I 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.
Procedural fluency is the basis for conceptual fluency. Maths is very layered: every layer builds on the next. You can't do algebra if your arithmetic is slow, as every algebra problem has half a dozen arithmetical subproblems. And you can't do calculus if your algebra is slow, as every calculus problem has half a dozen algebraix subproblems. And every differential equations problem requires you do to a bunch of calculus.
You can't understand a topic without doing lots of examples, so that you can feel out what is incident to the problem and what is inherent to the class of problems: when do we do integration by parts? When do we do integration by substitution? Etc.
So as a result you need to build procedural mastery at every layer before moving to the next and being able to build that conceptual understanding.
I strongly disagree. That's just how education is done as a matter of pragmatism.
In general it's very very difficult to impart conceptual knowledge to someone else because of the nature of human brains. We don't understand how we understand, so to speak, so we can't directly explain how to understand something to someone else.
We teach through examples because that is the best we can do. You're exposing someone to any idea over and over again until it clicks, but that click is what's important, not the examples. If you could somehow perfectly model how a student's brain works and know the exact combination of words to say and models to draw that would make it instantly click for them, then that's all that would be needed, no procedural mastery. But we don't know how to do that.
> But we don't know how to do that.
That's because that's not how it works. From brains to LLMs [1], training creates a dense network of pathways that encode information and procedures. I lack many of the pathways to speak Swahili, and no mythical combination of words will change that. If I want to learn Swahili, I'll have to deliberately train myself to do so, building up those pathways incrementally. Then comes the click.
1. https://xkcd.com/2173/
How true what I said is depends on the domain. It is less applicable to subjects which involve simple facts with lots of rote memorization, and more applicable to subjects with difficult to grasp concepts.
You are comparing a subject near one of the spectrum (learning a language) to one that is probably as far as you can get to the other end of the spectrum (learning mathematics).
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...
One of the things mentioned in that comment thread is that, even with MA as it is today, some 4th graders can still benefit from it.
I can attest to this.
My son completed the 4th and 5th grade courses. They took about a year in total (5 months plus 7 months IIRC). During that time, I spent maybe 30 mins per week giving him some additional explanation. (At school he was studying Singapore Math 3A and 3B, which don't overlap much with these courses.)
If MA didn't exist, I would instead have my son speed run Beast Academy 4 and 5, to make sure he has no gaps, and then I would then need to tutor him 1:1 using the AoPS Prealgebra book, which is good, but a bit thick and intimidating for a child to self-study.
Honestly I’d do the BA. Later he’ll have memories of silly characters, funny pictures with hidden cultural references, and bad jokes, not just grinding XP. We still refer to Grogg and Captain Kraken.
Oh yeah, we have all the BA books and he's read most of comics in the guide books. He really likes them.
But the exercises in the practice books and BA online aren't as good as the MA exercises. And there's no spaced repetition.
Valid, my younger kid forgets a lot of stuff without that kind of reinforcement.