I’ve completed Calculus I, my fifth Math Academy course, and am again celebrating by posting another update on my Math Academy experience. (For past posts about my experiences, see my first Math Academy post, which contains links to all my other posts and updates.)
I should have already covered most of the material in Calculus I in prior courses, most notably Mathematical Foundations II and Mathematical Foundations III. However, I felt I had some significant holes in my knowledge, especially around hyperbolic functions (see below). So I wanted to make sure that I had complete coverage of single-variable calculus, especially before going on to more study of multi-variable calculus and other topics.
As I usually state: Not everyone will share my opinions on Math Academy, and not everyone will want to use the Math Academy system as I do. But my comments may be useful or interesting to at least some people.
Back on pace
After not quite meeting my 40 XP/day goal during the Linear Algebra course, I got back on track during Calculus I. According to my activity log, I averaged just under 42 XP per day. There were only 4 days when I did less than 30 XP, and just 1 day when I did no Math Academy work at all. However, I didn’t do so great on quizzes: I took 7 quizzes and did retakes on 6 of them.
I spent just under a month (28 days) taking Calculus I, as with Linear Algebra, a relatively short time that’s due to already having covered a lot of the material in the Mathematical Foundations courses.
Anki on the side
While working through Calculus I, I found myself struggling to remember all of the formulas that might come up in problems. This was especially true when I started the topics on hyperbolic functions, which introduce an entirely new set of identities and derivatives, similar to those associated with trigonometric functions but just different enough to cause confusion. I concluded that unless I could achieve better automaticity with these identities and formulas I was going to have a tough time going forward into multivariable calculus and other courses.
Unfortunately, Math Academy’s spaced repetition process wasn’t giving me enough review of standad formulas. Math Academy staff have teased a potential future “math facts” class; however it appears to be some ways off, and in any case sounds like it will focus more on elementary school material like multiplication tables.
It was therefore back to the old school spaced repetition solution for me, namely creating flash cards in the Anki app. (I wrote “app” singular, but the process is more complicated than that: I create cards using the Anki desktop app for macOS, synchronize them up to the Anki website, and then synchronize them down to the Anki iOS app on my iPhone.) Thus far I’ve added over 80 cards, from formulas for the volumes of spheres and other solids to the derivatives of inverse reciprocal hyperbolic functions.
Doing additional spaced repetition using Anki has helped a lot with simpler things like formulas for volumes and surface areas. However, I’m still having trouble with trigonometric and hyperbolic identities and formulas, where it’s easy to get lost in a maze of twisty little equations, all somewhat alike. I’ll need to continue working on this.
On to Calculus II
After finishing Calculus I, I’m immediately starting Calculus II. Per the Math Academy status information, I’ve already completed about 50% of its topics, so I should be able to finish up Calculus II well before the end of the year and conclude my study of single-variable calculus. Then it’s on to Multivariable Calculus and then Probability and Statistics. After that, who knows? I’d like to level up in my Python knowledge, so maybe I’ll look into the computer science course discussed on the recent Math Academy podcast by Jason Roberts and Justin Skycak.
That’s it for now, I hope to be back here with another update in a few weeks.