Improving reasoning at the point of answer

Here’s a simple, cost-free, whole-school idea for improving mathematical reasoning – when children give an answer to a question, don’t tell them (or infer to them) in that moment whether the answer right or wrong.

The basic principle is that the moment that a person answers a question, they are likely to go through an intense mental process to check that their calculation is correct. When probed, a child will justify, draw, explain, generalise and reason. The moment after the point of answer is precious, potentially very powerful and too often I have taken it away from the children in my class.

This will also demonstrate to the children that what you really value is their thinking, their justification, their strategy; not whether they have the correct answer. In doing so, especially when it is a collective approach, we will reduce the children’s anxiety about whether or not their answers are correct.

I was struck by the importance of valuing process over answers again this week. A child in my class was struggling with the calculation 1-0.003, so we had a conversation that went something like this:

Me: Ok, so what’s 1000-3?
Child: 997.
Me: How do you know?
Child: (silence, looks at me like I’m daft) Because it is.
Me: I know. But how did you know that? How did you work it out?
Child: It just is.

And so the conversation continued, with me trying to make a link between the two questions. What screamed out at me was that in order to facilitate a true understanding of maths, and understanding that can be built on, strategy must be the thing that is discussed, promoted and celebrated.

We know that, as teachers, our words have great power. I hope, in future, to use mine with ever more precision.

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2 thoughts on “Improving reasoning at the point of answer”

  1. Great advice Gareth. I have to put a brake on myself when questioning as the temptation is to rush on. Also Children tend not to listen to each other during q and a unless the teacher encourages this. Taking yr advice facilitates the process of the teacher guiding pupils into learning from each other.

  2. I have told my maths class that as far as I’m concerned the answer can be bananas each time – but I want to hear how they got there. Over 6 months of this style now sees them explaining their reasoning without pause which gives me a chance to check for understanding and an opportunity for peer to peer learning and support.

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