The finding aligns with a growing body of research suggesting that language plays a critical role in learning mathematics. TO 2021 meta-analysis Of 40 studies found that students with stronger math vocabulary tend to do better in math, particularly on complex, multi-step problems. Understanding what a “radius” is, for example, can make it more efficient to talk about perimeter and area and understand geometric concepts. Some mathematics curricula explicitly teach vocabulary and include glossaries to reinforce these terms.
But vocabulary alone is unlikely to be a magic ingredient.
“If a teacher simply stood in front of the classroom and recited lists of math vocabulary terms, no one would learn anything,” Himmelsbach said.
Instead, Himmelsbach suspects that vocabulary is part of a broader constellation of effective teaching practices. Teachers who use more math terms can also offer clearer explanations, guide students through many step-by-step examples, and offer interesting puzzles. These teachers may also have a stronger conceptual understanding of mathematics.
It’s difficult to isolate what exactly drives students’ math learning and what role vocabulary, itself, plays, Himmelsbach said.
Himmelsbach and his research team analyzed transcripts of more than 1,600 fourth- and fifth-grade math lessons in four school districts recorded for research purposes about 15 years ago. They counted the frequency with which teachers used more than 200 common math terms extracted from glossaries of the primary mathematics curriculum.
The average teacher used 140 math-related words per lesson. But there was great variation. The top quarter of teachers used at least 28 more math terms per lesson than the top quarter of teachers who used the fewest math words. Over the course of a school year, that difference amounted to about 4,480 additional math terms, meaning that some students were exposed to much richer math language than others, depending on which teacher they had that year.
The study linked these differences to student performance. One hundred teachers were registered for 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-achieving students were simply grouped with stronger teachers.
The lessons came from districts that primarily serve low-income students. About two-thirds of the students qualified for free or reduced-price lunch, more than 40 percent were black, and nearly a quarter were Hispanic—the same populations that tend to struggle the most in math and benefit the most from effective instruction.
Interestingly, students’ use of mathematical vocabulary did not seem to matter as much as the teacher’s 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. Exposure and understanding, rather than verbal facility, may be enough to support better math performance.
The researchers also looked for clues about why some teachers used more math vocabulary than others. Years of teaching experience made no difference. Neither did the number of professors of mathematics or mathematics pedagogy courses who had tasks at the university. Teachers with stronger mathematical knowledge tended to use more mathematical 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 prefer more familiar phrases, such as “put together” instead of addition, or “take away” instead of subtract. 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 educational research that uses machine learning and natural language processing (computer techniques that analyze large volumes of text) to look inside the classroom, which has long remained a black box. With enough recorded lessons, researchers hope to not only identify which teaching practices are most important, but also provide teachers with concrete, data-driven feedback.
The researchers did not examine whether teachers used math terms correctly, but noted that future models could be trained to do just that, offering feedback on accuracy and context, not just frequency.
For now, the conclusion is more modest but still significant: students appear to learn more mathematics when their teachers speak the language of mathematics more frequently.
Contact the staff writer Jill Barshay at 212-678-3595 or barshay@hechingerreport.org.
This story about mathematical vocabulary was produced by The Hechinger Reportan independent, nonprofit news organization focused on inequality and innovation in education. Enroll in Test points and others Hechinger Newsletters.
