> I teach at a college myself and I never do that. Why do those professors
> explain something it that order? Why don't they teach it after explaining
> XYZ? It looks like a good example: they want the students to *believe* them
> rather than learn. It's a good meme: "believe me, even if you don't
> understand it". Once you get used to it (and in many cases you will confirm
> they were right when you finally learn XYZ).
Which did you learn first, that the angles of a triangle add up to 180
degrees or the proof of it?
I didn't learn the proof until I took geometry in 8th grade. I learned
the angles added up to 180 in about 4th or 5th grade. I didn't have the
intelectual tools to understand the /concept/ of proofs when I was eleven,
but by fourteen I not only had the tools, but was hungery to make sure
everything I had been taught was "provable".
Sometimes the proof takes more time than is allowed or useful. Or is
something that can be thought out later at leisure, under less trying
circumstances. If your daughter, as a child, was reaching for a hotplate,
did you sit by, thoughfully explaining about heat transfer and retention
or cellular damage due to second degree burns, or did you say, "Don't
touch that, it's hot!"
-Prof. Tim