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.

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