Teaching Math Terms & Vocabulary

What Research Tells Us About Vocabulary Instruction

  • Direct instruction of vocabulary improves comprehension
  • Robust vocabulary instruction has these characteristics (Beck & McKeown 2002):
    1. Rich information about words and their uses
    2. Frequent and varied opportunities for students to think about and use words
    3. Enhanced student language comprehension
  • To learn a new word, students without a learning disability require 10 – 11 exposures to the word. Students with a learning disability require as many as 40 exposures to the word.

What Research Tells Us About Vocabulary Instruction

An understanding of math terms is crucial to students’ ability to understand and execute math problems. In order to support students’ comprehension of math terms, some vocabulary instruction practices may be useful. In particular, instruction of math terms and vocabulary should include (Allen, 2007):

  • Discussion and repeated exposure to the conceptual base of each term
  • Active exploration of examples for each term
  • Active exploration of the differences between terms

One instructional strategy to adopt and adapt is the Frayer Model (Allen, 2007). This strategy helps students learn new concepts through the use of attributes and nonattributes. Students learn a concept by seeing examples and non-examples of the concept. Here are the steps:

  1. Define the concept by showing the properties of the concept.
  2. Show students how this concept differs from other similar concepts. (Highlight non-critical properties.)
  3. Give examples and explain why these are examples.
  4. Give non-examples and explain why these are non-examples.
  5. Give students examples and non-examples and ask them to decide whether they are examples or non-examples.

Here’s an example of the Frayer Model, using a graphic organizer.

Define the concept

A rational number is a fraction. It is made by dividing one integer by another integer.

Define how the concept is different from similar concepts…
Irrational numbers are numbers that cannot be written as fractions. They can be written as non-repeating, non-terminating decimals.
Examples of the concept are…
4/1, 2/3, 5/8, 7/3, 1/16, 8/12
Non-examples of the concept are…
Pi = 3.1415….
Create your own example to help you remember the concept…


Allen, J. (2007). Inside Words: Tools for Teaching Academic Vocabulary. Portland: Stenhouse Publishers.

Beck, I., McKeown, M., Kucan, L. (2002). Bringing Words to Life: Robust Vocabulary Instruction. New York: Guilford Press.