Central to mastering mathematics is understanding its underlying structures. This involves being fluent at generalising and proof. We also see this as part of the problem-solving process, which can usually be thought of as having four stages:
The article and tasks below will support you in helping learners get better at generalising and, ultimately, at proving.
- Getting started
- Working on the problem
- Digging deeper
- Concluding
The expectation is that the majority of children will move through the programmes of study at broadly the same pace. ”¦ Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before acceleration through new content.
The article and tasks below will support you in helping learners get better at generalising and, ultimately, at proving.
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Mastering Mathematics: The Challenge of Generalising and Proof
This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.
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Transferring
This group of tasks offers opportunities for learners to transfer thinking from one example to another, new example (which might eventually lead to generalisation).
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Generalising
These tasks give learners chance to generalise, which involves identifying an underlying structure.
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Proving
These tasks provide opportunities for learners to get better at proving, whether through proof by exhaustion, proof by logical argument, proof by counter example or generic proof.
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Take one example
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.