# 5 principles for better primary maths teaching

The maths curriculum has changed, but teaching methods have remained the same. It's time to raise the bar, says this primary teacher

We are now well into the "new" maths curriculum, with its harder Sats papers and higher expectations. The game has changed, but maths teaching has remained largely the same.

I believe that it’s time to reconsider how we teach maths. So I have set out five simple principles that work in tandem with mastery approaches and are designed to invite deep mathematical thinking to flourish.

### 1. Start lessons with a question

How many teachers have started lessons with naive enthusiasm about multiplying fractions or algebraic notation, to be met with resistance and disengagement? Perhaps traditional learning objectives have had their day – in this brave new world of "making connections" maths, discrete learning objectives may actually be counterproductive and limiting to learning.

However, starting your lesson with a question, such as “Why does a quarter plus a quarter equal a half?” encourages children to reason, explain and justify – much better than the learning objective “to add fractions”. We all know that’s what they are learning to do.

### 2. Students need to wonder and struggle

Mathematics should be about exploring, reasoning and challenging thinking, rather than learning rote rules for calculations and facts. While memorising key facts is essential in early mathematics, once children have acquired the basics, these skills ought to be used and applied in real-life contexts.

### 3. You are not the answer key

To develop reasoning in maths, I ban the word yes from my vocabulary. When children ask me if they are right, I get them to explain and justify their thoughts as to why they think they might be.

A child might say “a quarter plus a quarter equals a half because a quarter is half the size of a half and so two of those added together makes a half”. Rather than agreeing and moving on, I probe deeper: “show me using a model” or “would it work with any shape?” Denying children answers allows them time to think, struggle (comfortably) and learn.

### 4. Encourage your students’ original ideas

This principle links to the previous two. Let’s stick with the example of a lesson about fractions. After allowing children time to wrestle with your questioning, bring them together for a whole class discussion. Share the range of different models they have used to prove the starting question.

This could include concrete representations, such as using multi-link cubes to represent fractions. Physical modelling should not just be for those children considered traditionally least able, but accessible for all.

### 5. Play

Give children free rein to experiment with an extended investigation. For example, I used the series of numbered, coloured circles from Dan Finkel’s TED talk about play in maths and posed the question: "what's going on with the colours?"

Initially I got a lot of blank faces. But after a few minutes the magic started to happen. Children began making notes, wondering, playing and discovering.

On day one, they left the classroom with more questions than answers. But by day two, they were fully exploring concepts linking to odds, evens, multiples, division, prime numbers, composite numbers, prime factors and fractions of numbers.

The need to redesign our collective approaches to maths is overwhelming. Isn’t it time that we raised the bar?

John Bee is a Year 6 teacher at South Street Community Primary School in Gateshead. He tweets @mrbeeteach and blogs at mrbeeteach.blogspot.co.uk

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

## Latest stories

### 5 simple tips to help teachers reduce money stress

Teachers' worries about personal finance can often be eased relatively quickly, says Eileen Adamson

### Covid: Rates 'soaring' where schools returned earlier

Virus has 'really accelerated' in pupils in Leicestershire, where autumn term started earlier than average, experts say
Amy Gibbons 17 Sep 2021

### Reshuffle: Who are the new team at the top of the DfE?

Boris Johnson replaced the entire team at the Department for Education this week. So who are the new people in charge?
Catherine Lough 17 Sep 2021

### Round-up: Nadhim Zahawi, the vaccine and sex education

Tes presents a round-up of the biggest education news stories and features from the past week
Tes Editorial Team 17 Sep 2021

### Powerful knowledge: What teachers need to understand

Powerful knowledge can’t be reduced to a list – it's a way of seeing knowledge in terms of its creation and purpose, writes Mark Enser
Mark Enser 17 Sep 2021

### Financial literacy: have you tried a classroom economy?

Allowing students to earn and spend 'money' during lessons is an easy way to embed financial education, says Amy French
Amy French 17 Sep 2021

### Is standing up all day bad for teachers' health?

From heart disease to varicose veins, standing up all day has health risks - but what can teachers do about it?
Gemma Corby 17 Sep 2021

### Number of pupils off school because of Covid falls

But the daily school attendance rate in Scotland remains some way off pre-Covid annual norms
Henry Hepburn 17 Sep 2021

### GCSEs 2022: Non-white authors on exam syllabus doubled

Move means A level study can include Bernardine Evaristo's Booker prize winning novel Girl, Woman, Other at A level from September
Catherine Lough 17 Sep 2021

### Why now is the time for the DfE to prove its worth

After almost two years of chaos, confusion and distrust, the DfE has an opportunity to start afresh, says Geoff Barton
Geoff Barton 17 Sep 2021