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by seba_dos1 808 days ago
Are you trying to acquire a tool for your toolbox, or are you trying to understand the concepts that allow you to invent such tools?

Teaching math is all about the latter, while some people are only interested in the former and struggle.
3 comments
alejohausner 808 days ago
When I studied group theory, I would have been so much happier if someone told me we were talking about nonzero numbers, or invertible matrices, or functions. A little of bit of concreteness would have helped enormously to motivate the topic.

When I took real analysis, I would have been so much happier if the teacher had presented some historical context: what pitfalls had mathematicians fallen into by misunderstanding infinity?

That’s just how my brains work. I need some context. I suspect other brains are like mine too.

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ThrowawayR2 808 days ago
I'm sympathetic to that view but most engineering disciplines are just interested in having the tool for their toolbox. Their interest in understanding the concepts that allow them to invent such tools is focused on their own discipline, which is not mathematics.

Motivating students with real world applications first is IMO the only real chance to potentially spark their interest in learning broader concepts.

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atoav 808 days ago
Your metaphor works both ways. If you teach the kids in kindergarden the theory of intricate japanese wood joints before they know which end of the saw to hold you are wasting your (and their) time.

As I said, all things have their place, but some mathematicians have the habbit of starting at the most general (and therefore most abstract and most distant from the layperson) point to then move to more concrete applications. My suggestion wasn't to skip the general perspective, it was to teach it at a point where people already know and maybe even use the thing that is being generalized.

That being said, not everybody is a mathematician. For some (and I'd argue: most) people using the fourier transformation as "just" a means to figure out the partials of any given signal is the tool they are looking for.

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