Mathematical Language

This informal CPD article, ‘Mathematical Language’, was provided by Karen McGuigan, Education Consultant at Maths For Life, who provide a differentiated approach to the maths curriculum that lays down solid foundations, is framed in practical understanding, and delivers the essential maths needed for life.

‘How many blue triangles?’ seems such a simple question. However, to be able to answer it you need to understand what ‘how many’ means, realise that ‘blue’ is a colour and distinguish it from other colours and identify ‘triangle’ as a shape that has three sides and recognise it amongst other shapes. Suddenly the simple question doesn’t seem so simple.

When you say ‘maths’ most people immediately think of numbers. This is quickly followed by that anxious feeling when their brain makes the connection to times tables. But maths is more than numbers and indeed begins long before numbers with underpinning mathematical language.

Maths begins with the development of prenumber skills, which are defined as:

• Making simple comparison
• Identifying same and different
• Matching
• Simple classification

These skills are largely developed through play in the early years and form a part of the Early Years Foundation Stage curriculum delivered at preschool and during the reception year at school. They are assumed to be secure when starting KS1 maths curriculum in year 1. However, the reality is that in many cases this is not the case, and it is necessary to continue to explore and reinforce further as the child gains in life experience.

Mathematical language underpins the understanding of number and number formation: How can we form a ‘5’ with a ‘hat, neck and a big round belly’ if we have no idea what ‘round’ means? How can we draw a ‘7’ as two ‘straight’ lines if no one has ever defined what ‘straight’ means? How can we see that ‘9’ is an upside down ‘6’ if we can’t visualise what ‘upside down’ means?

By ensuring that mathematical language is modelled daily in everyday life, children can visualise, understand, and apply that language to their learning at school.

“Which one is different? That one. Why? Because it’s upside down. Now can you see that a ‘9’ is an upside down ‘6’?”

“Which one is different? That one. Why? Because it is the wrong way around.”

If you visually model the concept of ‘wrong way around’ in enables you to explain to a student how has drawn a mirror image of the numeral ‘5’ that it is the ‘wrong way around’ and they understand what you mean.

We are too quick to move on from prenumber skills. We tick the box on ‘secured’ when a child can do the obvious ‘the same’ and ‘different’ question. However, it is working through the subtle and classification type questions that really cement the language and connections for the future. It is never about the right answer. It is about being able to articulate the why and having the language to support the rational thought process.

Positional language is another topic that isn’t really seen as maths but again underpins a child’s ability to understand a maths question or indeed a basic instruction.

Child to parent, “Mummy, I got into trouble today at school.  Miss Jones told me to go stand behind Maya in the line.  When I didn’t do it, I got in trouble.”

Parent to child, “Why didn’t you go stand behind Maya?”

Child to parent, “Mummy, I don’t know what ‘behind’ means!”

Children often exhibit a natural tendency to follow one another. Reception teachers rely on the older children in the classroom to understand the instructions and for the younger children to follow them. It is assumed that by following the instructions all the children will develop the understanding of what they mean. This isn’t always the case. It is essential to explicitly teach this positional language and ensure that every child understands. 

Positional language is not only used daily in instructions, but it also underpins understanding of maths questions. Think of this question, “How many prime numbers are there in between 10 and 20?”  Even if you know what a prime number is, you can’t answer this question correctly if you don’t understand the meaning of ‘in between’.

When we read an English comprehension or a book, we can get the general gist of the story and context without understanding every single word. We can answer questions and explain what is happening in our own words. In maths it is important to listen and understand all aspects of the question. For example, if we take the question ‘How many boys play football after school on a Wednesday?’ – when we look at the data to select the answer, we must understand that it is only boys, playing football, after school and on a Wednesday that we need to count.

Maths is a series of building blocks and connections. Just like when building a house, you need solid foundations. A key element of this is mathematical language. If we spend more time ensuring that the language of maths is understood in real life, children will have a more secure platform to make the connections in maths. Parents, teachers, teaching assistants can all make a difference by being more aware of mathematical language and using it daily outside the remit of the maths lesson.

We hope this article was helpful. For more information from Maths For Life, please visit their CPD Member Directory page. Alternatively, you can go to the CPD Industry Hubs for more articles, courses and events relevant to your Continuing Professional Development requirements.