Unlike Neo in The Matrix, we can’t upload knowledge about eigenvectors directly into our brains. For that we need Math Academy. Image © 1999 Warner Bros. Entertainment Inc.
I’ve completed my fourth Math Academy course, Linear Algebra. As has become a habit by now, I’m celebrating by posting another update on my Math Academy experience. (For my experiences with my first course, Mathematical Foundations II, see my original series of posts summarizing the book The Math Academy Way and reviewing MFII. For my experiences with the Mathematical Foundations III and Mathematics for Machine Learning course, see my first and second updates.)
My usual disclaimer applies: 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.
(Not quite) keeping up the pace
During the Linear Algebra course I didn’t quite maintain the daily goal of 40 XP that I set while taking the Mathematics for Machine Learning course. I averaged about 38 XP per day for 33 days, according to my activity log; there were 9 days when I did less than 30 XP, and 3 days when I did less than 10 XP, including 1 day when I did no Math Academy work at all. I took 8 quizzes and did re-takes for 3 of them; for 1 quiz I got 0 XP the first time.
All in all, I spent just over a month taking Linear Algebra, a relatively short time that’s due to already learning a fair amount of linear algebra in the Mathematics for Machine Learning course. (When I started the Linear Algebra course, Math Academy indicated that I had already completed 75% of the course topics.)
I know eigenvectors
As I’ve mentioned multiple times, my original interest in Math Academy was sparked by my desire to finish learning linear algebra, a process that I abandoned short of learning what an eigenvector was. I am happy to relate that I now know what an eigenvector is, as well as an eigenvalue.
This is not knowledge in the “knowing what” sense; that I could have gotten from Wikipedia or (if I wanted to be au courant) by asking an LLM. It’s “knowing how” knowledge, the result of filling lots of sheets of paper calculating eigenvalues and their associated eigenvectors, and then using them in various contexts (e.g., singular value decomposition and principal component analysis). Do I know all of this cold, able to employ any of those techniques with full confidence and automaticity? Not quite yet, I’ll no doubt need further review sessions. But I can’t look at a matrix anymore without thinking about computing its eigenvalues and eigenvectors.
More Math Academy musings
It’s also a tradition for me to include in these updates more of my thoughts on the Math Academy system itself. Here are two for this post:
Math Academy and Alpha School. In my post on Joe Liemandt’s intterview about Alpha School, I discussed TimeBack, the software stack (“education OS”) used by Alpha School and being licensed to other private schools. As it happens, TimeBack includes a number of third-party learning systems, including Math Academy. In fact, according to a TimeBack developer, Math Academy is among the most-used applications in the Alpha School TimeBack platform. A subsequent tweet details the criteria used for selecting applications for inclusion; it’s clear that Math Academy does well on all of them.
It’s interesting to speculate whether Alpha School is paying for individual Math Academy subscriptions for each student, or whether Alpha School is using Math Academy under some sort of enterprise site license. Based on various things I’ve read, it appears that the TimeBack system wants and needs clear feedback on student interaction with the learning application, and that’s difficult to do with a third-party application. Joe Liemandt also has a goal of deploying a version of TimeBack to a billion children, and that will be difficult with Math Academy’s current pricing. Thus I wouldn’t be surprised to see Math Academy and other third-party applications eventually replaced in the TimeBack stack with similar applications developed in house.
Does Math Academy need a “slow mode”? In a recent post titled “Frustrated and Confused,” Reddit user cmredd sounds off about Math Academy: “I think I’m quite close to cancelling my subscription unless a few (basic but key) things are fixed or added.” Their core complaint is that Math Academy doesn’t provide enough reviews, especially for students who only have enough time to do a few XP per day (e.g., 15 or less), and doesn’t provide a simple way for students to request more reviews. Hence the idea of a “slow mode” for such students that prioritizes reviews of prior material over the introduction of new material.
I made a number of comments in response to that post, and won’t repeat them here. But I did want to add that The Math Academy Way has an extensive set of FAQ chapters that respond to various questions and concerns about how Math Academy works, including some touching on the points that cmredd raises. These FAQs are well worth reading at length. Whether you agree with Math Academy’s general approach or not, there’s no question that its developers can provide coherent and onsistent answers for why it works the way it does.
However, I think there is a question about how useful Math Academy can be for a student without a good mathematical background who can spend only a few minutes per day on the system on average. I’m not a believer in XP-maxing (like people who brag about doing 100+ XP per day), but it seems like it wouldn’t be cost effective to pay $49 a month for a service where you can do (say) only 10 XP or less a day on average (e.g., just a single lesson, review, or quiz), need to do lots of reviews due to experiencing difficulty with the material, and therefore may take a year or even two to finish a given course. As I’ve written before, Math Academy is not for everyone, and I think such students would be better served by looking at alternatives.
(The folks at Math Academy agree, and it factors into their economic model. From the response to the FAQ “Why isn’t Math Academy free?” in The Math Academy Way: “Math Academy . . . must be priced in a way that the company’s solvency is not dependent on a massive user base.”)
Where to next?
As discussed above, I’ve now completed my original goal of learning linear algebra (at least to a first level), and in only 9 months compared to my original estimate of 1 year. The question now is, what to do next?
In my last update, I floated the idea of taking Multivariable Calculus and then Probability and Statistics, rounding out my knowledge of topics that the Mathematics for Machine Learning course provided an introduction to.
However, now that I’ve finished Linear Algebra ahead of schedule I’m thinking of instead taking Calculus I and then Calculus II, Math Academy’s university-level introductory calculus courses. There were areas of calculus that I didn’t get lessons on in Mathematical Foundations I and II, like hyberbolic functions, and I’m still a bit shaky on topics like differentiation and integration of the less common trigonometric functions. I’d like to have more automaticity on those topics before tackling the full Multivariable Calculus course.
But no matter what I decide, I plan to be back here in a few months writing about the successful completion of another step in my Math Academy journey.