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ChristianKl comments on Rationality Quotes September 2013 - Less Wrong
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I don't think my mathematics education was 100% fact based. We did discuss various thought experiments. We also did puzzles that were designed to train thinking skills.
The ability to work an hour with focus on a math proof is a lot more valuable than the axioms and theorems that I learned in the process.
Instead of trying to teach math facts it makes a lot more sense to concentrate on creating situation of deliberate math practice.
In university we had math courses we were allowed to bring us much paper into the exam as we wanted because the things that they wanted to teach us wasn't written down facts but our ability to deal with them.
Math is a funny case, being very much a skill that needs training rather than a body of knowledge that needs learning. But it's not as if you were learning mathematics on the basis of 'fancy' or fiction either.
Most of the problems that were printed in our school math textbooks were fictional. They were made up by the author of the book to illustrate some mathematical principle.
I don't see how the sense in which those problems are fictional is relevant to the discussion. Tapping out.
The topic is about whether to teach through fiction or facts. Whether something is fictional seems relevant.