Everyone’s talking about oracy.
As a maths teacher who has weathered numerous whole-school literacy initiatives - you know, the kind where you’re suddenly supposed to integrate 10 minutes of extended writing into every lesson - I’ve grown a bit sceptical.
And yet, I’m optimistic about the oracy trend. Talk, done right, has a big role to play in making us better at maths.
Declarative knowledge matters
It’s almost a cliché to say maths education often prioritises procedural knowledge at the expense of understanding.
But there’s truth behind this criticism. While procedural fluency is a necessary condition for being good at maths, it is not sufficient. We’ve all encountered students who can follow steps correctly but who can’t explain what they’re doing and falter at the first non-standard application.
This is because they lack declarative knowledge, the knowledge they need to make explicit what they are doing and why.
This is the difference between being able to add 1/3 and 1/2 together to make 5/6, and being able to explain how a common denominator makes fractions with unequal denominators addable. Without this declarative knowledge, a pupil is unlikely to be able to deploy this procedure in problem-solving settings, for instance when asked to add 1/3333+1/2222.
What’s a great way to practise recalling and applying declarative knowledge? Talking about maths.
A well-deployed “turn and talk” after watching an example or completing an exercise can be the difference between learning a procedure and learning what that procedure is doing and how it does it.
There is no answer book in the sky
Because so much of school maths is spent developing fluency, pupils can easily become conditioned into thinking that the purpose of maths is to find the solution in the answer book. This is, of course, not how real maths works.
There is no answer book in the sky against which mathematicians check their solutions. The goal of maths is to produce a robust argument that leads to your solution, so you and others can be confident in it.
In real life, answers aren’t checked against an answer book, but against reality or the scrutiny of the mathematical community. This places a much greater emphasis on justification and proof. Working out does not exist to collect marks in the event that one’s answer is wrong; it exists to convince the community of one’s answer.
This shift from seeking the right answers to justifying them demands a greater emphasis on logic and proof. Encouraging students to articulate their reasoning helps to cultivate these skills.
They may not need the formal logical notation used by professional mathematicians, but they do need to practise clearly and confidently explaining their thought processes.
Learning to talk to ourselves
When I solve a problem in maths, I am constantly talking to myself. This self-talk narrates my problem-solving. It is how I test out ideas, challenge myself to think differently and encourage myself to keep going. Talk is the start of reasoning.
It is also how one keeps on track and changes course if necessary. The Education Endowment Foundation has long told us about the importance of metacognition, and in problem solving that happens through self-talk.
When children are attempting problems, they often fail to monitor their progress towards a solution and don’t change tack when they are veering off-course. Experienced mathematicians regulate themselves through an “inner dialogue”.
Children learn this internal self-talk through external practice. First, they see it modelled by a teacher thinking aloud as they work through problems. Then they practise doing it out loud to a peer or teacher before internalising it into something that they do naturally in their own mind.
Not another ‘write a paragraph in every lesson’
I’m optimistic about oracy. Great maths lessons have long used talking as part of their toolbox for developing a true understanding of the maths that pupils are doing. Mathematical institutes and clubs have long prized the presentation of a proof or solution as the end goal.
This is why one of our goals at Axiom Maths is to make pupils more articulate. Not because oracy was a trend when we started out but because articulation is such an essential part of mathematics.
A generic approach to oracy would be bad. We don’t need a diktat that every lesson must include a debate or a speech. But a disciplinary approach, one that recognises the crucial role of speaking and listening in maths, could pay dividends.
David Thomas, CEO of Axiom Maths, is a former maths teacher, secondary headteacher and Department for Education adviser
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