In High-Performing Math Classrooms, Words Matter

Picture two different fourth-grade classrooms. In one room, the teacher asks, “How many times does 6 go into 45?” and talks about “what’s left over.” In another, students discuss the divisor and dividend, calculate the quotient, and identify the remainder. 

Both explanations have their place in math instruction, but according to a large-scale 2025 study of upper elementary math instruction, the use of precise mathematical terminology may matter more than we think.

Across more than 1,600 fourth- and fifth-grade math lessons, researchers tracked how often more than 200 math-specific vocabulary words showed up in classroom talk. In some classrooms, teachers used precise math terms about 185 times per lesson; in others, closer to 84 times. The difference added up to students hearing roughly 4,500 more math words over the course of a school year, compared to peers in classrooms where math vocabulary was used infrequently. Meanwhile, students placed with teachers who used math vocabulary on a regular basis made larger gains on standardized tests, the researchers found.

But simply tossing around terms like rhombus or hypotenuse isn’t enough to improve outcomes. Instead, the researchers found that precise math language often goes hand in hand with a range of other strong teaching moves—clarifying concepts with visuals, pressing students to explain their reasoning, structuring discussions that deepen understanding, and keeping students actively engaged in the work of the lesson. Lead study author Zachary Himmelsbach described vocabulary use in class as a “strong predictive signal” of teacher effectiveness in a recent interview with Education Week. Vocabulary alone isn’t a panacea—but it’s often a visible marker of strong instruction and a high-impact place to start.

Here are several ways to build academic math language into daily lessons so students don’t just hear precise terms but also begin using them to think and communicate mathematically.

Let Students Define Words First

When fifth-grade teacher Kathleen Palmieri asked her students to define 10 key math terms before a unit—words like exponent or equivalent fractions—only 40 percent could write a basic definition. The issue, she realized, wasn’t just vocabulary; it was deeper understanding.

Instead of reading definitions aloud to her class, or asking students to copy the textbook definition, Palmieri shifted her approach to asking them to draft their own working definitions of terms after learning a concept. After solving exponent problems, a student might write: “An exponent tells you how many times to multiply the base by itself,” for example. During a fraction unit, students might define equivalent fractions as: “Fractions that look different but are the same amount—like 1/2 and 2/4.” 

As students encounter the terms again and again, they revise and refine their definitions, adding examples, diagrams, or non-examples. Over time, Palmieri says, the glossary they build becomes a living document rather than a static word list.

Literacy specialist Rebecca Alber uses a similar approach at the start of a unit. She asks students to skim a chapter, identify key terms they think will matter, and label each as “know it,” “sort of know it,” or “don’t know it.” Students then draft their best guess at a definition, a low-stakes strategy that surfaces prior knowledge and misconceptions. The resulting list helps students make sense of new vocabulary while giving teachers valuable information to guide next steps in instruction.

Get Playful With Low-Stakes Word Games

Turning vocabulary practice into a game can make an otherwise dry routine more engaging—and lower the stakes for students to try out new academic language. 

Pictionary works well in math classrooms, for example: One student sketches visual clues while classmates guess the term. A triangle with one sharp corner might prompt acute angle; a rectangle divided into equal parts could suggest area model or fraction.

To flip the format, try a game of “What’s My Term?” A student offers verbal clues—“I’m the answer to a multiplication problem,” prompting classmates to guess product. Because students must describe the concept without naming it, they practice precise language in the process, Palmieri writes.

In a fun twist, language specialist Rebecca Rolland asks students to generate non-examples. An acute angle may look “sharp,” but not “curvy,” “wavy,” or “square.” Explaining why something is not an example helps students clarify the boundaries of a term, deepening understanding, she writes. 

Or try simple matching games—pairing terms like factor with definitions or worked examples. “The game itself is perhaps less important than the act of engaging students to commit the terms to memory,” Palmieri says. 

Target Precision With Semantic Gradients

Some math terms seem straightforward—until students are challenged to compare or distinguish them from each other. Semantic gradients, a strategy in which related words are placed along a continuum to tease out degrees of meaning, invite students to sort terms and defend their reasoning. The goal isn’t to get the order “right,” says Joshua LaFleur, a doctoral candidate at Western University—it’s to spark discussion that sharpens meaning and understanding.

For example, during a unit on multiplication and division, students might arrange terms such as factor, product, multiple, and quotient along a continuum from smallest value to largest and explain their thinking. The conversation quickly moves beyond memorized definitions. Is a product always larger than a factor? Can a quotient be greater than the dividend? 

Semantic gradients also work well prior to introducing new content. Before a unit on integers, students might sort terms like negative number, zero, and positive number along a number line from least to greatest and explain their choices. Their reasoning—right or wrong—gives teachers insight into misconceptions before formal instruction begins.

Bring Word Walls To Life

Instead of posting math terms herself to a classroom word wall, Palmieri asks students to write key words on colorful Post-its and add them to a shared word wall. When studying powers and place value, for example, students define terms like base, expanded form, or equivalent decimals—and include sample problems, diagrams, or visual models to show what the word means. Students also present their term to the class before posting it. 

Because students must define the term, connect it to examples, and visually represent its meaning, they encode the vocabulary more deeply in memory—transforming a word wall from static decor that kids mostly ignore into an evolving tool for learning. The wall becomes a shared reference point that reinforces key ideas and helps students “own the word wall,” says Celita Lewis-Davis, a math instructional specialist who has her Algebra 1 students fill out index cards before posting them for a similar exercise.

Talk About It 

Before students begin solving a word problem, ask them to talk about the math first. Researchers Rachel M. Restani and Suzanne Abdelrahim of the University of California, Davis, recommend previewing open-ended word problems, for example, with structured whole-class sense-making. Students read the problem aloud several times, restate it in their own words and then, in small groups, identify key mathematical features and vocabulary.

If a task involves dividing a cake equally at a birthday party, students might first identify the number of slices and attendees, clarify what it means to divide equally, and pinpoint what they’re trying to find. Teachers can nudge precision by asking, “What’s the dividend here?” or “What will our quotient represent?” During the problem-solving stage, students then work individually and explain their strategies in small groups using sentence frames such as, “First, I divided the ___ by the ___ because… .”

Another conversational way to reinforce vocabulary is through structured math interviews, where students explain their thinking to a partner using scripted questions. After working independently, students might ask one another: “How did you solve the problem?” or “Why did you divide here?” As they talk through their reasoning, middle school math teacher Connell Cloyd listens and prompts them to use precise terms—such as independent variable or dependent variable—rather than vague phrases like “I divided this by that.” He often asks students, “Are you able to articulate yourself using that math language?” Over time, as students explain ideas, question peers, and restate strategies, the language begins to stick.