Defining math fluency with Jason Zimba

Math is sometimes described as a language, with its own syntax, symbols, and power to explain. That’s why it’s possible—actually, necessary—to develop fluency in math. Here’s what that means, and what it looks like in the classroom.

By Amplify Staff | October 16, 2023


When we think of fluency, especially as a goal, we might think of speaking or reading a language. But fluency is also a goal in learning math! So what is math fluency? And what does it look like in the math classroom? In Season 6, Episode 1 of our Math Teacher Lounge podcast, Amplify’s own Jason Zimba helps us understand—using some analogies to baseball and chicken, of course.

Definitions of math fluency

We can develop fluency in many things, from coding to cooking. On the Math Teacher Lounge podcast, Amplify Chief Academic Officer of STEM Jason Zimba recounted becoming fluent in…roast chicken. 

Jason describes practicing one particular recipe until it was perfect. For Jason, that meant not just that the outcome was flawless or delicious, but that he was eventually able to make it from memory, without thinking—and to naturally adjust and calculate for variables like a smaller or larger chicken, or an unfamiliar oven. 

Math fluency works the same way. Practice brings effortlessness—freeing up time and mind space for new opportunities. 

The word “fluency” comes from the Latin fluentia, which means “flowing.” When applied to math, it means ”skill in carrying out procedures flexibly, accurately, efficiently, and appropriately,” says podcast host and math teacher and advocate Dan Meyer. As with someone fluent in a language (or a recipe), someone fluent in math is able to think and calculate mathematically without struggle or effort—that is, with fluidity. 

Podcast host and elementary educator Bethany Lockhart Johnson adds this informal description: “It’s that thing you don’t even think about anymore. ‘Cause it’s in there. You’re not still thinking about addition facts, because you’ve got it. And it fuels you. It’s the foundation that allows you to do all the other cool stuff.”

Fluency in the math classroom

What does fluency look like in practice? A young learner fluent in math will be able to smoothly recite the number word list in order (“one, two, three…”) and write the numerals from 0 to 9. As the student grows, so does their fluency with multi-digit calculation, rational-number arithmetic, and eventually even variable expressions. 

“It’s a wordless but still somehow almost verbal sort of fluency, with properties of operations as the grammar of the language,” says Jason.

But “it’s not fact recall,” he says. “Recall is remembering or just knowing. Fluency refers to calculation.”

Why and how to improve math fluency

There are different paths to fluency, but all can lead to “conceptual richness and mathematical joy,” says Dan.

If fluency provides that crucial foundation, what happens to students who are not math-fluent? 

“When kids don’t have access to [fluency], it keeps them from diving into the juicy parts of math,” says Bethany. “Math is so much bigger than addition facts, but when they don’t know those addition facts, that becomes all math is.” 

Without fluency, students miss opportunities to progress in (and enjoy) math, and may even develop math anxiety

So how can you support math students in developing fluency? 

For one thing, it’s important not to underestimate the value of practice and repetition. These approaches—especially when used in combination with other, more organic modes—can be highly productive, says Jason. “I worry about whether discomfort with repetitive practice is short-changing students of the power and confidence that fluency can bring.”

Dan compares it to achieving excellence in a sport—”like shooting from the same spot on the court over and over again,” he says. That kind of rote repetition is valuable in sports, and should also have its place in math instruction. 

It’s also important for students to understand why they’re learning and even drilling their numbers, arithmetic, or times tables, Jason notes. They need to be “invested in understanding and agreeing that this is going to do something for them.” 

One thing that helps: providing students a sense that they’ve accomplished something. “We need to have moments for them to reflect on what has been learned and what is now easy that was previously hard,” Dan says. He calls this process “humanizing fluency”—and Math Teacher Lounge will be here all season to help math educators do just that.

Save the date

Join us at NCTM in October for a live Math Teacher Lounge podcast recording with Dan Meyer and special guest Jennifer Bay-Williams! We’ll be investigating math fluency and finding fun ways to get all students engaged in math instruction. 

Math Teacher Lounge LIVE!
NCTM | Oct. 27 | 2:30 p.m. EST (doors at 2:15) | Room 158AB

Math classroom math fluency math instruction

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