Are your primary maths lessons too quiet? Ahead of her upcoming workshop on strengthening talk in primary maths, NACE associate Sarah Carpenter explains why effective discussions are key to deepening and extending learning in this core subject. 
 
Often there’s an assumption that primary mathematics is about numbers, concepts, operations – and not about language. But developing the language of maths and the ability to discuss mathematical problems is essential to help learners explore, reflect on and advance their understanding.
 
This is true for learners of all abilities. But for more able mathematicians in particular, regular opportunities to engage in talk about maths can hold the key to deeper, more secure understanding. Moving away from independent, paper-based work and the tunnel-vision race to the answer, discussion can be used to extend and deepen learning, refocus attention on the process, and develop important analytical, reflective and creative skills – all of which will help teachers to provide, and learners to be ready for, the next challenge.
 
If you’re still not sure why or how to use discussions effectively in your primary mathematics lessons, here are five reasons that will hopefully get you – and your learners – talking about maths… 

1. Spoken language is an essential foundation for development. 

This is recognised in the national curriculum: “The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. 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.” – National curriculum in England, Department for Education, 2013
 
Or to put this another way, when else would we expect learners to write something if they cannot say it? As Anita Straker writes: “Sadly, children are frequently expected to write mathematics before they have learned to imagine and to discuss, and those who do not easily make connections are offered more pencil and paper work instead of vital talk and discussion. Yet in other subjects it would be unthinkable to ask children to write what they cannot say.” – Anita Straker, Talking Points in Mathematics, 1993

2. Practice is needed for fluency… 

… and fluency is what the new SATs expect – not only in numbers and operations, but in the language of mathematics as well. For mathematical vocabulary to become embedded, learners need to hear it modelled and have opportunities to practise using it in context. More able learners are often particularly quick to spot links between mathematical vocabulary and words or uses encountered in other spheres – providing valuable opportunities for additional discussion which can help to embed the mathematical meaning alongside others.
 
Free resource: For assistance in introducing the right words at the right stage to support progress in primary maths, Rising Stars’ free Mathematical Vocabulary ebook provides checklists for Years 1 to 6, aligned with the national curriculum for mathematics.

3. Discussion deepens and extends mathematical thinking. 

The work of researchers including Zoltan Dienes, Jerome Bruner, Richard Skemp and Lev Vygotsky highlights the importance of language and communication in enabling learners to deepen and extend their mathematical thinking and understanding. Beyond written exercises, learners need opportunities to collaborate, explain, challenge, justify and prove, and to create their own mathematical stories, theories, problems and questions. Teachers can support this by modelling the language of discussion (“I challenge/support your idea because…”); using questioning to extend thinking; stimulating discussion using visual aids; and building in regular opportunities for paired, group and class discussions.

4. Talk supports effective assessment for learning. 

More able learners often struggle to articulate their methods and reasoning, often replying “I did it in my head” or “I just knew”. This makes it difficult for teachers to accurately assess the true depth of their understanding. Focusing on developing the skills and language to discuss and explain mathematical processes helps teachers gain a clearer picture of each learner’s current understanding, and provide appropriate support and challenge. This will be an ongoing process, but a good place to start is with a “prior learning discussion” at the beginning of each new maths topic, allowing learners to discuss what they already know (or think they know) and what they want to find out.

5. Discussion helps higher attainers refocus on the process. 

More able mathematicians often romp through learning tasks, focusing on reaching the answer as quickly as possible. Discussion can help them to slow down and refocus on the process, reflecting on their existing knowledge and understanding, taking on others’ ideas, and strengthening their conceptual understanding. This slowing down can be further encouraged by starting with the answer rather than the question; asking learners to devise their own questions; pairing learners to work collaboratively; using concept cartoons to prompt discussion of common misconceptions; and moving away from awarding marks only for the final solution.
 
During her 20-year career in education, Sarah has taken on a variety of roles in the early years and primary sectors, including classroom teaching, deputy headship and local authority positions. After a period as literacy and maths consultant for an international company, she returned to West Berkshire local authority, where she is currently school improvement adviser for primary maths and English. As a NACE associate, Sarah supports schools developing their provision for more able learners, leading specialised seminars, training days and bespoke CPD.