Guide to Mathematical Vocabulary - For Comprehending and Solving Word Problems - Using and Teaching a Menu of Routines

Sep 28, 2026

Uploaded by dabgoudw

A practical guide focused on mathematical vocabulary development for teachers and students, emphasizing comprehension through strong word knowledge. It explains why vocabulary knowledge predicts understanding, argues against a single teaching method, and introduces a reusable “menu” of routines built from a word list. Guidance includes starting with a word list, using targeted activities (e.g., barrier games, word walls), and applying tiered vocabulary instruction across tiers one to three. It also details direct methods: explanation, student restatement, representation, refinement, peer discussion, and spaced practice, supported by research and a reference list.

LanguageEnglish

CategoryExam

FormatPDF

Pages32

Reading Time1 h 21 min

AccessFree to download

Using this Guide

Menu-based routines

Starting Point: A Word List

Teaching Vocabulary

Tier One, Tier Two, Tier Three

Direct Methods

The six steps for learning vocabulary

Opportunities for discussion and spaced practice

Summary

References

A Guide to... MATHEMATICAL VOCABULARY For Comprehending and Solving Word Problems About: Vocabulary Vocabulary knowledge is a predictor of comprehension ability. Hirsch and Nation (1992) indicate that students need to know between 90 to 95 % of the words in a text in order to comprehend the text* . There is no “one method” for teaching mathematics vocabulary. In this guide we present a collection of routines that may be used over and over which we call a ‘menu’. Once you (the teacher) become familiar with the routines you will find that you can easily differentiate the activities to meet the needs of your class. *It should be noted that they were discussing general reading and not the technical type of reading required in mathematics and science where the text is dense. If anything, the requirement for mathematics may be even higher. Starting Point: A Word List Purpose: To begin, you need a word list. Material: My Word Book Mathematics contains appropriate word lists by year level You’re not required to use our word list to use this guide. See also: A free set of NAPLAN word flash cards for Year 3 can be found at [www.drpaulswan.com.au/maths-topics](www.drpaulswan.com.au/maths-topics). [NAPLAN word flash cards for Years 5 & 7 are available to buy at](NAPLAN word flash cards for Years 5 & 7 are available to buy at www.drpaulswan.com.au/shop)[ ](NAPLAN word flash cards for Years 5 & 7 are available to buy at www.drpaulswan.com.au/shop)[www.drpaulswan.com.au/shop](NAPLAN word flash cards for Years 5 & 7 are available to buy at www.drpaulswan.com.au/shop). Question 1: do you have a word list? Question 2: do you use it? Having an exercise bike and using one are two different things. This guide is about using the word list. Guide to Mathematical Vocabulary © P. Swan & D. Dunstan Page 1 [www.drpaulswan.com.au](www.drpaulswan.com.au) ... Using this Guide This guide is set out around the idea of a ‘menu’. You pick items off of a menu based on your needs. The menu is presented in a general order, starting with simply exposing the children to the words, moving through using the words and ending with defining the words. All items on the menu draw on the same ‘ingredients’ -the word list. Your students might know most of the vocabulary related to number, so you may want to use the Knowledge Rating Scale to assess and check, proceeding as needed. However you may know that their geometry vocabulary is lacking, so you could begin with a Barrier Game or a Children’s book. It is recommended that you use a combination of several activities to build the students’ mathematical vocabulary. Teaching Vocabulary Beck, McKeown, and Kucan (2002) outline three tiers of vocabulary that need to be taught. Tier One Everyday words that students generally come to school with or words they learn in the early years\# . Tier Two Words that are more academic but not specific to any one discipline. Words like analyse or evaluate would qualify as a Tier Two words. Tier Two words tend to receive less attention because they do not belong to anyone discipline. Tier Three Words that are content specific words, such as ‘hypotenuse’, that Marzano (2004) would call academic vocabulary. Tier three words are typically used only in the school or University setting, hence why they are referred to as academic vocabulary. Direct Methods Marzano (2004) suggests six steps when learning vocabulary: 1. The teacher provides an explanation or example/description of the word or phrase in simple terms. The Junior Illustrated Dictionary provides some support. Note the definitions used here are less formal than Maths Terms and Tables 2. Students restate the description in their own words. Students using the words and describe them \#Students whose first language is not English could have gaps in their knowledge here and will need assistance. Guide to Mathematical Vocabulary © P. Swan & D. Dunstan ... 3. Student

FAQs

Why is vocabulary knowledge important for solving mathematical word problems?

Vocabulary is an essential element of solving word problems. Strong word knowledge supports comprehension, and mathematics can demand even higher vocabulary requirements due to dense text.

What is the “menu” approach described in the guide?

The guide presents a collection of reusable routines called a “menu.” Teachers select items from the menu based on class needs, starting with exposing children to words, then using them, and finally defining them.

How does the guide suggest teaching vocabulary using tiers?

It outlines three tiers: Tier One everyday words students come to school with, Tier Two more academic general words, and Tier Three content-specific academic terms like “hypotenuse.” The guide recommends teaching across these tiers.

What are Marzano’s six steps for learning vocabulary, according to the guide?

The steps include: teacher provides a simple explanation or example; students restate in their own words; students represent the term through drawing or other representations; teacher expands and refines word use; students discuss words with peers using spaced practice; and strengthening word knowledge through repeated menu activities.

Sep 28, 2026

Uploaded by dabgoudw