Math is, by definition, a subject about numbers. But at the National Conference of Teachers of Mathematics this week, math educators said the subject has its own language, too—and knowing how to speak it is critical to success.
In presentations and discussions at the annual conference, held this year here in Chicago, teachers, administrators, and higher education faculty enumerated the ways that math literacy unlocks students’ understanding.
Some words have one meaning in general conversation, but another meaning in math. Others, like “square,” can have two different math definitions: the geometric figure, and the square of a number, a type of exponent. Math also has its own grammar—decimal points, commas, parentheses, and brackets, for example, all have meanings distinct from those in an English/language arts class.
Internalizing and using this language is one way that students build math knowledge, said Gladis Kersaint, the vice provost for academic affairs at the University of Connecticut, in a presentation on supporting English learners in the subject.
For every lesson, she said, teachers should ask themselves: “What language objective do I have to attend to so that my content objective can be achieved?”
Presenting multiple definitions could help students understand new math concepts
Emily Illig, a 4th and 5th grade math teacher in Chicago schools, said she sometimes has trouble defining abstract concepts with her students.
When Illig can’t demonstrate ideas with physical manipulatives like counters, “there becomes this disconnect,” she said in a Q&A session at the conference. “And then I’m like, well, how do I get them ready for middle school, when things get more abstract?”
In a separate presentation, Matthew Winsor, an associate professor of mathematics at Illinois State University, explained one strategy he used to help English learners grasp complex definitions when he taught high school.
Winsor tasked students with creating “word squares”—index cards divided into four quadrants. In the top left quadrant, students wrote a math term in their own language; in the top right quadrant, they wrote the term in English. Then, they wrote a definition in their own words in the bottom left quadrant—in whichever language they chose—and drew a picture or wrote an example in the bottom right.
Students rely on these tools throughout the course, Winsor said: “I’ve had a student come back to me the year after and say, ‘Hey, Mr. Winsor, I used my word squares today.’”
Other educators used similar strategies with younger students.
In a presentation on supporting struggling elementary schoolers, Laura Drechsel and Carolyn Stadlman, both math educators in the Crystal Lake school district in Illinois, discussed using the Frayer Model, another way to diagram vocabulary words.
In this model, students write the word they’re defining in the middle of a four-quadrant box. In each of the squares, they write 1) the definition in their own words, 2) facts and characteristics of the concept, 3) examples, and 4) non-examples.
“When I first started teaching kindergarten, I thought, ‘I’m going to just learn the curriculum, and that’s going to be OK,’” said Drechsel, now an interventionist. She soon learned, she said, that she needed tools like this model to help shore up some students’ understandings.
English learners will face specific math challenges—but also bring unique founts of knowledge
During Kersaint’s talk on supporting English learners, several teachers identified a hurdle in assessing their newcomer students’ math knowledge.
Many recent arrivals have experienced interruptions to their education in their home countries, they said. It can be hard to distinguish when students truly have gaps in their knowledge from when students know the material but don’t have the math language in English to communicate it.
Math teachers need to be “listening hard” to their English learners, Kersaint said. For example, a student might offer a partial definition in English, a Spanish word, and draw a picture—teachers should consider all of this information as students’ demonstration of their knowledge, she said.
English learners may also bring unique skills to math class, said Larisa Bukalov, a math teacher at Bayside High School in New York City.
When these students learn English, they often get explicit instruction in diagramming sentences—a skill that can help them parse word problems. “If you’re not a native speaker, you’re a lot more sensitive when you try to translate the [words in the] problem to the algebra,” Bukalov said during Q&A after Kersaint’s presentation.
For this reason, she said, she often has English learners model how they solved word problems for the group—positioning them as classroom leaders.
