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.
Here are two reasons. First of all, we want to communicate that what we value is children’s thinking, their justification, their strategy; not simply whether they have the correct answer. In doing so, especially when this is a whole-staff approach, I believe that children become less anxious about making mistakes.
Also, by creating a moment of doubt at the ‘point of answer’ we give children the space to check their thinking and explain their thought process. Generally speaking, the greater the child’s certainty, the greater the seed of doubt I try to plant. This can be great fun, and it certainly gives children an incentive to justify and explain.
I always liked Jo Boaler’s three levels of reasoning:
I can convince myself
I can convince a friend
I can convince a sceptic
And don’t be surprised if more able children can find it harder to explain their thinking in certain contexts. I remember Mike Askew saying that if children have found an answer without much of a ‘grapple’, they are likely to have almost automatised that thought process. This can make it harder (but still very important) for a child to explain their solution.
I hope this principle gives you many great classroom moments – it certainly has for me!