Math class doesn’t seem like the most obvious choice for word walls, glossary lists, and word of the day games. But a strong understanding of math terms is essential for mastering concepts—meaning strategies for building robust vocabulary are surprisingly useful.
Recently, fifth-grade math teacher Kathleen Palmieri began to wonder how well her students understood the complex terms used in textbooks and word problems. So she performed some action research by pulling out 10 key terms—including exponent, base, equivalent, and estimate—and asked students to define those terms using words or numbers, she writes in a recent piece for MiddleWeb. About 40 percent of her kids could write a basic definition, exposing significant gaps in conceptual fluency.
“What I discovered in my students’ responses was that learning math terminology is more than studying a list of words,” she said, concluding that regular practice with new math terminology facilitates mathematical discourse and understanding. “It is much more of an architecture of learning where concepts need to be explored and a pathway of understanding needs to be blazed before a mathematical term can be attached to establish true meaning.”
Here are a few of the ways Palmieri and other teachers “immerse students in the language of math”—while keeping student engagement high.
1. Let students do the defining: Students need to contextualize words before they can understand them, and need repeated exposure to them before they sink in.
As an alternative to Palmieri’s baseline assessment, have students pull out the key terms they think will be important later. Literacy specialist Rebecca Alber asked her students to skim a chapter from a textbook and identify their own vocabulary list. Students would then rate each term by whether they “know it,” “sort of know it,” or “don't know it at all.” Afterward, they wrote out a definition or took their best guess at the term’s meaning.
“Before they turn in these pre-reading charts, be sure to emphasize this is not about ‘being right,’” she advised. “They are providing you with information to guide next steps in class vocabulary instruction.”
Similarly, Palmieri provides some introductory context and asks students to add to an expanding glossary. Research has largely dispelled the practice of writing out memorized definitions from textbooks, so Palmieri takes a different tack. Students take an active role in coming up with definitions based on their learning. As students learn more about the terms and how they’re used, they update definitions. At the end of the lesson, to consolidate learning, it may prove helpful to review all the terms as a class.
2. Get creative with word walls: Instead of writing terms on a word wall and hanging it up for students to glance at, Palmieri has students write terms on colorful Post-Its and affix them to bulletin boards. She also gets great engagement from letting students use art supplies to creatively show what they’ve learned: “Bubble letters, examples of problems and definitions with graphics are truly fun ‘math’ activities,” she explains. “Students present and explain their term and then proudly display their poster in the classroom.”
Unlike static word walls, these strategies involve principles of constructivism, an active and social learning theory where learners build on previous knowledge and create new learning themselves. As students learn new concepts, they can define terms in real-time, make adjustments as the concepts deepen, and hang them around the classroom for others to learn from.
3. Make it a game: Math instruction doesn’t have to be drab, says Palmieri. You can introduce familiar word games like Pictionary, where students draw out clues and others try to guess the concept. She also plays a game called “What’s My Term?” where “students verbally give clues as others listen.”
Likewise, language specialist and Harvard lecturer Rebecca Rolland suggests a game where students show they know what terms mean by listing “non-examples” of things they are studying. For instance, acute angles can look “‘sharp’ but not ‘curvy’ or ‘wavy’ or ‘square,’” she says. Ask students to come up with creative non-examples and explain their thought processes. “That same acute angle might look like a door that’s partly shut, but not like a smile or a cloud.”
Still others play match games with index cards face down on a table, or encourage students to create definitions that rhyme or fit to music. In these cases, the game itself is perhaps less important than the act of engaging students to commit the terms to memory.
4. Word(s) of the day: To reinforce specific concepts, Palmieri has the class come up with a word of the day or week, depending on the duration of the lesson. Students count how often the word is used and in which contexts (e.g., in word problems, during class discussion, in small group activities).
Inspired by research she had done that suggested students need to use a word between six and 30 times to truly learn it, sixth-grade teacher Megan Kelly began picking three words to focus on for a day and reviewing the terms at the start of class. During class, she emphasizes the words herself, and asks students to use the words as many times as they can with a partner.
“I used the words a ton in my directions and made a big deal whenever I heard a student say one of our goal words,” she says. “Everyone wants to be in on the fun, so each time I praised someone for using the word, there was an increase in others using them too.”
5. Break down word problems: Word problems are notoriously difficult, especially when challenging language obscures the intent of the question. Before students solve word problems numerically, Palmieri has the whole class perform a close read for sense-making. Together they pull out key words and create a written response. Working out word problems as a group is a well-established strategy. Teachers at Concourse Village Elementary School in New York City use a 3-read protocol: First, they read the word problem aloud to the class without numbers, then students read the complete problem on their own and pull out key terms before reading it together as a class. The 3-read protocol clarifies “what they’re reading and helps to build their fluency,” says Blair Pacheco, a teacher who has used the strategy with her students.