While this idea is initially appealing, what it lacks is (ironically enough) examples of examples!
Judy Yero

Good points, Judy. I’d like to highlight your point about the comparison of examples. I think the feedback from comparing and contrasting examples generated by students can be a *very* effective teaching tool. If a student can answer *why* something is or isn’t a good example of a particular principle, then they have gone a long way towards mastering a concept.

I discovered only as an adult the powerful insight into original mathematical proofs. It’s one thing to memorize rote Pythagorean theorem; it’s another to see the proof Pythagoras offered of his hypothesis.

I learned the theorem as a secondary school student, but I never really grasped the why and how of it until I saw a youtube video showing how Pythagoras proved his theorem.

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