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OP: What seems to be missing as taught is an explicit indication of the plan. Even though this is far afield from your concentration on geometry, it illustrates your point. Michael Sipser's text, Introduction to the Theory of Computation, includes many "proof idea" sections prior to launching into each formal proof. I've taught from this text and ...


I think maybe the correct answer to this question is something simple like Sure, do something else if you like. I also recommend reading this question because the good answer there may give you some insights into how imposing a structure on proofs can help and how it can hurt.

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