# The value of precise mathematical vocabulary

The national curriculum requires that children use mathematical language. It states that ‘the quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof’.

In each phase there is reference to children using mathematical vocabulary. This article, written by Mathematics Adviser Caroline Clissold, outlines the value of using precise mathematical vocabulary and offers some useful background information and ideas for your classroom.

We are often told that to achieve mastery in mathematics children need to use precise mathematical vocabulary. But what is the precise mathematical vocabulary that we should use? Over the years vocabulary posters have been produced and displayed in classrooms around the country that show numerous words for addition, subtraction, multiplication and division. These days I often think that we introduce too many words which prevent most of the children developing the precise vocabulary that they need.

Over the last year or so, precise vocabulary used in higher performing jurisdictions around the world has started to be used in some of our English classrooms. It would be helpful for the children we teach if we all used the same terminology. Most of these words are based on Latin terms. It is really interesting exploring them and discovering their roots. The purpose of this article is to introduce you to some of them and for you to consider using them with the children.

For addition, precise terms include: augend, add, addend, equal and sum. Augend is the amount that you start off with, addend is what you add to it and sum is the result. Augend comes from the Latin augendum, a thing to be increased. Addend comes from the Latin word addendum which is an addition made to something. Sum comes from the Latin word summa, which means highest. You can see how these words make sense in mathematics!

The precise terms for subtraction are minuend, subtract, subtrahend, equal and difference. Minuend stems from the Latin minuendus which means to be diminished or make smaller. Subtrahend comes from the Latin subtrahendum which means to delete from a list or take away. The difference, from the Latin word differentia meaning carrying away, is the result of the subtraction.

In multiplication the precise terms are: multiplicand, multiplied by, multiplier, equal and product. Multiplicand comes from the Latin word multiplicandus which means to be increased or multiplied. Multiplier is the number you are multiplying by and product is the result of the calculation.

Dividend, divided by, divisor, equals and quotient are precise terms for division. Dividend comes from the Latin dividendum which is an amount to be divided into groups. Divisor is the number by which another number is divided. Its original Latin word was divider. Quotient comes from the Latin word quotiens which means ‘how many times’.

Have you ever heard the term ‘the bus stop method’ in relation to the short written method for division? Division has nothing to do with bus stops. The lines around such a calculation are called the division bracket, which makes a lot more sense.

Commutative is another word that children need to understand and begin to use. Commutativity is an important part of addition and multiplication. If they understand this they would only need to learn half of their number facts and multiplication tables.

In place value it would be worth introducing the terms positional, multiplicative and additive to help the children understand these key areas of place value. It would also help to explain that our number system increases and decreases in powers of 10.

When dealing with fractions we need to be specific about the terms used when this area is introduced to children. Often in KS1 we call the numerator the top number and denominator the bottom number. Year 1 children are used to calling specific parts of words by their correct names, for example phoneme and grapheme. So they should be introduced to numerator and denominator as correct vocabulary. The line that separates the two is a vinculum, which in Latin means ‘bond’.

When working on ‘greater than’ and ‘less than’ it is important to teach mathematical ways to remember how to use them. I know of publications which show crocodiles eating larger numbers. Again this is not mathematical. I saw this example, used in Shanghai, of how to demonstrate this mathematically:  You can see clearly here how 2 is less than 4 and 4 is greater than 2 – and there is no crocodile in sight!

The equals sign is a symbol of equality which the children often misconceive to be the answer to a calculation. It is important from the start that they understand its meaning. 2 clearly doesn’t equal 4, but what could we do to the 2 or the 4 so that they are equal?  We could subtract 2 from 4 or add 2 to 4!

Using precise vocabulary is important. Why not try introducing your children to the terms discussed in this article?