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.
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