Four strategies for pupil success in mathematical reasoning at KS2

4 Strategies for Pupil Success in Reasoning at KS2

I really like how it enables pupils to develop communication skills as well as reasoning skills as they have to talk through the problems and explain their thinking

Maths Lead, Hartlepool

What is mathematical reasoning?

Reasoning can be seen as “the glue that helps mathematics make sense”, enabling children to make use of all their other mathematical skills. When pupils first encounter a new challenge, it’s their reasoning skills that help them identify what prior knowledge they can make use of, based on their past mathematical experiences. Reasoning helps pupils use logical thinking, choose the best or most efficient way to start tackling a problem, identify what they do and don’t know, pick an approach from those that they’ve used before, decide if the answer is sensible, or find all solutions when there are multiple possibilities.

Why is mathematical reasoning so important in KS2?

Reasoning skills are crucial for developing confident and able mathematicians, and a core element of success in KS2 assessments. It is clearly prioritised in the national curriculum, where the second aim states that all pupils will:

  • “reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.”

Maths Reasoning and Problem Solving in the KS2 SATs

Over 71% of the 500 teachers that we surveyed about the 2019 maths SATs said that they found this year’s Reasoning Paper 1 to be harder than last year’s. The majority of schools who responded felt they need to invest in teaching reasoning and problem solving earlier to improve their KS2 maths attainment. 

How to teach pupils reasoning skills in maths

Reasoning can be hard to define, but if you look at what pupils are required to do when they’re reasoning it’s a combination of evaluating answers, picking strategies, drawing conclusions, describing solutions, and – importantly – reflecting on how they reached them.

This means that, as well as systematic thinking, it is essential that pupils develop an ability to articulate it. They need to learn to do so clearly, succinctly and logically. This can be a real challenge, especially in a busy class of 30 pupils with lots of curriculum content to cover.

How Third Space Learning supports all KS2 pupils in their maths reasoning

At Third Space Learning, our programmes of 1-to-1 interventions and high quality resources provide schools with a wide range of opportunities for developing reasoning skills, both in whole class settings and through 1-to-1 conversations.

Every week, a school’s chosen target pupils receive an online 1-to-1 lesson from their own dedicated maths tutor, delivered in our online classroom. This helps plug gaps, address misconceptions and provide extended opportunities for reasoning. Alongside this, Third Space Learning schools get access to hundreds of resources which enhance whole-class teaching and support the development of reasoning and problem solving for all pupils.

Four Key Principles for Developing Maths Reasoning at KS2

Prompt pupils to articulate their thought process

Rather than moving on once a pupil reaches their solution to a problem, pause and spend some time getting them to explain. How did they reach the answer? Why did they do that? How do they know their answer is correct? This allows for greater learning gains and depth of understanding.

Often it’s the quietest learners who benefit most from careful, probing questioning. 1-to-1 lessons provide an ideal opportunity for this. Our tutors work 1-to-1 with pupils, talking to them over a headset, Tutors personalise lessons for each pupil and prompt them to explain how they reached an answer and to justify and prove that they are right.

Make reasoning in maths a regular activity throughout your school

Practice makes perfect! Schedule in frequent and regular reasoning practice, either as part of your maths lesson, or as a separate independent or small-group activity.

As well as through the weekly 1-to-1 lessons, schools signed up to our programme also get the opportunity for regular reasoning practice through ‘Rapid Reasoning’, a structured daily scheme of reasoning activities spread over 36 weeks. This resource provides everything teachers need to make sure their all pupils in Years 3-6 get at least 5-10 minutes of reasoning practice everyday.

Get pupils talking more in maths lessons

Reasoning requires children to use mathematical vocabulary so active talk is essential to help pupils learn to articulate the steps they’re taking to solve a problem.

In maths lessons, partner talk tasks are a great way to do this. Aim to provide an opportunity for this in every maths lesson, with sentence stems or talking frames if possible. Schools using our programme get access to our complete range of downloadable ready-to-go lesson slides for KS2 (and Years 1-2 from September!) – each include a “talking time” activity or question which encourage partner talk.

For quieter or less confident pupils, the weekly online 1-to-1 lessons are a great way to encourage verbal participation. Pupils often feel more comfortable talking in this low-stakes environment, where they’re not afraid of making mistakes in front of their peers.

Model high quality, structured reasoning

Pupils need to see and hear reasoning to know what it looks like. So, as teachers, it’s helpful for us to be thinking aloud as we model solutions in our maths lessons.

Through their 1-to-1 lessons, pupils taking part in Third Space Learning have the opportunity to hear even more reasoning as tutors guide pupils through a question or problem and talk through the solution as they’re reaching it. This exposure to high quality reasoning gives pupils a wider range of models and examples to use in their own work.

See it for yourself!

Want to see first-hand how our online 1-to-1 maths interventions help pupils develop reasoning and problem solving skills? Let us know a date and time that works for you to:

  • Find out more about our intervention programmes
  • See how our online 1-to-1 tuition works
  • Explore our comprehensive resource library
  • Get a quote for your school

Available for primary schools in the UK only. If you’re a parent looking to support your child, please visit:

Read our terms and conditions and privacy policy.

  • This field is for validation purposes and should be left unchanged.