Hi,

I love using skritter for learning Chinese, and since I started using it my progress has been dramatic. I was wondering if anyone knew of a similar application for mathematics or other subjects?

Cheers

AT

Yes, there is, at least for the memorisation part of your studies. I've been using Anki to memorize proofs, standard solutions etc. The fastest way for me was to compile the answers in a separate book and then only give the numbers as the solutions (instead of doing all the LaTeX input ...).

The book had 80 pages at the end of the semester. Being sure about definitions and standard exercises allows you to stay focused on doing tougher exercises during final exam revision.

As far as I know, no one has applied spaced repetition to a system that can generate new math problems of a given type, which would be just ridiculously awesome for most of the math that's taught in schools. I know Khan Academy has a math problem generator that it uses like that, and the coolest thing I think that could be done would be to add spaced repetition zazz to that. I've heard this idea proposed by someone else, too. So perhaps it'll get done. If I wasn't so busy, I would go help out and do it.

Then again, probably there are some math systems like that that I just haven't heard about. So if you have heard of one, I'd love to know.

But there are a lot of different ways you could go about using Anki to learn math and such, too, if you are creative, including what K书窝 mentioned. I use Anki to study all sorts of other stuff.

@nick When I was a math professor, the closest thing I saw to what you're describing is a system called ALEX which is sold by McGraw Hill. It basically adapts to what it estimates is the student's level and presents him exercises it thinks he needs to work on.

The problem with using a traditional SRS for math is that math is not learned like foreign language vocabulary, with lots of little facts which are essentially arbitrary, it's learned by building skills using other skills, and new skills on top of those skills. Memorization is only a small part of math.

James

Interesting. ALEKS sounds similar to what the Khan Academy already had for math:
http://www.aleks.com/video/quick_tour
http://www.khanacademy.org/exercisedashboard

But being able to apply any specific problem-solving skill will follow similar forgetting curves as memorized facts. If you forgot how to identify that for this problem you need to do integration by parts, or if you forgot that the key insight to problems of that type is that they can't be assumed to follow a binomial distribution with small samples sizes, then that's the kind of forgetting that SRSing tiny, randomly generated problems requiring those techniques could staunch.

So yeah, I agree that you would need a nontraditional SRS to do it!

@nick basically you would need to drop the traditional SRS assumption that answers to different questions are independent of one another. If someone forgets how to integrate, period, they have also forgotten how to integrate by parts. This is somewhat similar to the logic you have relating to scheduling words vs. characters in those words, if I'm not mistaken.

Independence just means it's more efficient. If you have dependent knowledge, then the earlier-level cards are going to be mostly obsolete, because they won't ever be "due" when the harder cards that also use that skill are being studied.

So in this example, your basic integration card can be tossed once you replace it with an integration-by-parts card. Or you could keep the earlier card and just eat the inefficiency. However, for many skills, you can make them a little more independent: for the integration-by-parts card, just get to the point where you've separated it into the two different parts, and don't actually finish the integral. Smallest chunk possible.

Good insight about the independence assumption in most SRS; I hadn't thought of it that way. Skritter does take the opposite approach where studying the characters in a word does mean you don't have to study the characters again independently, and also that related character and word items are pushed back out of the way when you study one (other systems do this to a lesser extent). It's likely that you could squeeze a bunch of efficiency out of many problem domains by having the SRS know about card dependence in this way. It's a tough problem, though.