In retrospect, much of my struggle with later math can be traced back to the tedium of trigonometry.
I've struggled with memorization for as long as I can recall.
The emphasis on memorizing the trig identities and relationships between the functions is at odds with that.
It affects other subjects as well, so I know it's not just math.
Obviously trig is a fundamental subset of math.
In any case, had trig been taught alongside or in close relationship with the aspects of math where it's used,
as a set of tools to solve problems
– when and where to use it –
not only would I have found it far more interesting,
it would have clicked better.
Trig was actually one of the courses that helped me a lot in my later math degree, because I only had to memorize a few key facts and identities, and the rest were variations derivable from the key information. A lot of my earlier math courses "clicked" when I realized this. When I studied further areas of math I found that it was often the case that there was a large set of information to learn, but most of it could be derived from a small-ish core. If I studied and understood the core, and memorize the commonly used parts of the rest (couldn't help but memorize because it was common, didn't need special study effort) that most classes were straightforward.
But,
> In any case, had trig been taught alongside or in close relationship with the aspects of math where it's used
I took it concurrent with a physics course and we did apply trig quite a bit so my practice with it was more than just whatever was needed for the trig class itself.
> Trig was actually one of the courses that helped me a lot in my later math degree, because I only had to memorize a few key facts and identities,
Yes!
Trig is key for later math,
and that's why I place learning it better as central to my retrospective.
I struggle so much with memorization, though, that I was having to derive from first principles all the time.
