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NYC Helpline: How To: Teach Math
Effective Mathematics Vocabulary Instructional
Strategies You Can Count On Part 1

Luzviminda “Luchie” B. Canlas

Have you ever wondered why teaching mathematics vocabulary is challenging and why our students have a difficult time learning it? Would you like to know some effective ways to develop students’ understanding of mathematics vocabulary?

There are so many reasons why teaching and learning mathematics vocabulary can be very difficult and demanding to both teachers and students. One reason is that the math text is so dense, and “crowded” with words that are ambiguous and have multiple meanings. There are words that we use in day to day discourse that mean something different when we use them in math. There is the additional demand or “burden” for the student to know that these words have different meanings when used in a math context. Some examples are the words “mean,” “mode,” “function,” “right,” “complementary,” “vertical,” “table,” “change,” ‘multiple,” “evaluate,” “origin,” “odd,” “difference,” “prime,” “composite,” “radicals,” “natural,” “complex,” “real,” and “irrational.” The student can be easily confused when we ask him/her “What is the difference between 9 and 12?” The child might give you the answer “3” as a result of performing the subtraction operation. However, it is possible that some will say “9 is odd while 12 is even.” Of course the anticipated response is “3” but because of the nature of some math terminology, some students might say the latter. It is very easy for a teacher to unintentionally add to a child’s confusion. Imagine telling a student that a number is “irrational.” The student who is not given the opportunity to “know” this term or not pre-taught will probably ask: “How can an inanimate and abstract concept possess such a trait? How can a number lack coherence and reason?” Similarly, a student who just learned the word “radicals” in a science class will be definitely perplexed when asked to comprehend that same word in a math context. Moreover, a square is both a shape and a number in math. We are actually asking them to set aside what they already know and replace it with another meaning. I can go on and on but my point is that we need to be aware that this abundance of double meanings is a hindrance and impedes vocabulary acquisition. It compounds the confusion, difficulty, and complexity of the teaching and learning of math words.

In essence, teaching math is more difficult than teaching a foreign language. Not only are we dealing with teaching math nouns (content) - numbers, objects, measurements, shapes, patterns, data, functions, and graphs, we are also teaching the math verbs (process) - problem solving, formulating, manipulating, conjecturing, reasoning, representing, inferring, visualizing, bisecting, adding, dividing, estimating, approximating, counting, measuring, graphing, communicating, and connecting. To make matters more difficult, we need to teach math symbols (pictorial) that have double meanings, too. For example, the subtraction operation symbol "-" is also the negative sign. Teaching both content and process words increases the challenge of teaching them well. The teacher needs to know how to use his/her craft well. If math vocabulary is not taught directly and explicitly by educators who know the art and science of teaching, our students will be lost and perhaps become less interested in learning it. Keep in mind that they’re faced with words, processes, numerous abstractions, symbols, and technical representations that are potentially confusing. However, with adequate and appropriate support, encouragement, challenge, and effective instructional strategies, our students will deepen their understanding of math terms and concepts. We will also help facilitate procedural fluency.

How can we help students develop understanding of mathematics vocabulary? What are some of the best practices that we can implement?

Before we learn the ways to support our students, I would like to share this useful website. It is the New York State Education Department website. It contains glossaries that include the necessary mathematical words and terms used in Pre-Kindergarten up to Grade 8. The site encourages educators to use these terminologies constantly and regularly throughout the learners’ stay at school.  


This site also contains the “Suggested List of Mathematical Language by Grade Level.” These lists will assist the educators and students in “building a mathematical language” and it’s recommended that we use it in conjunction with the glossary.

*check back next month for strategies we can use to help students master math vocabulary

If you have a question or comment about this article e-mail Luchie.


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