by Jill Barshay, The Hechinger Report
January 5, 2026
Students, parents and school principals all instinctively know that some teachers are better than others. Education researchers have spent decades trying — with mixed success — to calculate exactly how much better.
What remains far more elusive is why.
A new study suggests that one surprisingly simple difference between stronger and weaker math teachers may be how often they use mathematical vocabulary, words such as “factors,” “denominators” and “multiples,” in class.
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Teachers who used more math vocabulary had students who scored higher on math tests, according to a team of data scientists and education researchers from Harvard University, Stanford University and the University of Maryland. The size of the test score boost was substantial. It amounted to about half of the benefit researchers typically attribute to having a highly effective teacher, which is among the most important school-based factors that help children learn. Students with highly effective teachers can end up months ahead of their peers.
“If you’re looking for a good math teacher, you’re probably looking for somebody who’s exposing their students to more mathematical vocabulary,” said Harvard data scientist Zachary Himmelsbach, lead author of the study, which was published online in November 2025.
The finding aligns with a growing body of research suggesting that language plays a critical role in math learning. A 2021 meta-analysis of 40 studies found that students with stronger math vocabularies tend to perform better in math, particularly on multi-step, complex problems. Understanding what a “radius” is, for example, can make it more efficient to talk about perimeter and area and understand geometric concepts. Some math curricula explicitly teach vocabulary and include glossaries to reinforce these terms.
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But vocabulary alone is unlikely to be a magic ingredient.
“If a teacher just stood in front of the classroom and recited lists of mathematical vocabulary terms, nobody’s learning anything,” said Himmelsbach.
Instead, Himmelsbach suspects that vocabulary is part of a broader constellation of effective teaching practices. Teachers who use more math terms may also be providing clearer explanations, walking students through lots of examples step-by-step, and offering engaging puzzles. These teachers might also have a stronger conceptual understanding of math themselves.
It’s hard to isolate what exactly is driving the students’ math learning and what role vocabulary, in and of itself, is playing, Himmelsbach said.
Himmelsbach and his research team analyzed transcripts from more than 1,600 fourth- and fifth-grade math lessons in four school districts recorded for research purposes about 15 years ago. They counted how often teachers used more than 200 common math terms drawn from elementary math curriculum glossaries.
The average teacher used 140 math-related words per lesson. But there was wide variation. The top quarter of the teachers used at least 28 more math terms per lesson than the quarter of the teachers who spoke the fewest math words. Over the course of a school year, that difference amounted to roughly 4,480 additional math terms, meaning that some students were exposed to far richer mathematical language than others, depending on which teacher they happened to have that year.
The study linked these differences to student achievement. One hundred teachers were recorded over three years, and in the third year, students were randomly assigned to classrooms. That random assignment allowed the researchers to rule out the possibility that higher performing students were simply being clustered with stronger teachers.
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The lessons came from districts serving mostly low-income students. About two-thirds of students qualified for free or reduced-price lunch, more than 40 percent were Black, and nearly a quarter were Hispanic — the very populations that tend to struggle the most in math and stand to gain the most from effective instruction.
Interestingly, student use of math vocabulary did not appear to matter as much as teacher use. Although the researchers also tracked how often students used math terms in class, they found no clear link between teachers who used more vocabulary and students who spoke more math words themselves. Exposure and comprehension, rather than verbal facility, may be enough to support stronger math performance.
The researchers also looked for clues as to why some teachers used more math vocabulary than others. Years of teaching experience made no difference. Nor did the number of math or math pedagogy courses teachers had taken in college. Teachers with stronger mathematical knowledge did tend to use more math terms, but the relationship was modest.
Himmelsbach suspects that personal beliefs play an important role. Some teachers, he said, worry that formal math language will confuse students and instead favor more familiar phrasing, such as “put together” instead of addition, or “take away” instead of subtraction. While those colloquial expressions can be helpful, students ultimately need to understand how they correspond to formal mathematical concepts, Himmelsbach said.
This study is part of a new wave of education research that uses machine learning and natural language processing — computer techniques that analyze large volumes of text — to peer inside the classroom, which has long remained a black box. With enough recorded lessons, researchers hope not only to identify which teaching practices matter most, but also provide teachers with concrete, data-driven feedback.
Related: A little parent math talk with kids might really add up
The researchers did not examine whether teachers used math terms correctly, but they noted that future models could be trained to do just that, offering feedback on accuracy and context, not just frequency.
For now, the takeaway is more modest but still meaningful: Students appear to learn more math when their teachers speak the language of math more often.
Contact staff writer Jill Barshay at 212-678-3595, jillbarshay.35 on Signal, or [email protected].
This story about math vocabulary was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for Proof Points and other Hechinger newsletters.
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