Fluency, reasoning and problem solving in primary maths

Sian Evans
25th May 2017
primary maths, maths mastery, fluency, reasoning, problem solving, ks1 maths,ks2 maths, white rose maths hub, mathematics mastery

Develop fluency, reasoning and problem solving within any topic as part of a mastery approach

The skills of fluency, reasoning and problem solving are well-known to all primary maths teachers. In mastery teaching, they play an essential role in helping pupils to gain a deeper understanding of a topic. But what does this look like in practice?

For more information on mastery, check out this handy introduction.

Firstly, problem solving is at the heart of mastering maths. While there is nothing new about using problem-solving questions to consolidate understanding, mastery gets teachers to rethink the traditional lengthy word-problem format. Instead, problem-solving questions are often open-ended, with more than one right answer. 

Problem solving is an important skill for all ages and abilities and, as such, needs to be taught explicitly. It is therefore useful to have challenges like these at the end of every lesson.

Secondly, verbal reasoning demonstrates that pupils understand the maths. Talk is an integral part of mastery as it encourages students to reason, justify and explain their thinking. This is tricky for many teachers who are not used to focusing on verbal reasoning in their maths lessons. You might, for example, get young learners to voice their thought processes. Older students could take part in class debates, giving them the space to challenge their peers using logical reasoning.

Introducing scaffolded sentence structures when talking about maths gives pupils the confidence to communicate their ideas clearly, before writing them down. A mastery classroom should never be a quiet classroom.

Finally, fluency, reasoning and problem solving underpins the deepening of understanding. Fluency alone doesn’t give students the chance to delve deeper into the mathematics. They may well be able to answer the questions, but can they also justify their answer or explore other possibilities?

Typically, teachers start new topics by developing fluency in order to give learners confidence with the skill. However, sometimes starting with a problem-solving question – eg, Prove that 4+3=7 – deepens understanding sooner. How? Pupils have to be reliant on resources they’ve used elsewhere, such as concrete manipulatives and pictorial representations, to help them explain the maths.

When planning, try not to get hung up on whether an activity focuses on either reasoning or problem solving as often it is a combination. Instead, turn your attention to using these types of questions to secure fluency and ensure that all children move beyond it into a world of deeper understanding.

Fluency, reasoning and problem solving in your classroom

Embedding these concepts into your everyday teaching can take time so patience is key! Mastery specialists recommend being more fluid with your planning and investing more time in making resources that will allow you to be reactionary to progress made in the lessons.

We’ve hand-picked these useful ideas to get you started:

This blog post was written with grateful thanks to Jenny Lewis, Primary Maths Specialist at the White Rose Maths Hub, and Helen Williams, Director of Primary at Mathematics Mastery, for their insights.

Want to know more about primary maths mastery? Check out our collection of free resources, quality assured by mastery experts and helpfully mapped by topic to year groups and learning objectives.

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