clipka <ano### [at] anonymousorg> wrote:
> Am 09.12.2010 21:29, schrieb Kevin Wampler:
>
> >> That reminds me vividly of something which I have noticed and realized
> >> all by myself: I have never seen *anywhere* the *logical* explanation of
> >> how you can easily calculate, for example, the sum of all the integers
> >> from 1 to 100. It's *always* just the raw and sterile formula, and that's
> >> it. No explanation, no intuitive nor logical way of deducing it. Just the
> >> formula and that's it.
> >
> > I can't say I've had the same experience. I've seen plenty of
> > explanations of that formula, probably more so than any equation other
> > than the Pythagorean theorem.
>
> Same here. Maybe I was lucky in having maths teachers who loved maths
> just as much as I do; maybe it's the difference in educative system;
> maybe it has changed over time.
>
> In my case, our teacher did...
>
> - show us how to deduce the formula for that sum;
>
> - give us historical background of how the basic idea behind the formula
> was discovered by later mathematician Carl Friedrich Gauss when he was a
> kid, to the surprise of the teacher who had thought he had found a way
> to keep his pupils busy; and
>
> - use it as an introductory example for mathematical induction, which
> they then trained us to apply to other problems (and by that I mean
> types of problems, not just the same problem with different parameters).
>
> So I think I did get a truly mathematical education. I might add that
> this was German Gymnasium in the 80's. I'm pretty sure pupils at
> Hauptschule weren't that lucky; maybe even today's Gymnasium pupils
> aren't either, but I hope things haven't changed that dramatically.

Precisely my same experience, the Gauss story and all.  Perhaps the education
system just needs more such motivated teachers.

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