GENERIC PROVING: REFLECTIONS ON SCOPE AND METHOD

We analyze the role of generic proofs in helping students access difficult proofs more easily and naturally. We present three examples of generic proving--an elementary one on numbers, a more advanced one on permutations, and yet more advanced one on groups--and consider the affordances and pitfalls...

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Bibliographic Details
Published in:For the learning of mathematics 2013, Vol.33 (3), p.24-30
Main Authors: LERON, URI, ZASLAVSKY, ORIT
Format: Article
Language:English
Subjects:
Group theory
Interaction
Learning
Logical proofs
Logical theorems
Mathematical Concepts
Mathematical Logic
Mathematical objects
Mathematical permutation
Mathematical theorems
Mathematics
Mathematics education
Mathematics Instruction
Simulation
Teacher Role
Teachers
Teaching Methods
Validity
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Summary:We analyze the role of generic proofs in helping students access difficult proofs more easily and naturally. We present three examples of generic proving--an elementary one on numbers, a more advanced one on permutations, and yet more advanced one on groups--and consider the affordances and pitfalls of the method by reflecting on these examples. A virtual classroom scenario is used to bring out the role of the teacher and of classroom interaction in generic proving. Finally, we speculate on the question: Which proofs are more or less amenable to generic proving?
ISSN:0228-0671