A balanced review of Math Academy
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A balanced review of Math Academy
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Re: A balanced review of Math Academy
#2Author mentions Simmons' Differential Equations with Applications and Historical Notes (1972), which is at Internet Archive:
https://archive.org/details/differentialequa0000simm/page/n6...
Re: A balanced review of Math Academy
#3> But should you learn integration before differentiation? I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered,
Ha, I learned calculus integration first from Ivan Niven's "CALCULUS An Introductory Approach," copyright 1961, that as a kid I found in the attic in my dads undergrad engineering books. When I got to high school and took calc, I was able to do all the stuff they were teaching, but in weird orders and methods compared to more modern books.
Now, 40+ years later, I still have that book on my bookshelf in the calculus section :)
Till now, it's it only book I've seen that teaches it this way.
Re: A balanced review of Math Academy
#4I had a longer comment but it was too all over the place. For me, ultimately, I think Math Academy has really helped me. That being said, I put a lot of time and effort into it, and I imagine it would be difficult for people with a lot of commitments. I sometimes reach for supplementary materials, sometimes get ChatGPT to re-explain something, but mostly I manage.
I think the article gives the impression that MA is like Duolingo, but it's not. There's no flashy animations, sound effects, or mascots, the interface is spartan like Hacker News. It can't be (effectively) done in five minutes a day. It requires total concentration and a lot of time commitment.
Re: A balanced review of Math Academy
#5> But should you learn integration before differentiation? I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered, Ha, I learned calculus integration first from Ivan Niven's "CALCULUS An Introductory Approach," copyright 1961, that as a kid I found in the attic in my dads undergrad engineering books. When I got to high school and took calc, I was able to do all the stuff…
Calculus by Thomas Apostol (also from the sixties) teaches integration before differentiation as well. Great textbook!
Re: A balanced review of Math Academy
#6> So why do some learning resources designed for autodidacts—such as Math Academy, or the generally very good Execute Program—rely so heavily on dependency graphs?
I went to a university where the upper-division undergraduate math courses didn't have much in the way of prerequisites.
A foreseeable consequence of this approach is that the first several weeks of each ten-week class are spent covering material that's shared with other classes, because that material is relevant to both classes but isn't included in the lower-division prerequisites. This is very bad as a matter of curriculum design, but good if you're more interested in making sure students never have scheduling conflicts.
Another example of dependency graphs is that when my sister signed up for Portuguese classes, she took "Portuguese 1 for Spanish speakers" rather than "Portuguese 1". You can learn Portuguese from an English perspective, or you can learn it from a Spanish perspective, and those are both approaches that can work, but they're not approaches you'd want to combine. In this case, one of the approaches is clearly superior - if you can relate Portuguese to your knowledge of Spanish, that will work better than relating it to English - but even where no particular dependency structure is preferable to another, it remains true that the plan for going from A to B isn't the same as the plan for going from B to A, or the same as the plan for going from nothing to B. So the curriculum needs to rely on a dependency tree.
Re: A balanced review of Math Academy
#7This review reads very much like one written by someone who reluctantly is trying to find excuses to criticize it. Many of the things he says feel made up.
For example,
> Many of the questions I answered correctly were in areas that I don’t feel I understand well, but where I suppose I had drilled enough in the past for my procedural fluency to survive 20 years of atrophy.
The author is complaining that he felt like he should have done worse because emotionally he thought he knew it less than he actually did. This is an entirely fictional, made-up criticism. He obviously knew it better than he "felt" he did.
The entire review reads like this, trying to make up real-sounding criticisms that to me just don't make very much sense. The DAG criticism as well doesn't make sense. There is no "one way". The DAG approach probably works for many if not most students, but of course there are other students it won't work for. Exactly like how phonics works for many students but some need to be taught whole word reading. You can't criticize the DAG approach just because some students can't learn that way, but they have to pick one method. I would expect a teacher to have a better critcism than that.
Re: A balanced review of Math Academy
#8I like that this review is written by someone who gave Math Academy a serious try. He mentions comments by a couple of other math educators (Michael Pershan and Dan Meyer), but I haven't seen any evidence that either of them has used Math Academy for enough time to evaluate it.
(At the time I recommended my son start doing Math Academy, I had done 3722 XP myself, which is about 60 hours' worth.)
It's true that there's a stronger emphasis on procedural fluency than on conceptual understanding. But honestly I think that's good: there's so much good material online for conceptual understanding.
Imagine you're studying linear algebra: use Math Academy for rigorous introductions to topics and exercises and feedback, and watch 3Blue1Brown videos for conceptual understanding.
For younger kids (my son is 8.5yo) I wish Math Academy had some animated or video explanations. For example, the prealgebra course includes the product rule for surds. It was hard for my son to grok based on reading the written explanation. Not because the explanation was bad, but because my son has the attention span of an 8.5yo. So I spent a few minutes walking through that same explanation with him, using a paper and pencil to guide his attention.
I also wish they had a mascot and a streak feature. Those features on Duolingo somehow help to motivate my son.
Re: A balanced review of Math Academy
#9This review reads very much like one written by someone who reluctantly is trying to find excuses to criticize it. Many of the things he says feel made up. For example, > Many of the questions I answered correctly were in areas that I don’t feel I understand well, but where I suppose I had drilled enough in the past for my procedural fluency to survive 20 years of atrophy. The author is complaining that he felt like…
He made the initial diagnostic test sound like it has a massive impact on what you'll study. It doesn't. Even if MA thinks you know a topic well based on the diagnostic test, that doesn't mean you won't encounter it again. He seems to have missed the fact that every time you answer a question, this affects the estimate that MA has about your comfort with one or more topics.
The excessive focus on procedural fluency is a reasonable criticism but, as I said in another comment, this doesn't bother me at all. There are plenty of other sources for this. And procedural fluency is a good enabler for developing conceptual understanding.
Re: A balanced review of Math Academy
#10I like that this review is written by someone who gave Math Academy a serious try. He mentions comments by a couple of other math educators (Michael Pershan and Dan Meyer), but I haven't seen any evidence that either of them has used Math Academy for enough time to evaluate it. (At the time I recommended my son start doing Math Academy, I had done 3722 XP myself, which is about 60 hours' worth.) It's true that there'…
This tracks with my experience. I had to start from the very basics, but now I'm able to watch 3B1B and really understand what he's talking about. During lessons I occasionally reach to ChatGPT to help explain a concept or (rarely) a Khan Academy video.
I agree that the other articles mentioned didn't seem to give much of a chance. The Perhan thread has a comment chain between the author and the MA director [1] which is easy to miss. It's notable to me when users complain of negative XP, I've been working on MA every day for six months and got my first negative XP today! I've gotten 0 XP plenty, but if someone's getting negative XP often, they're half-assing it.
> I also wish they had a mascot and a streak feature.
I believe a streak calendar is coming based on the developers' Twitter. I dislike streaks but I imagine they will be optional as leagues are. I edited it out but my previous comment on this thread said "the day they get a cute mascot is the day I quit forever!" Maybe that was too harsh ;) But I do like the serious tone of the site as an adult learner.
1. https://pershmail.substack.com/p/math-academy-wants-to-super...