A common theme is developing, so I thought I’d point it out. The lessons I’m sharing are from my own mistakes, entirely. In this case, the mistake was neglecting to fully grok the trig functions and identities while trying to learn calculus. Now, whether you choose to fully understand trig before you work on calculus, you absolutely do need to be able to work with the functions a bit, and be aware of some identities. This is what I meant my mundane in the title. There will inevitably be tidbits you don’t want to study for their own sake, but need to understand for something else you’re trying to learn.
Memorize it. Use flash cards, mnemonics (these have always worked great for me.), whatever you need to. There are a few reasons, as I see it, to do this:
- To prevent frustration. Frustration is inevitable when teaching yourself, but you don’t want to go looking for it. Too much frustration caused by jumping in over your head is, I suspect, one of the major reasons people give up on teaching themselves.
- To enable you to move forward quicker. Instead of stopping and reading a full on trigonometry book, I’m memorizing the identities necessary to manipulate equations enough for calculus. Since I’ll now be able to effortlessly recall these values, problems that would have required groping around in the dark before will now merely be challenging. You need to build up islands of techniques and facts, to use as tools in understanding the big picture.
- To support intuition. As I think of intuitive insight, it works like this: You build up the aforementioned islands of techniques and facts. Having internalized these techniques and facts makes higher level patterns that were incomprehensible before, just jump out at you. But you absolutely have to learn those mundane, seemingly irrelevant facts first.
It’s a balancing act. Rote memorization is not learning, our generation is well aware of this. Perhaps, though, rote memorization of mundane facts is the quickest way to mastery of higher level concepts.
A final note: I had this post written up yesterday, when it was scheduled to be posted. In fact, it was a much better post then. Unfortunately I lost internet while writing, the better content wasn’t saved, and I couldn’t post. The bulk of it’s still here, but I apologize for the delay and lower quality.