The finding is consistent with a growing body of research suggesting that language plays a critical role in mathematics learning. A A 2021 meta-analysis of 40 studies found that students with better math vocabulary tended to perform better in math, especially on multi-step, complex tasks. Understanding what a “radius” is, for example, can make it more effective to talk about perimeter and area and understand geometric concepts. Some math curricula specifically teach vocabulary and include dictionaries to reinforce these terms.
But the dictionary itself is unlikely to be a magic ingredient.
“If a teacher just stands at the front of the classroom and recites lists of terms from the math dictionary, nobody learns anything,” Himmelsbach said.
Instead, Himmelsbach suspects that vocabulary is part of a broader constellation of effective teaching practices. Teachers who use more mathematical terms may also provide clearer explanations, take students through many step-by-step examples, and offer engaging puzzles. These teachers may also have a better conceptual understanding of mathematics themselves.
It’s hard to isolate what exactly drives students’ math learning and what role vocabulary plays, per se, 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 how often teachers use more than 200 common math terms drawn from the dictionaries of the primary mathematics curriculum.
The average teacher uses 140 math-related words per lesson. But there was a great variety. The top quarter of teachers used at least 28 more math terms per lesson than the quarter of teachers who said the fewest math words. Over the course of a school year, this difference amounts to approximately 4,480 additional terms of math, 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 achievement. One hundred teachers were enrolled for 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 higher-performing students were simply grouped with stronger teachers.
The lessons come 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 Latino — the very populations that tend to struggle the most in math and could gain the most from effective instruction.
Interestingly, students’ use of math vocabulary did not seem to matter as much as teachers’ use. Although the researchers also tracked how often students used math terms in class, they found no clear relationship between teachers who used more vocabulary and students who said more math words themselves. Exposure and understanding, rather than verbal facilitation, may be sufficient to support better mathematical performance.
Researchers are also looking for clues as to why some teachers use more math vocabulary than others. Years of teaching experience did not matter. Nor the number of math or math pedagogy courses the teachers took in college. Teachers with better math knowledge do tend to use more math terms, but the relationship is 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 “addition” instead of addition or “subtraction” instead of subtraction. While these colloquial expressions can be helpful, students ultimately need to understand how they correspond to formal math 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 into the classroom, which has long been a black box. With enough recorded lessons, the researchers hope to not only identify which teaching practices are most important, but also provide teachers with specific, data-driven feedback.
The researchers did not examine whether the 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.
So far, the takeaway is more modest, but still significant: Students seem to learn more math when their teachers speak the language of math more often.
Contact the staff writer Jill Barshay at 212-678-3595 or barshay@hechingerreport.org.
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