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Teaching for Mastery: Five Big Ideas


Created on 09 March 2017 by ncetm_administrator
Updated on 27 July 2017 by ncetm_administrator

Five Big Ideas in Teaching for Mastery

A central component in the NCETM/Maths Hubs programmes to develop Mastery Specialists has been discussion of Five Big Ideas, drawn from research evidence, underpinning teaching for mastery. This is the diagram used to help bind these ideas together:

large 'five big ideas diagram'
(click to enlarge)

A true understanding of these ideas will probably come about only after discussion with other teachers and by exploring how the ideas are reflected in day-to-day maths teaching, but here’s a flavour of what lies behind them:

Coherence
Connecting new ideas to concepts that have already been understood, and ensuring that, once understood and mastered, new ideas are used again in next steps of learning, all steps being small steps

Representation and Structure
Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation

Mathematical Thinking
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others

Fluency
Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics

Variation
Varying the way a concept is initially presented to students, by giving examples that display a concept as well as those that don’t display it. Also, carefully varying practice questions so that mechanical repetition is avoided, and thinking is encouraged.

 

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