# Everyday versus mathematical language

## Everyday versus mathematical words

In mathematics, students move from using less specific or informal language to more specific and formal language.

### Examples of common words

A 'square' is a special 'rectangle', even though students may not initially classify a square as a rectangle

'Sum' might be used informally to refer to a calculation, but students need to learn that 'sum' formally means addition.

This aspect of mathematical language can cause confusion for students as it can create ambiguity between terms used in the mathematics classroom and those used in the context beyond school (Zevenbergen, 2001). There are a range of common words which have different meanings in mathematics compared to everyday use.

## Teaching mathematical meanings

Teachers can explicitly teach mathematical meanings by highlighting and emphasising words that have a distinct mathematical meaning. Scaffolding can then be used to support students to develop meanings for words in context and also be more precise with their use of words in explanations and forming questions (Adams, 2003).

Teachers can:

• Explain to students that technical terms in mathematics are sometimes words that they know from everyday language but that their use in mathematics is more formal, more specific and sometimes quite different.
• Give an example word (see below for some examples).

Have you seen this word before?
What does it mean in everyday language?
What does this mean in the maths classroom?

• Ask students to work in pairs using online references to either, complete the table for the words you have chosen, or to choose their own words to explore.

### Common examples of words with different meanings

An example below could be used in a Year 9 class on statistics (VCMSP326). The definitions come from the Victorian Curriculum F–10: Mathematics glossary.

Example
Word
Everyday (dictionary)
Mathematical definition (from Mathematics Glossary)
mean
nasty

Also called the average. The sum of values in a data set divided by the total number of values in the data set. For example, if a data set consists of the values  then the mean  is defined as:

For example, for the following list of five numbers {2, 3, 3, 6, 8 } the mean equals

average

ordinary or even less than ordinary

Average: Also called the mean. (see above)

median

The strip of land in the middle of a major road that is between the lanes going in opposing directions; a central reservation.

The median is the value in a set of ordered data that divides the data into two equal parts. It is frequently called the 'middle value'. Where the number of observations is odd, the median is simply the middle value. For an even set of elements, the mode is taken to be the average of the two middle values. For example, the median of the numbers 1, 3, 4, 5, 7 is 4, while the median for 1, 3, 4, 5 is the average of the two middle values, that is
(3 + 4) ÷ 2 = 3.5.

The median provides a measure of location of a data set that is suitable for both symmetric and skewed distributions and is also less sensitive to outliers than the mean.

arc

​ark (homophone), a boat or ship

The arc is part of a circle's circumference

chord
cord (homophone), a thin flexible rope

The chord is a line segment joining two points on the circumference of a circle or on a curve

pi

pie (homophone), a baked dish

Pi is the ratio of the circumference of any circle to its diameter

The strategy above can also be applied to support student understanding of mathematical words that sound the same as everyday words with other meanings (homophones) (Adams, Thangata & King, 205).

Definitions for the mathematical terms have been taken from the Victorian Curriculum F–10 Mathematics Glossary.