The full effects of lockdowns and reduced social contact during the pandemic have yet to be fully understood. But already some teachers are reporting that the children they teach are less verbal and less articulate than in previous classes they have taught, particularly in Key Stage 1. In this article, we look at practical ideas for improving mathematical talk in the classroom and suggest some resources.

Expressing mathematical ideas orally helps children to build communication skills. It can also form an important part of developing understanding of mathematical concepts and the ability to reason mathematically.

Teaching children specific mathematical vocabulary encourages precision, giving pupils a door on the world of the mathematician. It also supports those with English as an additional language to participate on equal terms with their English-speaking peers.

Eavesdropping on pupils’ mathematical conversations will give you essential insight into their conceptual understanding and allow you to pick up misconceptions that may be causing more widespread problems. It also gives an opportunity to share great insights you overhear with the whole class.

Teachers in our regular Tuesday night Twitter chat, on 15 March 2022, discussed the question,
How do you help KS1/2 pupils become competent communicators about mathematics? The suggestions below are taken from the conversation.
(A related chat among secondary teachers followed a fortnight later, How do students learn to communicate clearly and effectively in mathematics?)

1 Create an expectation of mathematical talk

Mathematical talk is not something that can be expected of pupils occasionally or suddenly – it takes practice, and the expectation needs to be built up over time. The following are suggestions that can help build that expectation:

Some teachers suggest that choral repetition of whole sentence answers can help pupils to engage better with more independent mathematical talk, by modelling and giving them the tools they need to begin to construct their own sentences. Setting an expectation of full-sentence answers, even to short, closed questions, can develop some of the skills and confidence needed to respond orally to more complex mathematical problems.

Opportunities to talk about something other than ‘the answer’ can create a more discursive atmosphere and reduce inhibitions by removing the anxiety of being ‘wrong’. For example – classifying, comparing, focusing on method rather than solution. Questions such as ‘What do you notice?’ or ‘What do you think would happen if…?’ can be useful.

Younger children need more scaffolding and support with mathematical talk. Some Year 6 teachers reported that talk happens much more spontaneously in their classrooms after pupils have become accustomed to mathematical talk over a number of years.

2 Introduce vocabulary

In order to effectively develop mathematical talk, pupils will need to acquire mathematical vocabulary. Teachers in our chat were strong advocates of using technical and precise mathematical language and introducing this very explicitly to their pupils, carefully planning its introduction and use.

Mathematical terms can be fun for children to learn to use correctly and can be an opportunity for a bit of historical or etymological exploration and good stories! Examples include equation, addend, subtrahend, subitise and calculate. See below for suggestions of mathematical dictionaries or search ‘etymology/history of…’.

Beware of words that are often used imprecisely and can therefore cause confusion: words such as sum (when used generically beyond addition calculations), equals, average, and half.

Beware also of words that have a meaning in English that is different from or less precise than the mathematical meaning: words such as takeaway, mean, difference, adjacent, factor, negative and range.

The Frayer model is a graphic organiser that can be used to introduce and embed understanding of new vocabulary (see link in resource list).

3 Support children in beginning mathematical talk

Generic sentence starters can help give a structure in which children can express their ideas. Examples might be ‘I agree because…’/ ‘I disagree because…’/ ‘If I know…, then I know…’.

Stem sentences are more specific to the maths being learned but give children a clear ‘full-sentence’ structure in which to put their own answers. ‘This is the number 42. The 4 shows we have 4 groups of ten. The 2 shows we have 2 extra ones.’ is an example (when learning about place value in Year 2 – sentence taken from the DfE 2020 maths guidance p.51).

The teacher modelling an oral answer to a question is also a powerful way to demonstrate expectations. ‘My turn, your turn’ is one method for doing this: the teacher first models the answer to a question and then asks pupils to answer a question with a very similar structure, gradually building up the complexity of questions.

4 Encourage more reluctant talkers

‘Think, pair, share’, where pupils first get a chance to try their ideas out with a partner, can increase confidence in sharing with the class. When the idea is shared more publicly, because it is ‘our idea’ rather than ‘my idea’, this can feel less exposing to the contributor.

Asking an individual ‘What might someone say in response to this question and why?’ can also give children confidence to express an idea they are unsure about, or to identify potential misconceptions.

Drawing other pupils into a discussion that has been started by a more vocal child can help create a climate of discussion and allows the less confident child to comment on a response already given. Use prompts such as ‘Do you agree/disagree?’, ‘Could anyone explain it a different way?’, and ‘Did anyone get the answer another way? How? Which is easier?’.

Want to explore mathematical oracy further?

Many Maths Hubs have active professional development Work Groups learning about and trying out oracy techniques in their own classrooms. To find out more about this project you can read the third case study in our feature on research and innovation. Or contact your local Maths Hub to find out if they can offer any support to develop mathematical oracy in your school.

Resources

The resources below were recommended for supporting mathematical oracy by teachers in the Twitter chats.

Recommended for further exploration of mathematical talk

• Making Number Talks Matter is a YouTube discussion between two teachers from California, in which they offer advice, and suggest strategies and tasks, to help pupils become confident communicators in mathematics.
• Private talk, public conversation (Mike Askew, King’s College, London) explores how to make mathematical discussion more meaningful, particularly through pair work followed by class discussion.

Recommended for introducing mathematical language

• NCETM Mathematics glossary for teachers in Key Stages 1 to 3 from 2014
• Illustrated Mathematics Dictionary (mathsisfun.com)
• Frayer Model, part of a teacher-training website developed in Texas, containing examples of Frayer Models (graphic organisers) and guidance about ways of using them effectively.

Recommended for finding stem sentences to support learning and oracy

• Mathematics guidance: key stages 1 and 2 (DfE 2020): the pale blue ‘Language focus’ boxes provide ideas for stem sentences and vocabulary to be used in each topic area.
• Stem Sentences is a part of the Enigma Maths Hub website, providing examples of stem sentences and ways in which they may be used.

Recommended for promoting discussions wider than ‘the answer’

• Which One Doesn't Belong? (WODB) is a Canadian website that complements the book Which One Doesn’t Belong – A Shapes Book by Christopher Danielson. No answers are provided for any of the many thought-provoking ‘puzzles’ that it contains because, for each ‘puzzle’, there are many different, correct ways of choosing which one doesn’t belong. This can support discussion, reason and argument without the focus of a ‘correct’ answer.
• Rhombus vs Diamond is an illustrated blog, about using WODB examples effectively, by a teacher from Delaware, USA.