# 5 ways to improve mathematical reasoning

As I travel far and wide, training and talking to teachers, common questions occur…

How can we improve the mathematical reasoning skills of our pupils and how can we support them as well as gather evidence for it?

To address these questions, firstly, we need to understand what mathematical reasoning is and understand why it is such a vital skill that needs to be cultivated.

1 – What is Mathematical reasoning?

Mathematics helps us all to make sense of the world in which we live as we go about our daily lives. Reasoning is part of a much wider set of skills that are required to help us to develop mathematically and allow us to think critically. To do this successfully, we must continually gather and interpret information to solve problems and make informed decisions based on what we know. We must then plan, organise and communicate our ideas effectively. Therefore, reasoning skills should be cherished and be an integral part of learning for our children, rather than a bolt on at the end.

The ability to communicate lies at the heart of reasoning and again this is something that, as teachers, we need to really encourage.

2 – Developing discussion

A strategy I often use with children is giving them permission to “Brain Talk.” Through establishing a culture whereby discussion is valued and seen as an important contributor to cognitive development, I incorporated this rigorously into part of my maths lessons. Giving the children opportunities to talk to their partners or to a wider audience by asking about what they notice, what they wonder and asking key questions like What is the same?, What is different?, What if…, Prove it/ Convince me… and getting them to investigate and demonstrate using manipulative resources or pictorial representations allowed the children to come up with some fantastically creative ways to demonstrate their understanding and justify their thinking. It gave them opportunities to suggest hypotheses and make conjectures in a non-threatening way. I found that they were keen to show off that they could use the appropriate mathematical language and symbols, introduced and displayed up on the working wall, and they began to gain confidence in their own judgements and decisions that were based on validated reasons or evidence.

3 – Getting terminology right

Something I have come to appreciate is that, as a school, it is vital that there is a consistent approach to the mathematical terminology being used by both staff and children in their reasoned mathematical discussions. Otherwise children can become quite confused if this is something that is chopped and changed between classes or year groups. Have you had staff discussions about whether to use “ones or units, exchange or regroup” etc.? There needs to be a coherent approach throughout the school and to aid this; it is worth including a glossary to your calculation policy or developing a simple maths dictionary that can be referred to. I have also found it beneficial sharing these with parents who can be rather overwhelmed with “how different maths is to when we were at school!”

4 – Building test skills

Reasoning is a major part of the mathematics National Curriculum and is tested in separate papers at the end of Key Stages. Therefore, it is vital to give children plenty of practice at being able to answer these types of questions and prepare them for these tests in similar conditions. It is equally important that when the pupils do them in May, they see them as part of the normal assessment process. I found it most beneficial to phase in and build up to the tests by giving the children plenty of practice over the course of the year in the form of quizzes, spot the mistakes, mark these, paired brain talk and group presentation exercises to eventually build up to “flying solo” tests. The children really enjoyed these “Let’s see what you can do” sessions and so when the time came for the actual tests, they were very keen to demonstrate exactly what they could do. Numicon Test Practice Questions can help with this preparation.

5 –  Supporting Parents

Why not hold an informal evening with parents? By doing so for my Year 2 and Year 6 pupils, I explained what the tests were and this helped to get them fully on board. They were always keen to do all they could, and it was important that they were informed about the best way for them to help and support their children. They need to be made aware of all the strategies they can encourage at home to get their children to reason and talk mathematically. For general maths support visit Oxford Owl for Home.

Tracy is a highly-experienced educator, having worked for over 30 years in the primary classroom with children across the whole primary phase. She was an Advanced Skills Teacher with a proven track record for supporting school improvement and now she is an Independent Primary Maths Adviser under the name of Mathsknowhow, working throughout the UK and internationally.

She supports LAs, senior leaders, teachers, subject leaders, teaching assistants, parents and governors to create mathematical environments which engage all children. She is passionate about the effectiveness of using the CPA approach and using manipulative resources and pictorial representations in mathematics, and it has always been the best part of her practice.