The reason to reason

Ian talks about empowering students to draw their own mathematical conclusions through conversation.

It’s important to have great maths conversations because they guide students to use precise mathematical language in their reasoning.

When we think of maths, we tend to think of numbers and how we can manipulate them, using logical methods to find definitive solutions. But maths is more than numbers: we need to ensure that we’re providing students with the opportunity to develop precise mathematical language to justify the numbers, methods and calculations they use.

The conversation above was between me and a Year 11 after a mock exam where many students had lost marks in questions that said ‘Give a reason for your answer’. Questions like these, that ask students to ‘Describe’ or ‘Explain’, can stump students who are able to reach the correct numerical answers, but often struggle with (or, in some cases, completely ignore) the requirement to give mathematical justifications for their method and solution. Without this reasoning, the student’s depth of understanding is unclear.

Reasoning skills can be developed in other areas of the maths curriculum, such as transformations for example. I like to challenge pupils to work in pairs to precisely describe transformations, asking questions like “how much information do you need?” and “would someone be able to perform the transformation given the information you’ve written down so far?”. Asking students to verbally criticise each other’s answers gives them the practise they need in using mathematical language precisely before they write their own descriptions down.

Mathematical reasoning shows that students haven’t just stumbled upon the answer or learnt a method by rote, it demonstrates they have a deeper understanding and a solid grasp of mathematical concepts that can be applied to increasingly complex problems. As teachers, we need to guide students through conversation and tease out what detail is needed to answer a question.

These conversations promote the use of precise mathematical language to convey methods accurately and, rather than giving a set of stock phrases to learn, empower students to draw their own mathematical conclusions and increase the possibility of them making new, meaningful contributions to mathematics in their futures.