The Language of Math: Using SWI to teach Math Vocabulary

written by: Nancy Martin, EHS Reading Department Chair

Listen to Nancy Martin read her blog

During the past two school years in the Reading Department, we have been using Structured Word Inquiry (SWI) as one approach to helping our students better understand how the written language works.
SWI is a linguistically-based approach where words are studied in context versus isolation. Using scientific inquiry to study spelling instruction, SWI always starts with a word’s meaning, and is taught using explicit multisensory instruction. It dovetails well with our educational philosophy at EHS in that it teaches and reinforces critical thinking, and it can be individualized and organic because learning is based upon student interest.

SWI has a process that begins by asking 4 questions:

  1. What does a word mean? (here we look at the definition of the word in the context in which it is being used)
  2. What are its relatives? (here we study the etymology or history of the word to learn where it came from and to which other words it might be related)
  3. How is it built? (here we look at the morphology or structure of the word. What is the base element that holds the main meaning? Does it have any prefixes or suffixes?)
  4. How does its pronunciation construct mean? (here we look at the phonology or sounds of the letters to see if they may change sounds in different variations of a word).

In one reading tutorial class this year, the students and I have been studying words related to math. Students sometimes have issues in math (or other academic issues) simply because they do not understand the language or terminology being used. By connecting discipline specific terms to a greater context, this sometimes creates greater understanding. Some of the math terms we have investigated include fraction, numerator, denominator, equation, operation, addition, subtraction, multiplication, and division. Here are a few interesting findings we have discovered: Most students know that the word fracture means a broken bone. They also know what a fraction is, but may have a more difficult time defining the term. Both come from the same base fract which means “break”. Knowing this helps in understanding that a fraction is less than a whole number. Also in the same family is frag as in fragment and fringe as in infringement. All come from the Latin root frangere. By investigating one word, students are exposed to many more. Understanding a connection to related words helps us remember their meanings and possibly determine potential meanings of unfamiliar words. For example, the base of equation is equ which means “even or fair”. Two sides of an equation equal (also a word in the same family). However, a more surprising related word is adequate. Something that is adequate meets ones needs. It’s not great, it’s not awful, but more in the middle or fair.
The base of addition is one letter: d and it means “give”. The word is built as follows:

ad + d + ite/ + ion –> addition


The words numerator and number are from the same word family. The word number is a free base, meaning it can stand on its own with no other morphemes (units of meaning) required to make an English word. The base of numerator is a bound base, which requires additional morphemes to make an English word:

numer + ate/ + or –> numerator

The base of denominator is nome which means “name”. In a fraction the numerator is a “count number” and the denominator “names the whole of the group”. Other words in this family include denomination and nominate. I have heard SWI described as a way to “learn one word and get many free”. When we illuminate language for students with language processing issues, concepts suddenly make more sense. Math (and other disciplines) become more understandable, and students exponentially increase their vocabulary. Students may begin to see cross-curricular connections as their discipline-specific vocabulary and understanding deepens.

Here are some more illustrations created in class using SWI to understand the language of math: 


add subtract


numerator denominator

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