Words matter: Teachers who use math vocabulary can help students do better in math
This finding is consistent with a growing body of research showing that language plays a key role in mathematics learning. A 2021 meta-analysis of 40 studies found that students with stronger math vocabulary tend to perform better in math, especially on multi-step, complex problems. For example, knowing what “radius” is allows for more effective discussions of perimeter and area and understanding of geometric concepts. Some math courses teach vocabulary explicitly and include glossaries to reinforce these terms.
But words themselves are unlikely to be the magic ingredients.
“If the teacher just stands at the front of the room and recites a list of math vocabulary words, no one is going to learn anything,” Himmelsbach said.
Instead, Himmelsbach doubts that vocabulary is part of a broader practice of effective teaching. Teachers who use more mathematical terminology are also likely to provide clearer explanations, walk students step-by-step through numerous examples, and provide engaging puzzles. These teachers may also have a deeper conceptual understanding of mathematics itself.
Himmelsbach said it can be difficult to distinguish between what exactly drives students’ math learning and what role the vocabulary itself plays.
Himmelsbach and his research team analyzed transcripts from more than 1,600 fourth- and fifth-grade math classes in four school districts recorded for research purposes about 15 years ago. They tallied how often teachers used more than 200 common math terms from primary school math curriculum vocabularies.
Teachers use an average of 140 math-related words per lesson. But there are big differences. The top quartile of teachers used at least 28 more math terms per lesson than the teachers in the bottom quartile who used the fewest math words. Over the course of a school year, this difference equates to approximately 4,480 additional mathematical terms, meaning some students are exposed to much richer mathematical language than others, depending on which teacher they happen to have that year.
The study links these differences to student outcomes. One hundred teachers were recorded over three years, and in the third year, students were randomly assigned to classrooms. This random assignment allowed the researchers to rule out the possibility that better-performing students were simply clustered with more capable teachers.
These programs come from districts that serve primarily low-income students. About two-thirds of students qualify for free or reduced-price lunch, and more than 40 percent are black and nearly a quarter are Hispanic — groups that tend to struggle the most in math but also benefit most from effective instruction.
Interestingly, students’ use of mathematical vocabulary appears to be less important than 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 understanding, rather than language ability, may be sufficient to support stronger mathematics performance.
The researchers also looked for clues to explain why some teachers use more math vocabulary than others. Years of teaching experience make no difference. There has also been no increase in the number of mathematics or mathematics pedagogy courses teachers take in college. Teachers with stronger mathematical knowledge did tend to use more mathematical terminology, but this relationship was not significant.
Himmelsbach suspects personal beliefs play an important role. He said some teachers worry that formal math language will confuse students and prefer to use more familiar phrasing, such as “put together” instead of adding, or “take away” instead of subtracting. While these verbal expressions can be helpful, students ultimately need to understand how they correspond to formal mathematical concepts, Himmelsbach said.
The study is part of a new wave of education research that uses machine learning and natural language processing — computer techniques that analyze large amounts of text — to peer into classrooms that have long been black boxes. With enough course records in hand, the researchers hope not only to determine which teaching practices matter most but also to provide teachers with concrete, data-driven feedback.
The researchers did not check whether teachers were using mathematical terms correctly, but they noted that future models could be trained to do this, providing feedback on accuracy and context, not just frequency.
For now, the conclusions are milder, but still meaningful: Students seem to learn more math when teachers speak the language of math more often.
Contact a Staff Writer Jill Bacher 212-678-3595 or barshay@hechingerreport.org.
This story is about math vocabulary is made of Heckinger Reportis a nonprofit, independent news organization focused on inequality and innovation in education. register proof point and others Heckinger Communications.
