Comment by ChuckMcM
6 years ago
I think this is very insightful. I hated higher level mathematics specifically because I couldn't see any use for it. Due to a variety of circumstances I ended up taking my math classes out of sequence with the physics and EE classes in my EE degree and as a result I'd get a concept introduced in math that had no apparent use, only to find out the next semester or year what you would use it for. Very frustrating at the time.
As I developed my 'self learning' style it became clear that I was way more successful (retained more knowledge with a better understanding) if I could "make up" some problems and then work them out with the thing I was trying to learn.
>>> I hated higher level mathematics specifically because I couldn't see any use for it.
That's why I loved it. But I think this is a dilemma of teaching any number of subjects: How to convey both the useful aspect and the intrinsically interesting aspect, for lack of a better term.
You loved something because you didn't see any use for it ?
Why not? It's a stereotype for pure mathematicians to like what they do because it's not applied, even though - like all stereoptypes - it has to be taken with a grain of salt.
The thing is, once something is applied, it has to deal with all the complexity and uglyness of the real world. But if you stick to abstract ideas, you are only limited by your imagination and logic. The mundane aspects of an applied field can detract from the pure beauty of an abstract subject.
I am not saying that this is always true, and sometimes it is nice to see applications of some abstract concepts. But many people intentionally shy away from applications towards a more theoretical field.
My relationship with math had two sides. In college, I majored in math and physics, plus I was also learning electronics and programming on my own. So I was immersed in the uses of math.
But you kind of get to a point after a couple years or so where you've learned enough math to handle the physics coursework -- including being able to pick up new math topics quickly as needed. And that's also the point, like 3rd year, where math really begins to come alive as an end unto itself. I loved the abstract stuff and the beauty of proofs, and it was as much of an escape from reality as a way to engage with it.
Abstract math is a good proxy for how human mind works and deduces and reasons about complex topics. I can understand if you do not see beauty in that, but stretching that to "you liked it because it had no use" is inappropriate.
Edit: I imagine you were just tongue in cheek, though.
While you could construe the negation to be what you propose, it's not uncommon to read it as "not having to have a use in mind".
Yeah, me too! It also opens up the question about how we adapt the curriculum to every individual student? Or at least select for more likeness in interests so the lectures would be more suited (though of course, majority of uni professors would feel it's either "my way or the highway").
The part I hated about maths was all the memorization required ;)