In Matthias' message below he hits on something that is not specific to proofs, but all problem solving. How do we teach students the process when all we present (most of the time) is the end product? This is like showing a student a cake baked from scratch and asking the student to reproduce the result without giving them the recipe.
If there is anyone out there with some good ideas on teaching the process of problem solving (or proofs or .... ) let's here them.
>Personally, I truly believe that it is absolutely critical to be much >more honest in this respect (this starts with not choosing delta=eps/4 >just so that at the end it works out with eps). The important objective >is that students build a tolerance for frustration, so that they keep >trying, rather than giving up when it does not work out right away; and >that they do not blame themselves if they do not right away find the/an >elegant proof themselves. > >This said, I have to admit to have had rather bad experiences w/ >presenting (or rather, allowing the class to move into) the (often >obvious) deadends or "blind alleys". Over and over again, students >said that they wanted to see the right way, I should not waste their >time with wrong ways, and, quite often, even (in end-of-semester >student evals) that I did not know the material..... > >Probably, I just don't present the deadends in the right way; and I >would like to hear from others how they manage to get student-buy-in >to spend substantial class-time on trying to prove the same thing over >and over again until it finally works out (rather than showing perfect >proofs and COVERING all the other topics that clearly had to be omitted >due to my personal quirk).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ M. E. "Murphy" Waggoner Assistant Professor of Mathematics Simpson College 701 North C Street Indianola, IA 50125 email@example.com www.simpson.edu/~math ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is an unmoderated distribution list discussing post-calculus teaching and learning of mathematics.---David.Epstein@warwick.ac.uk
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