Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A balanced review of Math Academy

newsletter.ozwrites.com

Post reply on HN
Print view View original

21–25 of 25 posts

Re: A balanced review of Math Academy

#21

Post by julianh65 »

I've been using Math Academy for a couple of months now seriously (~3.5k XP). Initially I was reviewing topics / concepts that I already had an intuitive understanding of from college courses, and I believe for those it has helped take me to the next level in that I now can, 99% of the time, solve problems in those topics. As I start to approach topics that I haven't fully covered in college or have some intuitive understanding for I do find that I can mechanically carry out the operations, but I lack an understanding of "why" I'm doing this.

I think the author of this makes some good points to this effect. I believe that the best approach is a bit inverse of what the author is saying however. I think that Math Academy should be the base, where 80-90% of your time is spent. The remaining 10-20% should be used to supplement this. Either with lectures, textbook / edutainment reading or other ways to develop more of that intuition.

Re: A balanced review of Math Academy

#22

Post by turtleyacht »

aoki wrote: post #18
turtleyacht wrote: post #2

Author mentions Simmons' Differential Equations with Applications and Historical Notes (1972), which is at Internet Archive: https://archive.org/details/differentialequa0000simm/page/n6...

This shows as “Borrow Unavailable” for me. The Internet Archive lost a court case against the publishers, so many books (including all books that are still available for sale) have been (or are being) soft-removed :-/

Thank-you, you're right. Hopefully we can borrow it in the future.

Re: A balanced review of Math Academy

#23

Post by Asraelite »

milesrout wrote: post #20
rahimnathwani wrote: post #8

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'…

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 calc…

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.

Re: A balanced review of Math Academy

#24

Post by Rendello »

Asraelite wrote: post #23
milesrout wrote: post #20

Earlier quoted context omitted.

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 calc…

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 a…

> 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/

Re: A balanced review of Math Academy

#25

Post by Asraelite »

Rendello wrote: post #24
Asraelite wrote: post #23

Earlier quoted context omitted.

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 a…

> 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…

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).

Post reply on HN