenced, and how deeply they are included.

Reviews take 4–6 months. Ultimately, multiple educators will analyze every page of the materials, calibrate their findings, and reach a unified conclusion.

And in our case, it was this: Desmos Math 6–8 received perfect scores from EdReports and met expectations for every one of their gateways.

See for yourself

Request a free 30-day trial today!

IM 6–8 Math™ and Illustrative Mathematics® are trademarks of Illustrative Mathematics, which is not affiliated with Amplify. Amplify is not an IM Certified Partner. EdReports and associated marks and logos are trademarks of EdReports.org, Inc.

EdReports.org is an independent nonprofit designed to improve K–12 education. Among other things, its expert reviews help equip teachers with the highest-quality instructional materials.

The power of technology in the math classroom

You might say math and tech go hand in hand. And these days, of course, kids and tech go literally hand in hand. So it makes sense that using digital tools in the math classroom can help teachers reach students, and teach the math content they need to learn. But truly integrating technology into math instruction is not just a matter of adding random gadgets and gizmos. We need to do more—especially if we want to leverage the power of math technology to engage all students.

Why integrate technology into the math classroom

Integrating technology into instruction delivers numerous benefits in the classroom–perhaps especially in the math classroom.

Numerous studies suggest that technology can support student learning in the math classroom. This tech might take the form of graphic calculators, digital manipulatives, or learning software. In general, such tools have been shown to help students improve both their understanding of math concepts and their performance on tests.

Thoughtful tech has these effects in part because it can make math more engaging. Students are generally more excited to dive into a visually appealing and interactive program than a black-and-white math textbook.

Integrating technology into a math classroom also means:

  • Personalized learning: Students can work at their own pace and get tailored guidance and feedback.
  • Collaboration: Students can work together regardless of their physical location.
  • Real-world applications: Technology can simulate real-world scenarios that require mathematical reasoning and critical thinking skills.
  • Saving teachers time: Technology helps teachers assess learning more effectively, providing real-time feedback and helping them identify where students need support.
  • Preparing students for the future: After all, most jobs require the use of technology!

How to integrate technology into the math classroom

The most effective technology approaches in the math classroom are active, not passive. They also invite deep thinking and productive struggle rather than speed and rote memorization.

The National Council of Teachers of Mathematics (NCTM) includes this guidance in its Principles to Action:

“An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.”

The NCTM recommends that teachers: “incorporate mathematical tools and technology as an everyday part of the mathematics classroom, recognizing that students should experience ‘mathematical action technologies’ and physical or virtual manipulatives to explore important mathematics.”

Here are just a few approaches that enhance engagement:

  1. Use interactive whiteboards or projectors: You can display math problems and solutions, diagrams, graphs, and simulations, allowing students to interact with and manipulate visual representations of math concepts.
  2. Use graphing calculators and virtual manipulatives: They can help students visualize and solve complex math problems, and prepare them for more advanced mathematical concepts.
  3. Use gamification techniques: Can make math more engaging and fun for students.
  4. Use online collaboration tools: These tools can help students work together on math problems and projects, even when they are not in the same physical location.
  5. Use select social media and other online platforms: To create math communities where students can collaborate, share resources, and ask questions.
  6. Use math software and apps: These programs can help students practice math, solve problems, and visualize math concepts in 3D or interactive models.

How Desmos Math 6–A1 delivers

Desmos Math 6–A1 is just that kind of program. It provides dynamic and interactive digital math learning experiences, alongside flexible and creative print activities. Its teacher dashboard is designed to encourage classroom discussion and collaboration. It invites students to explore a variety of approaches—and invites teachers to celebrate and develop interesting thinking in their classrooms.

The dashboard also shows teachers actionable formative assessment data for each student and the entire class, and allows them to leave written feedback for students in their lessons.

And we know it works. Teachers and students in our pilot program said that students learned more with Desmos Math 6–A1 than with their prior program. (See case studies in a large midwestern school district and in Naugatuck Public Schools.)

What’s more, Desmos Math 6–8 has earned perfect scores and an all-green rating from EdReports. This is a powerful affirmation not only of our program, but also of high-quality instructional materials, student-centered instruction, and thoughtful technology in the math classroom.

Learn more

Start your 30-day free trial of Desmos Math 6–A1.

Pseudoscience examples for critical thinking skills

MIRACLE HAIR GROWTH! 

Quantum hair activation technology: This groundbreaking innovation goes beyond conventional science, delving into the realm of quantum energy to stimulate hair growth at the subatomic level. Blended with rare botanicals from ancient civilizations for luster and shine. Limited-time offer: Act now and receive a vial of stardust-infused hair serum!

Effective product…or pseudoscience? We’ll bet you guessed it. (Sorry, no stardust serum for you!)

While this hair product itself sounds like junk, reading about it can be a valuable experience for science students.

Teaching your students to identify pseudoscience in the world around them helps them learn to protect themselves from false claims that can be money-wasting at best, dangerous at worst.

And as they learn to discern, they also develop lifelong critical thinking skills!

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

—Melanie Trecek-King, biology professor and guest in Science Connections podcast Season 3, Episode 5: Thinking is power

Let’s explore how educators can use examples of pseudoscience to develop critical thinking skills—and incorporate NGSS (Next Generation Science Standards) science and engineering practices into their approach.

What’s the difference between science and pseudoscience?

Science is grounded in empirical evidence, rigorous testing, and the scientific method. Pseudoscience presents itself as scientific but lacks the fundamental elements of genuine scientific inquiry: evidence, peer review, and the capacity to generate accurate predictions.

Though pseudoscience may make vague claims, it has clear characteristics. When something is pseudoscience, it:

  1. Can’t be proven wrong: Makes claims that are unobservable or too vague.
  2. Professes “proof” without presenting actual evidence: Presents only anecdotal evidence, if any.
  3. Uses technobabble: See: “Quantum hair activation technology.”

For more characteristics of pseudoscience, check out Melanie Trecek-King’s episode of Science Connections!

To be sure, not all pseudoscience is harmful—pursuits and activities such as aromatherapy and astrology can be positive experiences in people’s lives—it just should not be defined as or considered science.

How addressing pseudoscience encourages critical thinking

When you teach students to identify pseudoscience, you are teaching them to use an evidence- and research-based approach when analyzing claims. Which is…science!

You are also:

  • Teaching them to engage in thoughtful and educational argument/debate.
  • Encouraging them to use their knowledge of science in the real world.
  • Creating real-world impact.

When students learn to identify pseudoscience—faulty products, myths, and disprovable “discoveries”—they’ll be prepared and informed when making real-world decisions.

Critical thinking exercises inspired by pseudoscience

We’ve talked about “miracle” hair growth treatments, which are more commonly targeted to adults. Students may have more commonly encountered claims about or ads for alkaline water or detox diets, conspiracy theories and instances of science denial, astrology, and more. These examples offer great opportunities to discuss how to determine the difference between science and pseudoscience.

Suggested activities:

  • Pseudoscience Sherlock: Ask students to find examples of pseudoscience in real life via social media, products sold in stores, or on the internet. Tell them to pay close attention to “articles” that are really ads.
  • Pseudoscience lab: Prompt students to back up their claim that a given example represents pseudoscience with evidence: e.g., lack of empirical evidence, controlled experiments, or unbiased sample; absence of peer-reviewed research; reliance on anecdotes; hyperbolic and unprovable claims.
  • Snake oil! Ask students to practice identifying pseudoscience by creating their own advertisements, commercials, or news segments for fake products or scientific “advancements.”
  • Spread the word: Ask students to create flyers, PSAs, or articles on how to identify the characteristics of pseudoscience.

Other activities that incorporate the NGSS while also sniffing out pseudoscience:

  • Asking questions: Encourage students to ask probing questions about pseudoscientific claims. How does this claim defy our current understanding of the natural world? What empirical evidence is missing?
  • Developing and using models: Have students create models that illustrate the differences between a pseudoscientific claim and a well-established scientific concept. This visual representation supports understanding and critical analysis.
  • Engaging in argument from evidence: Arrange debates where students argue for or against a pseudoscientific claim using evidence-based reasoning. This practice sharpens their ability to critically evaluate information.
  • Obtaining, evaluating, and communicating information: Ask students to research the history and impact of a specific pseudoscientific belief. Have them present their findings, highlighting how critical thinking could have prevented widespread acceptance of the claim.

Using examples of pseudoscience in your science classroom can help students learn to not only think like scientists, but navigate the real world, too.

Bertha Vasquez, former teacher and current director of education at the Center for Inquiry, has used these approaches with her students. As she shared on Season 3, Episode 6 of Science Connections: “I guarantee you that those students, when they walked into a store with their parents and they saw a product [with] a money-back guarantee [that] cures way too many things, and it’s based on ‘ancient plant wisdom’ and has ‘scientific’ language on the box, they may go, ‘Mom, I think these people are trying to sell you some pseudoscience.’”

More to explore

Boost student engagement with Science Seminars

What do you get when you cross a Socratic seminar with Curie, Watson, and Crick?

A Science Seminar.

Though Socratic seminars typically take place in ELA or social studies/humanities classrooms, we also know how strongly scientific and literacy approaches can support each other.

So let’s see what magic can happen when we bring a little Socrates into science!

More than just seminars on science

As you likely know, a Socratic seminar is a method of facilitated discussion that uses open-ended questions, active listening, and collaboration to encourage deep exploration of a text or topic.

Sound perfect for science? That’s because it is!

When a Socratic seminar becomes a Science Seminar, students focus on scientific evidence and work together to answer a question and come to the most convincing explanation of a phenomenon. Ideally, the teacher takes a supporting role, putting students and their ideas at the center of the discussion. In this way, Science Seminars form a powerful part of an NGSS-informed curriculum that teaches students to think, talk, evaluate, and collaborate like scientists.

The benefits of Science Seminars

Like Socratic seminars, Science Seminars:

  • Build critical thinking. They encourage participants to analyze and evaluate information critically, challenging assumptions and exploring multiple perspectives.
  • Provide practice in productive argument. Through structured dialogue, Science Seminars teach students to challenge each other respectfully and engage in constructive disagreements, supporting their ideas with reasoning and evidence.
  • Boost literacy skills. By actively participating in discussions, students practice active listening, oral communication, and analytical thinking—all serving to enrich their comprehension, vocabulary, and overall literacy skills.

And on top of all that, they also connect to key Next Generation Science Standards (NGSS) practices. Specifically:

  • Asking questions and defining problems.
  • Analyzing and interpreting data.
  • Constructing explanations and designing solutions.
  • Engaging in argument from evidence.
  • Obtaining, evaluating, and communicating information.

Tips for strong Science Seminars

Science Seminars are designed to be student-focused and student-led, but the teacher still plays an important role in setting students and seminars up for success. Here are some ways you can help them run smoothly and effectively:

  1. Set clear expectations. What’s the goal of the seminar? Make sure students know precisely what question they’re working to answer, and how they will know when they’ve answered it.
  2. Set ground rules. Before you start, help the students agree on how they will interact. Who has the floor? What words, phrases, and types of communication are helpful or not? What happens when students disagree?
  3. Involve all students. Plan in advance how more quiet students can take part. You might consider supplying conversational prompts to encourage participation.
  4. Take on a supporting role. Once you’ve set it all up, step back. If the conversation stalls, you might ask an open-ended question. You might also take notes—a reminder that the students are in charge and what they’re saying is important.

Free Science Seminar resource collection

We’ve created a free set of materials to help you host a successful Science Seminar. In this collection, you’ll get:

  • A helpful guide that dives deeper into how to get started.
  • Our top 10 Science Seminar tips for teachers.
  • Talk moves for grades K–1, 3–5, and 6–8.

Access your free Science Seminar resources here.

Even more to explore

Integrating AI in the science classroom

image of Science Connections podcast and host Eric Cross

How can you create new science lesson plans, adjust assessments, and design labs using only objects kids have at home?

Just ask—ChatGPT, that is.

In this recent Science Connections webinar, Science Connections podcast host Eric Cross tackles the topic of ChatGPT for teachers, along with other specific AI tools that (when used with your existing standards-aligned curriculum) can help make teaching more efficient, targeted, and interactive.

AI for science can save teachers time, deepen student engagement, and inspire collaboration and creativity all around, says Science Connections podcast host Eric Cross.

Eric describes some of the many ways science teachers can use AI in the classroom—as both shortcut and partner. “We can use it for personalized learning,” he begins. “We can generate questions and give instant feedback. We can differentiate. We can support our students with special learning needs. And that’s just a start. The more you use it to collaborate with other educators, the more fun it becomes.”

Generative artificial intelligence 101

There are a lot of AI tools out there, but the new one is generative AI. As Eric explains, the difference is that generative AI—unlike, say, AI that gives you driving directions—creates something that didn’t exist before: text, images, music, and, yes, new science experiences for the classroom.

As with any technology, the practically infinite uses and applications of AI raise important questions about accuracy, equity, biases, and more. In this webinar, though, we focus only on AI’s practical uses for science teachers.

Generative AI relies on and responds to prompts.

You’re telling it to do something and it communicates back to you in human language. The way you craft your prompts determines your output, so the better your prompt is, the better your output.

– Eric Cross
Host, Science Connections; Adjunct Professor of Learning and Technology, University of San Diego

Let’s see what AI has produced for Eric as a science educator, and the kind of prompts he’s used to get there.

How science teachers can use AI to prepare and engage

Teachers can use generative AI to create personalized learning materials, generate more practice questions, and explain topics at any level and depth.

In this webinar, Eric focuses on the AI tools that have given him the most mileage as an educator and that he thinks can provide the most value for others.

These include:

  1. Modifying assessments when students have used all the ones that a curriculum provides. A sample prompt: “You are a science teacher creating an assessment for middle school students. I will upload an assessment. Please recreate it in a similar tone and voice as the original with a similar level of rigor.” Response: Brand-new multiple-choice and written questions on the same topics, all adhering to the same NGSS. With a little more back and forth, Eric will have the exact number, style, and focus of questions that he needs—along with an answer key.
  2. Creating relevant, accessible lab ideas. Eric prompts AI for lab and hands-on project ideas to fit exact specs: topic, grade level, desired outcome, and objects found in a typical classroom or home. Result: Hands-on activity ideas students can do at home, like exploring lung capacity with a balloon and a ruler (delivered by AI complete with full supply lists, instructions, and more).
  3. Helping students connect. To support a student who’s stuck, you might prompt the AI by saying: “I’m a fifth grader and my teacher is talking about claim evidence reasoning and I don’t really understand it. Can you explain it to me in a way that would help me? And then: “Now can you help me explain it to my mom, but in Spanish?”

Eric also uses AI to interpret graphs, collate student data, build graphic organizers, create science games, and more.

Is everything AI provides him flawless and 100% accurate? No, says Eric. “You have to vet, and it helps to have a high-quality curriculum already in place. But it gets me 80 to 90% there—and that’s pretty good.”

More to explore

10 ideas for summer math professional learning

How many servings of coleslaw do you need for the picnic? What, on average, is the coolest time of the day? Exactly how likely is a lightning strike?

Math doesn’t stop when summer starts. This season is ripe with opportunities for challenging and stretching your math brain. It’s also the perfect time for math teachers to dive into professional learning without the time constraints of the classroom. Our recommendation? Kickstart your summer learning and set yourself up for even greater success in the new school year with our free professional development opportunities for math educators!

Check out our curated list of on-demand professional development and resources. Whether you’re seeking ways to incorporate more problem-based learning methods, wanting to learn more about implementing an instructional approach, or simply looking for fresh activities to bring to the math classroom, you’ll find a variety of options here that will fit any agenda and schedule.

Best practices and inspiration for math fluency, student agency, and more

Addressing math anxiety

Collaboration in class

More math resources

Still more to explore (as you head into fall, too) 

Problem-based learning in Amplify Desmos Math

This program brings problem-based learning into the math classroom, with an approach proven to help students develop math reasoning and problem-solving skills—not to mention deep understanding, fluency, and comfort with all things math. 

Let’s take a closer look at problem-based learning in math, and at the contours of this exciting curriculum. 

How problem-based learning helps math students—and math teachers

When you learned math, you likely started out learning arithmetic then moved on to solving word problems. You might have learned formulas, then practiced using them to determine the volume of a prism or which train will arrive at what time. 

But life works differently. Sometimes we tackle the problem first, not the formula. When you get a new piece of technology—a phone, a TV, a computer—you might read the user guide, or you might just turn it on and try some things. 

If that second style sounds like you, that’s common—and it’s an example of learning through problem-solving. 

“It’s something we naturally do,” says Kristin Gray, executive director of Amplify’s math suite.  “We’ve had a phone before, so we would pick up this new phone and try doing things that we know worked before, and then we would experiment. Does it work the same on this phone? This bouncing between experience and explanation is the foundation of how we learn through problem-solving.”

What does that look like in the math classroom? 

Students tackling interesting problems, raising questions about the math required, receiving an explanation, and applying it back to the problem—just as in the example of new technology. 

“When we show students how to get the answer, we send the message that math is solely about answer-getting and learning processes. Answers are important, but we want to use problems to teach the math, not just teach students to get the answer,” says Gray. 

Learning through problem-solving can also engage more learners in math, says Gray. By influencing the way students (and teachers) think about what it means to know and do math, problem-based learning has the potential to shift the way they think of themselves as mathematicians.

“Students are naturally curious and like solving challenges and trying things in new ways, so that’s a great start,” says Gray. 

And understanding is motivating. It inspires perseverance and confidence. It supports making connections, not learning concepts in isolation. 

When students are given a new problem and are able to use prior knowledge to help solve it, that “promotes the development of autonomous learners,” says Gray. 

Supporting the brilliance of student thinking 

Our program combines interactive problem-based lessons with explicit instruction, reinforcement, and practice. Lessons build a strong foundation in procedural and fact fluency, deepen understanding of concepts, and enable students to apply learning to real-world tasks.

To learn more about how and why it all came together, watch the following video featuring Amplify Director of Project Management Christina Lee, Amplify Math advisor and Desmos user Fawn Nguyen, and Desmos Director of Research Dan Meyer.

Christina: Hi, I’m Christina, the product manager at Amplify working on our K–12 math program. As you may have heard by now, Desmos Classroom is joining Amplify. This includes all of teacher.desmos.com, including all of the free activities, the free activity builder, and the Desmos math curriculum. I have Fawn Nguyen and Dan Meyer here to answer a few questions about what’s going on. Thank you both for joining! 

The first question is to you, Dan. One thing every Desmos user is going to want to know is, will the Desmos calculators and activities on teacher.desmos.com stay free to use forever?

Dan: Yes, period. It’s an important question and an easy one to answer. Our commitment to users, from day one, has been [to] whatever you can use for free. Now we’re not going to make you pay for that. We know how hard it is as a teacher to build your practice on top of software that could disappear, and Amplify shares that commitment in a rock-solid way.

Christina: That’s great to hear! Fawn, can you tell us a little bit about what you love about teacher.desmos.com? Why should a teacher who’s never used [it] check it out?

Fawn: How do I love teacher teacher.desmos.com? Let me count the ways! There’s nothing like it out there that allows teachers to build lessons from scratch. What makes it unique? Well, there are lots of things that are unique about Desmos, but the screen-by-screen build is a standout for me. It allows me to interact with students prior to moving to the next screen. More importantly, the interaction among the students and the teacher dashboard is just brilliant. It lets me see the students’ responses, especially the graphical ones, in real time. I feel like it’s a built-in formative assessment [in] the lesson. And not surprisingly, the structures from the five math practices by Peg Smith are built-in there with the selecting, sequencing, and connecting.

Christina: Dan, why does it make sense for Amplify and Desmos to build one core math program for grades 6–12?

Dan: We’ve been traveling on separate parallel paths for a really long time and it makes a lot of sense for us to go farther together. For instance, we’ve both been building a core curriculum based on the Illustrative Mathematics curriculum. We have both been doing that using core Desmos technology. We both share an understanding of the complexity of teaching, the brilliance of student thinking, and so it makes sense for us to merge together. Desmos brings to the table a deep understanding of how technology can support student learning, and Amplify brings to the table an understanding of how systems support students at scale. So we bring a lot of commonalities and a lot of elements that both of us need from the other.

Image showing an educational digital platform called Amplify Math in collaboration with Desmos Classroom. The interface includes various features such as textbooks, problem-based learning activities, interactive graphs, and practice exercises.

Christina: Fawn, you’ve been an advisor on the Amplify Math curriculum focused on problem-solving. In what ways do you think this knitting together of the two programs will help make teaching through problem-solving easier for teachers?

Fawn: I actually knit, Christina! So I really like your description of the partnership as knitting together the two programs. It’s like taking two luxurious fibers, if I may say––ironically, luxurious but free, which describes literally nothing except Desmos––and weaving them together to create a gorgeous and functional design. I’m thinking about a sweater vest for Dan, he would look great in it! Amplify truly understands what problem-solving is, that it’s non-routine. And Amplify’s math curriculum has many great activities. However, when this task can only live on a printed page it’s hard for it to stay as a problem-solving task. What I mean is that it’s hard for students to unsee things. So when it’s on paper, you have to show all the cards and that ruins everything to me, frankly. But with Desmos again, with that screen-by-screen build and the pause and pace functions, they are designed so that the timing of teacher moves can happen. I think the timing is really important. And then problem-solving is about tinkering with ideas and testing conjectures, and Desmos is built for such. It invites you to play, it invites you to take risks, and it doesn’t shame you when you make a mistake. So ultimately, Desmos brings school mathematics, which Amplify writes, closer to what doing mathematics looks like.

Christina: Dan, one final question for you. What’s going to happen to the Desmos calculators now?

Dan: The Desmos calculators, like all the other technology as part of this deal, will remain free into perpetuity. They’ll get spun over into a new corporation, a public benefit corporation called Desmos Studio, where they’ll have a lot more focus from the people who work on it and a lot more resources to expand and develop and do that work.

Christina: Thank you, Dan. Thank you, Fawn. Thank you both. I’m really excited about this opportunity we have to build something special for teachers and students! For more information about Amplify Math and Desmos Classroom, and everything else we’ve got going on, please visit amplify.com/futureofmath.

From math lesson planning to long-term success

Amplify Desmos Math makes it easy for both teachers and students to make the shift to a problem-based approach by providing captivating activities, powerful teacher-facilitation tools, and lots of support for differentiation and practice.

Lessons start with warm-ups that tap into prior knowledge and move into problems that require collaboration to solve. Teachers monitor, engage, and ultimately synthesize student work into the main idea. There are also ample opportunities for practice and reflection. 

Amplify Desmos Math will be available for 2025–26 school year implementation. Interested districts can pilot the beta release starting fall 2024.

Learn more about Amplify Desmos Math.

5 strategies to transform your math classroom

Want to shift your math teaching practices this year, but not sure where to start? That’s a good problem to have! 

You can boost your instruction this fall with problem-based learning, technology in the math classroom, and more—all in ways that put students at the center. 

“All students need the opportunity to feel like they can figure out mathematics,” says Jennifer Bay-Williams, Ph.D., an author and professor of mathematics education at University of Louisville. “That’s where they develop a math identity, [the idea] that they can do math. And they start feeling like, ‘I can figure this out.’” 

Bay-Williams spoke at our 2024 Math Symposium, along with other thought leaders and expert educators. Keep reading to see how their key takeaways can help you shift your math instruction this school year!

Center student ideas in a collaborative math classroom

Amplify Math Suite Executive Director Kristin Gray had great tips for teachers looking to center student ideas in the classroom. Simply put, it’s all about helping them make several types of connections. These can include any of the following: 

  • Connecting students’ classroom math experiences to real life
  • Connecting math ideas to one another
  • Connecting their ideas to the ideas of their classmates 

How do teachers foster these important connections? That’s where problem-based lessons come in. Rather than teaching a concept or formula in isolation, then having students practice it, try inviting students to collaborate on a real-life problem that will lead them to that math idea. (For example, you might ask them to work on designing a small traffic or subway system that requires developing ideas about distance, rate, and time.)

As a result, students build problem-solving skills collaboratively, feel their ideas are valued, develop their own ways to make math make sense, and learn from and with each other. Teachers also get to know and appreciate the different backgrounds and styles students bring to the classroom, opening up new opportunities for engagement—and connection. 

Reimagine student engagement

No matter how engaging you are as a teacher, it’s typically students who drive engagement—and that’s actually good news. You don’t have to reinvent the wheel or do somersaults to get their attention. In fact, a lot of engagement comes from creating routine and familiar opportunities for connection. And it can also come from allowing students to make mistakes. 

“We want all students to have an entry point into [math] tasks,” notes Amplify STEM Product Specialist James Oliver. “Those students that seem to always feel like they don’t fit or don’t have the identity in that math classroom, we want them to immediately have successes and have their curiosities tested.” Successes—and productive failures. “What we’ve learned is, you are not firing any synapses, nothing’s happening if you’re just getting it immediately correct.”

Nurture student curiosity

Which is better: letting students dive into a box of LEGO pieces to see what happens, or providing a step-by-step guide to building the airplane? 

It’s actually a tie. In both structured and loose approaches, the key is to spark curiosity and communication. “If we want them to be mathematicians, we should let them talk about math,” says Amplify Director of 6–12 Core Math Curriculum Kurt Salisbury, Ph.D. Here’s his 3D approach:

DISCOVER
Discovering the relationships among mathematical ideas is a key part of mathematical thinking. 

DESCRIBE
Students communicate their mathematical thinking by describing the processes, procedures, or relationships needed to work with a concept or pattern. 

DEVELOP
When students develop a strategy they can apply to a variety of contexts, their math thinking gets validation and purpose.  

So whether you lean into a more structured approach or prefer to let kids figure the LEGOS out themselves, small mindset changes like these can create more space for your students to discover, describe, and develop as mathematicians.

Make math fluency fun 

As with someone fluent in a language, someone fluent in math is able to think and calculate mathematically without struggle or effort—that is, with fluidity. 

In order to think and calculate fluently, students need to build a toolbox of strategies—and games are a great way to do that. 

While you’re making the learning fun, students are absorbing tools they’ll use throughout their lives. “When we ensure that every student has access to a range of strategies, and has regular opportunities to choose among those strategies, that’s what games do for us.” says Bay-Williams.

Elevate student voices 

When student thinking isn’t explicitly invited into the classroom, students may begin to narrow their focus, providing merely what they think their teacher wants to hear. But given genuine invitations to share, students are more likely to follow their thought process wherever it leads them, taking a more organic approach to problem-solving.

“Taking a step back as a teacher, and inviting students to take a step forward, [activates] students getting started with finding the answer,” says Stephanie Blair, vice president of Desmos Coaching. “And all of them might take a different step forward, which is okay.”

It’s time for math that does more for students

“All students need the opportunity to feel like they can figure out mathematics,” says Bay-Williams. We need to connect with our students, nurture their curiosity and comfort with math, and welcome their unique ways of thinking.

We hope the thought leaders and speakers from our Math Symposium have inspired you to do just that!

Meet Amplify Desmos Math

Meet Amplify Desmos Math, a new, curiosity-driven K–12 math program that builds students’ lifelong math proficiency. Lessons in Amplify Desmos Math are standards-aligned, easy to use, and fully customizable by educators. And every Amplify Desmos Math lesson includes suggestions for differentiation that support, strengthen, and stretch student understanding.

“Engagement is a real challenge in math classrooms,” said Jason Zimba, Amplify Chief Academic Officer of STEM. “Knowing this, we created a program with interesting problems that students are eager to solve, one that keeps them engaged and learning. Amplify Desmos Math achieves rigor and delight, motivating all students to explore new horizons and develop new understanding.”

We believe that math class is a place where teachers can elicit, celebrate, and build on their students’ interesting ideas. Those ideas fuel meaningful classroom conversations and drive the learning process. Read on to learn more.

Meet Amplify Desmos Math. This is math that motivates.

A structured approach to problem-based learning

The program combines the best problem-based lessons with tightly aligned personalized practice, assessments, and intervention, creating an integrated experience for teachers and students. Data informs instruction. Comprehensive student profiles provide full data on students’ assets and skills, empowering teachers to provide just-in-time scaffolds and targeted intervention when needed.

Amplify Desmos Math is a powerful suite of math resources that includes:

  • Core instruction: Amplify Desmos Math lessons provide a structured approach to problem-based learning, where each lesson builds on students’ curiosity using a Proficiency Progression™ to develop lasting grade-level understanding for all students.
  • Screening and progress monitoring: mCLASS® assessments and daily formative checks measure what students know and how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core instruction and intervention resources.
  • Integrated personalized learning: Personalized Learning activities help students access grade-level math through engaging, independent digital practice. The program’s signature Responsive Feedback™ adjusts to students’ work, providing item-level adaptivity to further support their learning.
  • Embedded intervention: Integrated resources like Mini-Lessons and math fluency games provide targeted intervention on specific concepts or skills connected to the daily lesson. Extensions are also available to stretch students’ understanding.

Amplify Desmos Math expands on the Desmos Math 6–8 curriculum, which is featured in a recent efficacy study led by WestEd that demonstrates increased math achievement across more than 900 schools in nine states.

Delightful digital activities and tools

To complement robust printed materials, Amplify Desmos Math leverages a digital platform that enables educators and students to connect with one another as they work through lessons, engage in personalized learning, and check for understanding. The interactive platform and facilitation tools foster mathematical discussions and allow educators to see student thinking in real time.

“Right now, teachers have to jump between platforms to access meaningful data, understand it, and use it,” said Alexandra Walsh, Amplify Chief Product Officer. “By combining instruction, assessment, and differentiation on the same digital platform, we’ve made student data more accessible, so educators can spend less time toggling and more time responding to student needs.”

Amplify Desmos Math is available:

  • Kindergarten–Algebra 1
    • As a beta release for the 2024-2025 school year, for pilot implementations and early adoptions
    • As a commercial release for the 2025-2026 school year
  • Geometry, Algebra 2, Integrated 1, Accelerated Grades 6 and 7
    • As a beta release for the 2025-2026 school year
    • As a commercial release for the 2026-2027 school year
  • Integrated 2 and 3
    • As a commercial release for the 2026-2027 school year

Try a free lesson.

Hundreds of free math lessons and activities from Amplify Desmos Math are available on Desmos Classroom, a free teaching and learning platform that places student engagement at the center of instruction. Desmos Classroom features free lessons, lesson-building tools, sharing features, and more. Built by math educators, the platform makes leaning into good pedagogy easier for teachers—which makes the lesson a more interactive experience for students.

You can teach these free lessons, but also customize them, or even build your own from scratch. Visit teacher.desmos.com to create a free account.

Learn more!