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by btilly
1097 days ago
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I still prefer the explanation that I prepared when I was teaching at Dartmouth College. https://docs.google.com/document/d/1_uwl3WDZk_BxNOUL7W0FiPMM... I literally gave everyone that handout and told them, "To make sense of it, you're all going to do the next proof. I'll just prompt you." They thought this was impossible. But I told them to trust me and I began. I went around the room. I asked one person what the next step in the flowchart was. I asked the next person to do it. I just wrote down what they said. Kept going until they had produced a complete proof of a result that, at the beginning, they did not know why it might be true. The best comment I got from that class later was, "Proofs are easy. It is kind of like filling out a shopping list." |
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For example, I broke down problems with to-dos, such as:
1. Find the definition for what math_term_X means in a particular problem.
2. (For breaking down part of the problem): Figure out how to show that a particular object is lesser than or equal to another project.
3. Write down headings for each case I need to prove.
...and so on.
Writing down explicit steps was far more practically helpful to me, than my previous conception of problem-solving from the quote about how Feynman solves problems (that is: "Write down the problem, think real hard, write down the solution"). Some people may not need to write down steps, but I was personally able to learn a lot more with a specific, more verbalized approach.
It's very neat and helpful to have a flowchart suited to any general problem, which I'll try out in addition to my current approach of writing down a list of to-dos for solving specific problems. Thanks a lot for sharing.