Even for students with an intuitive sense of math, its specialized vocabulary often gets in the way, but that doesn’t have to be the case. Find out how to use math vocabulary as a tool to broaden students' understanding of math and improve mathematical discourse.

## THE LANGUAGE of Math

Humans, according to Noam Chomsky and his fellow nativists, have an innate ability to learn language. Whether or not we have a similar ability for math is a matter of heated debate. The point is that language is how we mediate our understanding of the world around us, including mathematical concepts.

We may be able to conceive of “three” of something or recognize the unique characteristics of a “circle” separate from these words, but we still use the words to frame and communicate our understanding.

The connection between math and language is critical in a math classroom where words, spoken and written, are essential for students to take in new information and demonstrate what they already know.

In Curriculum and Evaluation Standards for School Mathematics, the National Council of Teachers of Mathematics (NCTM) makes specific reference to the way language forms a link between students’ informal intuitive conceptualization of math and the abstract symbolic form that characterizes math as a formal field of study.

## Helping Students “Speak Math”

In short, helping students do math means helping them learn to speak the language of math. Moreover, math vocabulary is rich and diverse, including unique terms, like asymptote and exponent, and everyday words with specialized meanings, like range and line.

Students don’t enter a math class using the special vocabulary of math they need, so teachers have to make a conscious and sustained effort to help them gain fluency in this language.

## WHY Focus on Vocabulary?

So if teaching students math vocabulary isn’t easy, why should math teachers, who already have enough on their plate, invest the extra work? We’ve already discussed the link between language and math, so how does that play out in a math classroom?

For one thing, it can be a major hurdle for some learners, particularly for a student who already believes they aren’t a math person.

Consider the student who has a good intuitive grasp of division but isn’t familiar with the word “quotient.”

It’s easy to see how this student might start to think that math is just too hard, despite their innate ability.

The problem is compounded for language learners who are new to decoding English.

After struggling to understand that the word “mean” has two different uses (“She was mean to me. What does that mean?”), they encounter an arithmetic mean; now they’re really confused.

Whether a student is new to English or fluent, a math whiz, or a mathephobe, they will have to face new words, and the teacher who ignores the pitfalls does so at their own peril.

## LANGUAGE as a Lens: The Need for Assessment

Math terminology doesn’t just cause problems for students in acquiring concepts and procedures; it can also hinder our ability to assess their mastery of those same concepts and techniques.

Most formative assessments a teacher will use regularly, and indeed the standardized tests for which they must prepare their students, require students to decode and use math vocabulary.

Assessments are a necessary part of the learning process because they provide a lens for examining evidence of learning. Assessments use language, and math assessments use math language; there’s no escaping it.

There are alternative math assessments that focus on performance tasks, but these often require a more significant investment of time and effort, and even these will inevitably use math terms.

## What the Research Says

Apart from the need to reduce the barriers to math fluency created by specialized terminology and the essential role of language in assessment, educational research supports the need for math vocabulary instruction.

Some studies suggest language is a necessary element of success in mathematics (Seethaler, Fuchs, Star & Brant, 2011). Other research indicates that students' competency in math vocabulary is a reliable predictor of math performance (van der Walt, 2009).

More informal research carried out by classroom teachers backs up the correlation between math vocabulary fluency and math performance and also indicates that students respond positively to activities focused on improving their math vocabulary (Periano, n.d.)

## TIPS for Teaching Math Vocabulary

Most math teachers have their go-to math vocabulary activities. If not, a quick Google search can turn up a list of 100 Math Vocabulary Activities on Pinterest.

The problem isn’t finding activities; it’s knowing which ones are likely to have the most impact on students.

Teachers know their classrooms best and can gauge for themselves which activities are helping them reach their goals, but here are four tips that form a helpful guide to evaluating and selecting math vocabulary activities.

### Start with the Concrete

Language is itself an abstraction. Trying to teach words using only words can be a self-defeating effort.

Students’ first exposure to new math vocabulary should include, whenever possible, a hands-on experience, providing a concrete context for the words.

The youngest learners explore numbers by handling and counting physical objects. Even differential equations can be introduced with a real-world context, such as the flow of air around a barrier.

Regardless of the age of the learner or the complexity of the concept, math vocabulary needs to be introduced in a concrete context. This idea aligns perfectly with the CRA math model that begins with concrete experience. The concept is central as well to the recently introduced Earn the Word model.

### Allow for Customization

Just as important as students’ real-world experience with the phenomenon that forms the ** context** for a math term is their personal connection to its

**. Students are more likely to remember a definition they came up with themself or at least collaborated on. The same is true for sample sentences, examples, illustrations, or other elements of vocabulary-building resources, such as the**

*meaning***Frayer Model**.

### Provide Convenient Access

Once students have been exposed to words through a concrete experience and made a personal connection to the word, they need repeated exposure to the word before they can understand and use it reliably. This means the teacher should take advantage of every opportunity to use the word in context and encourage students to do the same.

A Word Wall allows students to always have access to essential math vocabulary and acts as a visual reminder. Vocabulary cards, especially student-created ones, provide another way for students to have convenient access to the words in a way that also benefits tactile learners.

### Use Gamification in Review

Ideally, students would gain fluency in math vocabulary by constantly using the words in meaningful contexts. However, it’s not always easy to ensure all students get such opportunities and monitor how they use the terms. Independent review is often the most effective and efficient way to make sure all students get enough practice with vocabulary.

Tedious drilling, however, can be a mind-numbing experience for students and leave them less motivated to learn new words. Teachers can use gamification to make reviewing math vocabulary more engaging. The internet offers multiple lists of vocabulary games, but a creative teacher can take any existing word game and turn it into a math vocabulary game. Let’s look at three examples.

#### Hangman

Most of us are familiar with the old standby hangman. (For those who don’t, there is a YouTube video explaining it.) As a class, or better yet, in small groups or pairs, students can challenge each other to figure out the target word. Players play the game by drawing target math vocabulary words from three sources; a teacher-prepared list, words on the classroom word wall, or their personal set of vocabulary cards.

#### Pictionary

For anyone who has not played this game, the basic idea is that one player gets a target word and, through drawing alone (without using any character found on a standard keyboard), must get another person or group of people to guess the word. The word list can be drawn from the same sources listed above for hangman.

#### Taboo

This game is a bit more work to prepare, but it provides an extra challenge to players. As with the previous two games, one player’s goal is to get another player (or team of players) to guess the target word. The player who receives the target word is allowed to talk. They can say whatever they want to get the other players to guess the word; whatever they want except, that is, for certain words, which are not allowed, or taboo.

For example, a player might have to get their team to guess the word even without using the words; odd, divide, divisible, or two. Okay, that may be a complicated example, but you get the idea. For this game, players need not only the math vocabulary words, but each term needs its own list of taboo words.

One idea for making the game even more powerful is to have students create their own cards. It’s pretty easy to see how developing the best (read, most challenging) cards require a good grasp of the vocabulary, so this method provides a benefit not only in the playing of the game but in the building of the game as well.

## Vocabulary AS A TOOL

Students, like all humans, have an innate ability to acquire language.

Without even thinking about it, they learn to use hundreds of words associated with their interests, from soccer terms to dance moves, to the names of Pokemón.

Learning the appropriate vocabulary is a natural and necessary part of any human endeavor.

With the right approach and thoughtful practice, math vocabulary doesn’t have to be a barrier to learning. Teachers, in fact, have the power to help students make the correct use of math terms, one of the most important tools in their repertoire of skills.

**References**

Kay, P., & Kempton, W. (1984). What is the Sapir‐Whorf hypothesis?. American anthropologist, 86(1), 65-79.

Monroe, E. E., & Orme, M. P. (2002). Developing mathematical vocabulary. Preventing school failure: Alternative education for children and youth, 46(3), 139-142.

National Council of Teachers of Mathematics (1989) Curriculum and evaluation standards for school mathematics. Reston, VA

Peirano, K. (n.d.)“I Forgot that Quotient Meant to Divide so I Added Instead and Got the Wrong Answer”: The Link between Math Vocabulary and Problem-solving.

Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics: The importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235-252.

Seethaler, P.M. Fuchs, L.S., Star, J.R. & Bryant J. (2011). The cognitive predictors of computational skill with whale versus rational numbers; An exploratory study. Learning and Individual Differences, 21, 536-542.

van der Walt, M. (2009). Study orientation and basic vocabulary in mathematics in primary school. South African Journal of Science and Technology, 28, 378–392.