Thanks for this review, Oz, I kind of subliminally felt an unease towards Math Academy and the hype. Surely, they must be doing a great job in some aspect, but I felt that with the XP, it almost brought me to think of Duolingo. All fun, but it doesn't bring one to think deeply about a topic. Perhaps I will try them out to review some material, but I don't think they would serve me in my goal to apply math concepts to solve problems in my area of interest.
Yes, damn it! Finally, someone has actually put some thought into the review instead of just singing empty praises.
MA doesn’t connect the dots — it doesn’t help build a cohesive understanding of the subject. It’s just a grinding gym. If a student has access to a professor, a solid textbook, and lectures, then sure, MA can help improve their practical skills.
But if you're on your own and trying to figure things out using only MA, it’s a complete waste of time and energy — and an incredibly frustrating one.
The flow of MA is terrible. Those XP points and leagues look great at first, but once you get into it, you realize how poorly designed it is. Wrapping your head around a concept isn’t a competition. Building a skill isn’t a competition. Applying it might be — but MA doesn’t care. It offers only one explanation per topic, doesn’t let you skip anything, and forces you down a rigid, unchangeable path.
Worse still, if you're struggling with a topic, and you’ve Googled, read other explanations, and you're this close to that “Aha!” moment — MA kicks you out of the lesson with -10 points, making you switch to some other lesson that's simply irrelevant.
If I knew back then what I know now, I would’ve saved $500.
woah. I've only just started it and though that it was supposed to "connect" dots by asking integrating assumed knowledge into future questions. How well that does work?
That didn't work, at least for me. I've had to find a textbook and actually go through it before continuing. I've been to Math Foundations I-III, tried Proofs course, then ditched the Math for Machine Learning. It was too frustrating.
Yes, a fair point! I truly have no issue with people who are finding MA a fun way to do math and keep up their skills (or push through towards some goal). My review was oriented around MA's claims and ambitions, and honestly I was a bit grumpy about the gap between their claims and the product.
Anyway, I liked your review and you raise a bunch of interesting points. Thanks for it!
I know I'm late to the party, but I feel the critique that "the DAG (knowledge graph) is a lie" needs to be challenged.
The knowledge graph is a *model* of how mathematical knowledge is organized. Some models are effective, and some aren't. Models should be judged purely on their overall utility, i.e., how effective they are at delivering certain results. It's not about whether a model represents some universal truth; that completely misses the point. Not to mention that all models have their strengths and weaknesses, including some of the most celebrated models ever discovered!
Captured within the KG's structure, there are universal truths, and there are certain connections that are more subjective.
An example of a universal truth might be that two-step linear equations depend on one-step equations.
An example of a more subjective connection could be the relationship between radical expressions and the Pythagorean Theorem. One could teach the Pythagorean theorem with no reference to radical expressions, or you might choose to make radical expressions a prerequisite, and the one you opt for depends on a particular pedagogical goal (you could have multiple topics on the Pythagorean theorem if you want the ability to achieve both goals).
Is the knowledge graph a complete model of reality? No, but then, a complete model of reality does not exist, anywhere! Ever heard the phrase, "all models are wrong, some models are useful"? Well, it's exactly that.
The effective use of knowledge graphs has demonstrated enormous utility already, and it still feels very early. To whitewash that as a "lie" feels a little unfair.
In light of the some of the above comments about "developing intuition" and "conceptual understanding", I thought I'd share this feedback from a user I received very recently.
"I just wanted to say a huge thank you for MathAcademy. Back in school, I often struggled with understanding why certain equations, like the quadratic formula, work, and I was usually scolded for asking. With MathAcademy, I finally get to revisit these topics from the ground up, and the way the platform gradually explains the “why” has been an absolute pleasure. It’s shifted my perspective to truly value taking the time to build strong fundamentals. I also really really really enjoy how the platform builds up the subjects gradually, such as with trigonometry. I can literally see how the material builds toward concepts like rotation matrices, which are essential in areas like robotics."
Bingo! This user really gets how conceptual understanding in math actually works. It's very much a marathon, not a sprint. We build the curriculum in such a way that strong conceptual understanding is developed over time and revealed just when the student is ready to fully appreciate it. There's still a ton more we can do here to make this more effective, but we're doing it!
My advice to students is to keep working intelligently (the platform does not work well for students who are not engaged), think hard about the problems (don't just go through the motions), read the lessons carefully, and self-reflect on your own knowledge and understanding along the way. If you do those things, the true and complete understanding will come.
The beauty of mathematics shows itself to patient followers” — Maryam Mirzakhani
Hi. This is a strange place to give direct feedback but I've been using MA for a few weeks in earnest (MFI and II). I don't have much to say about the dependency graph except that it gets lots of transitive things wrong; it can assess that I understand x, and transitively y, but the way it tested my understanding of x was so trivial and superficial my deficiencies in y had no chance of surfacing. And so because the assessments are so trivial I'm sort of floating above this mass of clearly un-litigated deficiencies that can't be quantified and the system refuses to exercise.
That's the biggest issue with MA. It's not that the pedagogical theory is bad or wrong, because they're not - really, it's just that the material is not challenging.
I don't fault the system for being an engine for procedural fluency. That's what it's supposed to be. If you think that's important independently of generalized understanding, or that it supports generalized understanding, sure - automaticity lubricates deeper understanding. The problem is that there are two different kinds of procedural fluency: the real kind, and the fake kind. What I've found is, despite being an intrinsically motivated and engaged learner, what ends up happening is that I pattern match techniques to problem shapes. The problems are so scaffolded, so incredibly easy, and so stripped of any obstacle that would enhance understanding that you internalize nothing but the tuple (pattern, technique). The problems are identical to the examples with specific values shuffled around. With the best will in the world, you are massively over-fitting to the presented patterns. In some contexts, that's fine - you'll likely be able to pass a readiness test and recognize some kinds of problems in real courses, textbooks, etc.
But as soon as the shape of the problem changes even moderately, you're "out of book." To an extent that is the student's responsibility (you say that it's the student's responsibility to work "intelligently"); but that the platform makes literally NO effort to induce generalizable (that is, the real kind of) fluency is absolutely the platform's fault. The moment it really struck me was when I was doing a review set and noticed that all of the problems were *identical* to the ones in the lesson I'd taken 3-4 days earlier. I think admonishing students who progress through the system without building generalized/abstract understanding as "doing it wrong" is an utterly ridiculous cop out. That student should *fail to progress*.
Students may find their way to conceptual understanding with MA; calling it basically an edifice constructed of a sequence of trivial facts is more or less accurate. But what students are probably largely building is an edifice of disconnected, overfitted techniques that simulate proficiency in certain contexts. That might serve some people. It's not what you say it is at all.
I like that this review is written by someone who gave Math Academy a serious try. You mention 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.
"the two people [...] who did become professional mathematicians [...] didn’t drill at all, [...] interrogated gaps in their understanding, found novel ways to develop their intuition, and overall focused on subtle conceptual aspects of a topic"
Do you have any examples of how they interrogated gaps, or developed their intuition?
And do you know of any curricula where this is the primary focus?
I completely disagree with this article. As a senior software engineer at Microsoft, MA is a godsend for me. It's hard to juggle work, software engineer learning AND refreshing mathematics learned almost 10 years ago. This is where MA shines and I've even finally understood some conceptual nuances of why we did some steps because of the questions and explanations in MA on those topics. Overall I give MA a 10/10 for someone like who has adhd and time constrained.
Thanks for this review, Oz, I kind of subliminally felt an unease towards Math Academy and the hype. Surely, they must be doing a great job in some aspect, but I felt that with the XP, it almost brought me to think of Duolingo. All fun, but it doesn't bring one to think deeply about a topic. Perhaps I will try them out to review some material, but I don't think they would serve me in my goal to apply math concepts to solve problems in my area of interest.
Anyway, thanks for the thorough review
Yes, damn it! Finally, someone has actually put some thought into the review instead of just singing empty praises.
MA doesn’t connect the dots — it doesn’t help build a cohesive understanding of the subject. It’s just a grinding gym. If a student has access to a professor, a solid textbook, and lectures, then sure, MA can help improve their practical skills.
But if you're on your own and trying to figure things out using only MA, it’s a complete waste of time and energy — and an incredibly frustrating one.
The flow of MA is terrible. Those XP points and leagues look great at first, but once you get into it, you realize how poorly designed it is. Wrapping your head around a concept isn’t a competition. Building a skill isn’t a competition. Applying it might be — but MA doesn’t care. It offers only one explanation per topic, doesn’t let you skip anything, and forces you down a rigid, unchangeable path.
Worse still, if you're struggling with a topic, and you’ve Googled, read other explanations, and you're this close to that “Aha!” moment — MA kicks you out of the lesson with -10 points, making you switch to some other lesson that's simply irrelevant.
If I knew back then what I know now, I would’ve saved $500.
woah. I've only just started it and though that it was supposed to "connect" dots by asking integrating assumed knowledge into future questions. How well that does work?
Which course did these issues crop up?
That didn't work, at least for me. I've had to find a textbook and actually go through it before continuing. I've been to Math Foundations I-III, tried Proofs course, then ditched the Math for Machine Learning. It was too frustrating.
Yes, a fair point! I truly have no issue with people who are finding MA a fun way to do math and keep up their skills (or push through towards some goal). My review was oriented around MA's claims and ambitions, and honestly I was a bit grumpy about the gap between their claims and the product.
Anyway, I liked your review and you raise a bunch of interesting points. Thanks for it!
Thanks for stopping by Michael. I appreciated your article and agree about the gap.
How many XP did you earn before you wrote your review?
I did 3722 XP myself, before I recommended MA to my son.
What is the DAG?? Directed Acyclic Graph? 😀
Yes!
Hi. Curriculum Director of Math Academy here.
I know I'm late to the party, but I feel the critique that "the DAG (knowledge graph) is a lie" needs to be challenged.
The knowledge graph is a *model* of how mathematical knowledge is organized. Some models are effective, and some aren't. Models should be judged purely on their overall utility, i.e., how effective they are at delivering certain results. It's not about whether a model represents some universal truth; that completely misses the point. Not to mention that all models have their strengths and weaknesses, including some of the most celebrated models ever discovered!
Captured within the KG's structure, there are universal truths, and there are certain connections that are more subjective.
An example of a universal truth might be that two-step linear equations depend on one-step equations.
An example of a more subjective connection could be the relationship between radical expressions and the Pythagorean Theorem. One could teach the Pythagorean theorem with no reference to radical expressions, or you might choose to make radical expressions a prerequisite, and the one you opt for depends on a particular pedagogical goal (you could have multiple topics on the Pythagorean theorem if you want the ability to achieve both goals).
Is the knowledge graph a complete model of reality? No, but then, a complete model of reality does not exist, anywhere! Ever heard the phrase, "all models are wrong, some models are useful"? Well, it's exactly that.
The effective use of knowledge graphs has demonstrated enormous utility already, and it still feels very early. To whitewash that as a "lie" feels a little unfair.
In light of the some of the above comments about "developing intuition" and "conceptual understanding", I thought I'd share this feedback from a user I received very recently.
"I just wanted to say a huge thank you for MathAcademy. Back in school, I often struggled with understanding why certain equations, like the quadratic formula, work, and I was usually scolded for asking. With MathAcademy, I finally get to revisit these topics from the ground up, and the way the platform gradually explains the “why” has been an absolute pleasure. It’s shifted my perspective to truly value taking the time to build strong fundamentals. I also really really really enjoy how the platform builds up the subjects gradually, such as with trigonometry. I can literally see how the material builds toward concepts like rotation matrices, which are essential in areas like robotics."
Bingo! This user really gets how conceptual understanding in math actually works. It's very much a marathon, not a sprint. We build the curriculum in such a way that strong conceptual understanding is developed over time and revealed just when the student is ready to fully appreciate it. There's still a ton more we can do here to make this more effective, but we're doing it!
My advice to students is to keep working intelligently (the platform does not work well for students who are not engaged), think hard about the problems (don't just go through the motions), read the lessons carefully, and self-reflect on your own knowledge and understanding along the way. If you do those things, the true and complete understanding will come.
The beauty of mathematics shows itself to patient followers” — Maryam Mirzakhani
Hi. This is a strange place to give direct feedback but I've been using MA for a few weeks in earnest (MFI and II). I don't have much to say about the dependency graph except that it gets lots of transitive things wrong; it can assess that I understand x, and transitively y, but the way it tested my understanding of x was so trivial and superficial my deficiencies in y had no chance of surfacing. And so because the assessments are so trivial I'm sort of floating above this mass of clearly un-litigated deficiencies that can't be quantified and the system refuses to exercise.
That's the biggest issue with MA. It's not that the pedagogical theory is bad or wrong, because they're not - really, it's just that the material is not challenging.
I don't fault the system for being an engine for procedural fluency. That's what it's supposed to be. If you think that's important independently of generalized understanding, or that it supports generalized understanding, sure - automaticity lubricates deeper understanding. The problem is that there are two different kinds of procedural fluency: the real kind, and the fake kind. What I've found is, despite being an intrinsically motivated and engaged learner, what ends up happening is that I pattern match techniques to problem shapes. The problems are so scaffolded, so incredibly easy, and so stripped of any obstacle that would enhance understanding that you internalize nothing but the tuple (pattern, technique). The problems are identical to the examples with specific values shuffled around. With the best will in the world, you are massively over-fitting to the presented patterns. In some contexts, that's fine - you'll likely be able to pass a readiness test and recognize some kinds of problems in real courses, textbooks, etc.
But as soon as the shape of the problem changes even moderately, you're "out of book." To an extent that is the student's responsibility (you say that it's the student's responsibility to work "intelligently"); but that the platform makes literally NO effort to induce generalizable (that is, the real kind of) fluency is absolutely the platform's fault. The moment it really struck me was when I was doing a review set and noticed that all of the problems were *identical* to the ones in the lesson I'd taken 3-4 days earlier. I think admonishing students who progress through the system without building generalized/abstract understanding as "doing it wrong" is an utterly ridiculous cop out. That student should *fail to progress*.
Students may find their way to conceptual understanding with MA; calling it basically an edifice constructed of a sequence of trivial facts is more or less accurate. But what students are probably largely building is an edifice of disconnected, overfitted techniques that simulate proficiency in certain contexts. That might serve some people. It's not what you say it is at all.
I like that this review is written by someone who gave Math Academy a serious try. You mention 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.
"the two people [...] who did become professional mathematicians [...] didn’t drill at all, [...] interrogated gaps in their understanding, found novel ways to develop their intuition, and overall focused on subtle conceptual aspects of a topic"
Do you have any examples of how they interrogated gaps, or developed their intuition?
And do you know of any curricula where this is the primary focus?
This is a necro-comment but Gelfand's correspondence sequence and Art of Problem Solving are what you're looking for
If you are still taking votes for teachyourselfcs.com, as a self-learner I vote for:
CMU 15-445 Intro to Database Systems
For semesters when Andy Pavlo is teaching:
* All lectures are available on YouTube
* Class projects are available on github and non-CMU self learners have access to Gradescope autograder.
*.Homeworks are not autograded, but solutions posted.
* Great for learning about the implementation of databases (systems programming--not so much how to use a database but some exposure to SQL).
* Lots of history on the big ideas in databases
MIT 6.824 Distributed Systems
* Lectures on YouTube
* Projects available on github
* Comes with unit tests
* Example midterms and solutions
* Lots of discussion of original papers on big ideas in distributed systems
I gots lots of inspiration from teachyourselfcs.com. Thank you!
Andy
I completely disagree with this article. As a senior software engineer at Microsoft, MA is a godsend for me. It's hard to juggle work, software engineer learning AND refreshing mathematics learned almost 10 years ago. This is where MA shines and I've even finally understood some conceptual nuances of why we did some steps because of the questions and explanations in MA on those topics. Overall I give MA a 10/10 for someone like who has adhd and time constrained.