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Proof at A Level and GCSE

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Proof at A Level and GCSE

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    I would be grateful if contributors could give me their advice /opinions onthose proofs, relevant to the average specification, that might be accessible to high achieving GCSE students and A Level students ( not necessarily those studying FM either).  There is a major debate in the department and I am trying to elicit ideas/opinions from a wider perspective.  Many thanks.
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     Have a look at the MEP proof pdf

    http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/unitpbk.pdf

    Some good stuff in there.

    For me the distinction between proof and simply particular cases marks the beginning of the abstract thinking.

    Use of counterexample is also an aspect of proof, or disproof.

    I also found that this MEP document is a good source of examples in both how to set things out and how to use mathematical symbols.

    Some old SAT papers have the odd question on proofs. [punningly some are about odd and even numbers.]

    Island 

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    With a good group I would aim to prove every major theorem or result as I work through the course. So deriving the Quadratic Formula, Circle Theorems, 1/2 a b sinC, Sine & Cosine Rules, Differentiation from 1st principles, product rule, quotient rule, integration by parts, factor theorem, remainder theorem, dot product of vectors from the angle definition...

    I'm sure I've missed loads, but my approach has always been to insist that students never use a result that hasn't been justified to them at some point...

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