How the Vocabulary Math Teachers Use Affects Student Learning

Remainder. Product. Algorithm. Ordered pair.

Seemingly jargony words and phrases like these, referring to specific math concepts, might seem complex for elementary school students to grasp. But teachers who use them regularly are more likely to boost student math scores, new research finds.

The paper is one of the largest-scale studies to examine this practice—and it draws a link between specific instructional moves and teacher effectiveness.

The study, from researchers at Harvard University, the University of Maryland College Park, and Stanford University, used natural-language-processing techniques—a form of artificial intelligence—to analyze more than 1,600 transcripts of 4th and 5th grade math lessons from the National Center for Teacher Effectiveness Transcript Dataset, a bank collected from 317 classrooms across four districts between 2010-2013.

In these districts, schools assigned students to classrooms following business-as-usual procedures during the first two years of data collection. But during the third year, schools grouped students randomly, and researchers assigned teachers to each class. That design allowed the researchers in the new study to examine the effects of being assigned to one teacher over another in the third year.

They found that students assigned to teachers who used more mathematical vocabulary in their lessons made greater progress than students who were assigned to teachers who used less. Math-vocabulary use alone predicted about half of the variation among those teachers whose students improved the most, and those whose students learned the least.

“It is the teachers who are using more mathematical vocabulary that are the more effective teachers, on average,” said Zachary Himmelsbach, an investigator/instructor at Massachusetts General Hospital’s psychiatry department and Harvard Medical School, and the lead author on the study. “It provides this strong predictive signal.”

“Importantly, it’s not necessarily the case that it is the use of vocabulary itself that causes the improvements,” he added, as a caveat to the findings. “It could be that, or some portion of it could be that. But it also could be that teachers who use more mathematical vocabulary are doing other things as well.”

Why math vocabulary matters

Using math-specific vocabulary—saying “product” when teaching multiplication, for example, instead of something like “what you get when you multiply two numbers together”—is widely regarded as a best practice in math instruction.

The Institute of Education Sciences’ practice guides recommend it for elementary and middle school students who are struggling in math, and teachers have said vocabulary knowledge is key for students to succeed with standards and curricula that increasingly rely on problem-solving and explaining solutions. (IES is part of the U.S. Department of Education.)

In part, previous math research has theorized, vocabulary knowledge opens a portal to conceptual understanding, said Himmelsbach. Knowing what the radius of a circle is, for example, can provide a foundation for applying the concept of a radius elsewhere in math, especially as problems become more abstract, he said.

Put simply, “they need to know the words to be able to understand the concepts,” said Robin Anderson, an 8th grade math teacher at Andover Middle School in Andover, Kan.

Schoolwide, Andover uses a vocabulary routine to teach new terms related to core content: Teachers define the word, give examples, and then ask students to do the same. “We believe as a school, if we can teach them more vocab words in math and science and reading, they’re going to start to understand things on a deeper level,” Anderson said.

It’s a practice she uses regularly in her math class. This year those words include “coefficient,” “integer,” “linear pair,” “supplementary,” and “complementary.”

Previous research in math education has formed a “theoretical bedrock” that supports teachers’ use of math vocabulary, Himmelsbach said. But mostly that research hinged on small case studies, examining the practice of one teacher, or a small group. The new study shows on a larger scale that teachers who use more math vocabulary are consistently more effective than teachers who use less.

Teachers with more mathematical knowledge themselves were more likely to use math vocabulary, but other individual characteristics—such as how many years of experience teachers had—didn’t explain stronger math-vocabulary usage.

Interestingly, though having a teacher who used more math-specific vocabulary led to higher student scores, it didn’t make students more likely to use that vocabulary themselves.

Could artificial intelligence provide a ‘more granular picture’ of the classroom?

Beyond offering insight into effective math instructional practices, Himmelsbach said, the study also serves as an example of what new artificial intelligence technologies could reveal about what makes for good teaching.

“By looking at a much more granular picture of what’s happening in the classroom, we were able to construct a measure that is a strong predictor. We need to keep doing this,” he said.

“It would be wonderful to have a nationally representative sample of classroom lessons,” he added, similar to how the National Assessment of Educational Progress captures a sample of achievement.

Himmelsbach said that such a repository should be anonymized, used for research purposes only, and not connected to accountability for teachers or schools.

Still, the idea gives Anderson, the math teacher, pause.

She wouldn’t want the takeaway from research like this to be that teacher effectiveness is tied to one practice—no matter how powerful research found that practice to be. She instead favors a more holistic definition of teacher quality.

“Sometimes,” she said, “it’s more the rapport you have with students.”