Learning to prove: using structured templates for multi-step calculations as an introduction to local deduction

It is generally accepted that proof is central to mathematics. There is less agreement about how proof should be introduced at school level. We propose an approach—based on the systematic exploitation of structured calculation—which builds the notion of objective mathematical proof into the curriculum for all pupils from the earliest years. To underline the urgent need for such a change we analyse the current situation in England—including explicit evidence of the extent to which current instruction fails even the best students.