Using Maths Vocabulary to Develop Fluency & Reasoning

Here we share 5 simple lesson activities that can make a real difference to pupils’ confidence and Maths vocabulary at KS2.

As your pupils develop a variety of Maths words terminology, they will also progress in their reasoning skills – and provide lots of evidence for you to identify. The days of no talking in lessons are long gone thank goodness! Instead, the challenge now is to encourage children to talk mathematically, using the right vocabulary, in the right contexts.

Maths vocabulary

Mathematics is a language – one of symbols and numbers. It is also expressed and explained through written and spoken words. For our pupils to become great mathematicians it is essential that they are able to recognise, understand and apply a wide range of vocabulary.

Whilst this maths language may seem simple to us, remember the average child will have started primary school with a receptive vocabulary of 2,100 – 2,200 words. By the time they leave at the age of eleven, this will have increased to about 50,000. They have lots to learn during their time in primary school and it is no wonder at times they may struggle to link mathematical concepts, symbols and new vocabulary together.

The Third Space Learning model of intervention is highly personalised and this enables each of our tutors to ensure that the correct level of Maths vocabulary is being used for each pupil. Specialist Maths tutors provide affordable 1-to-1 tuition to the pupils who most need individualised support whether to support them to working at ARE, or to stretch and challenge. The Maths Hub of fluency, vocabulary and problem-solving resources, CPD and assessment is then available to the class teacher to plan and deliver mastery led Maths lessons to the rest of the class.

Maths vocab can create stumbling blocks in applied learning

As teachers, we can all think of those moments in class, when having taught a topic for days or weeks, a child is stumped as soon as they are given a word problem which they have to apply their learning to. One of the main reasons a child may struggle in this situation is the difficulty with understanding language and vocabulary. Sometimes it is a problem with new and unfamiliar words, sometimes it is learning that familiar words can have a different meaning in a mathematical context.

For example, a pupil may describe the difference between 7 and 23, as “one has straight lines and the other has curved lines”. In this situation, the teacher clearly needs to reinforce the meaning of the word, “difference”.

Mathematical reasoning

Another situation often encountered is when a child can quickly calculate the answer to a challenging problem but when asked to explain their answer, replies “I dunno, I just did it in my head.”

While it is encouraging that the pupil in question can confidently find the answer, they need to be able to explain their thinking. This is a key skill in mathematics and the 2014 National curriculum specifically states that pupils must learn to “reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language”.

To find out more about how reasoning and fluent mathematical vocabulary can have a positive impact on pupil progress, read our blog on the interactions between Fluency, Reasoning and Problem Solving.

Reasoning is also a key aspect of the SATs – the maths SATs have two papers devoted to it (compared to one for arithmetic), and these papers feature multiple different types of reasoning-based questions for pupils to recognise and work on. Our blog of 35 Year 6 Maths Reasoning Questions pulls apart each of these question types, explaining how pupils should approach them and what steps may be required to solve them.

Tools for the teacher

It is evident that a rich spoken language environment should be a key element included in any successful maths lesson. What’s more, its positive impact is not limited to the maths lesson and has an influence on a pupil’s cognitive, social and linguistic development across the whole curriculum.

So, in the primary classroom, what can we do to help our pupils understand new maths terminology?

1. Introduce new key vocabulary at the start of a topic

Plan the introduction of new words from the new curriculum in a suitable context, with relevant real objects, mathematical apparatus, pictures and/or diagrams, explaining their meanings carefully. Some topics lend themselves more easily to this, such as using cakes or pizzas to demonstrate fractions, but it is important to be creative and find an interesting way of firing the imagination for every topic.

UPDATE: One of the best ways to introduce new vocabulary into the classroom is through a Maths vocabulary list. Take a look at ours which contains the 96 key words every pupil needs to know by year 6 as a source of inspiration. This is a very versatile resource that you can use in any way you wish, from using each page as a Maths vocabulary poster through to using it as a diagnostic tool to test gaps in pupils knowledge. We are always interested to see the ways teachers use our resources, so get in touch and let us know how you use this Maths Vocab List in your classroom!

2. Make talk partners a routine element of a lesson

Talk partners are a super way to get children using mathematical vocabulary, providing the opportunity for every pupil to engage in in mathematical discussion in response to open questions. Allocating each child a set partner at the start of a term or unit of work ensures time is not lost in lessons and allows you to carefully match pupils, ideally pairing more confident and able learners with those who need a bit more support. Bear in mind that children need to hear how vocabulary is used effectively before they have a go themselves.

3. Allow time and space for pupils to engage in mathematical conversations

As maths teachers we are familiar with the importance of scaffolding work to support learners and guiding pupils through a process to find a solution. Yet at the same time we need to make sure that we give children the time and space to construct solutions for themselves through talk.

Maths Vocabulary List

A simple and easy to use resource that can help your pupils improve their knowledge of crucial Maths vocabulary to help them prepare for SATs in Year 6.

The key word is conversation. This should be a two way process, involving the pupil, as well as the teacher, and we need to be careful that we do not end up wasting any valuable one to one time, for example:

Teacher: “How have you done these?”

Pupil: [writes out calculation]

Teacher: “Oh, I see, you’ve put the numbers underneath each other”

Pupil: [nods]

Teacher: “Ah and then you added them”

Pupil: “yes”

The teacher has tried to check their understanding and response but a vital opportunity for developing his vocabulary and language has been missed. It is important to avoid the temptation to control the communication in order to get to a mathematical end that you have predetermined, but encourage mathematical thinking instead.

4. Always ask How and Why

The conversation in the example above could have been vastly improved by making use of these two simple words: how, and why. These questions encourage pupils to verbalise their understanding of a concept and develop their reasoning skills. Struggling pupils could be supported in their responses by giving them a word bank to refer to when answering. One of the luxuries we have during our one-to-one Maths lessons in school is that our tutors have the time to explore children’s answers and always probing for further explanation and reasoning.

Find out more about how our tutors use Maths talk to develop reasoning in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

5. Ask open questions

Asking closed questions limits the scope of a pupil’s response to a correct or incorrect answer and deprives them of the opportunity to talk through their thinking. By using open questions we encourage pupils to explain the steps they have made and make use of any new maths vocabulary they have learnt. It can be helpful to develop a bank of effective questions to refer back to at any time in lessons.

This blog has introduced us to the challenges that mathematical vocabulary and language can present to our pupils and some ways you can make it easier for them. Have a read of Talking in Maths Lessons [Part 2], which includes 5 tried and tested ways to engage your lower ability KS1 and KS2 pupils with mathematical language.

What strategies do you use to develop your pupils’ mathematical language in your own classroom?

Maths teacher and expert John Dabell discusses in his blog “Why KS2 Maths Terminology Matters” how he develops his pupils understanding of the often complicated terms that can be found in the Maths classroom, so check it our for inspiration.

David Leighton
David Leighton
Third Space Learning
Content Team
A former secondary teacher, David writes blog posts and Maths resources as part of the content team.
Downloadable resource

Maths Vocabulary List

A simple and easy to use resource that can help your pupils improve their knowledge of crucial Maths vocabulary to help them prepare for SATs in Year 6.

Download Now
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Downloadable resource

Maths Vocabulary List

A simple and easy to use resource that can help your pupils improve their knowledge of crucial Maths vocabulary to help them prepare for SATs in Year 6.

Download Now