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There is the ongoing pedagogical problem where the process is very seldom taught, at least in mathematics, where everything is generally presented in a linear fashion - because that's the easiest way to read it once you're done - and people start to imaging that's how the results were arrived at, which is almost never the case.
by Colman (colman at eurotrib.com) on Wed Jan 2nd, 2008 at 04:50:50 AM EST
[ Parent ]
That's exactly the problem I had when I was teaching "finite mathematics" which was the first undergraduate course where proof techniques were introduced.

I had to explain to my students that the proofs in their textbooks made no sense because they were discovered inductively in the opposite direction than they were written, and then sharpened for "elegance" in order to impress other professors so they will select the textbook. Take, for example, a typical epsilon-delta exercise from calculus. The official answer will start with "let epsilon equal blah blah bla" and the student will stop right there and scratch their head "how did they come up with that?". Well, that was the last thing they came up with.

We have met the enemy, and he is us — Pogo

by Migeru (migeru at eurotrib dot com) on Wed Jan 2nd, 2008 at 07:00:03 AM EST
[ Parent ]
I had similar troubles with proof techniques during secondary schooling... I could follow the logic of the proof, but not how anyone could come up with it out of thin air, which even then seemed slightly more important to me.
by Nomad on Wed Jan 2nd, 2008 at 07:25:30 AM EST
[ Parent ]
It's the pedagogy and sociology of mathematics that are broken, not the subject matter.

We have met the enemy, and he is us — Pogo
by Migeru (migeru at eurotrib dot com) on Wed Jan 2nd, 2008 at 07:28:33 AM EST
[ Parent ]


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