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The "Why?" wasn't a prompt for a formal proof, and probably not a prompt to regurgitate what was learned in class. At least back when I was a kid, it was clear
by sliverstorm 12y ago
The "Why?" wasn't a prompt for a formal proof, and probably not a prompt to regurgitate what was learned in class. At least back when I was a kid, it was clear to me that "Why?" was a way of forcing the student to think about the problem. To attempt to justify your yes/no answer requires thought, whether or not you are right or wrong! If you only write yes/no, the teacher cannot tell if you actually thought about it or guessed.
- j2kun 12y agoA proof need not be "formal" to be a perfectly good, elegant, insightful proof. For example, one could observe that an even number of quarters can be formed into two rows of the same size, and if you do this with two piles of quarters, you can put the rows together to make two big rows. This is as good as any "formal" proof, and I sincerely hope it's the kind of proof the teacher shows as an example of a good answer.