Here we share 5 simple lesson activities that can make a real difference to pupils' confidence and skill in talking Mathematically in class. As your pupils develop their talk for Maths, 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 vocabulary 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.

#### 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”.

#### 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 vocabulary?

#### 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.

#### 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.

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.