I don't suppose there are that many people here who have anything to say on this topic, but there might be one or two. Anyway - does anyone else/has anyone else attempted to use an SRS for studying maths? What are your experiences? I've been using Mnemosyne for this purpose for about six months, and have about 700 cards. I think/suspect/hope it is worth doing, as long as you keep the cards short and sweet - definitions, lemmas, even more complicated theorems can be entered in if you split them up. Do you think it's worth it? Or am I wasting my time?

Eh... ...if you already have 700 cards and done this for 6 months, maybe YOU can tell us if it has helped so far!

I'd be interested to know.

I have done it for some time but have abandoned it. I mostly put in definitions and some nice proof-sketches. I guess it helped a little, but as I am already nearing the end of my university-career so it was all pretty specialized stuff (Gromov-Hausdorff convergence, ...)
It was also pretty tough work typing in all the Latex-code.
If I would time-jump back to 2002 I would probably still use it for the first 2 or 3 years but in my special case it seems "too late".

Hmm, show an example of a card with a lemma/definition?

Mathematics for me was never a thing of memorisation for me, it was more of a 'learning how to do it' sort of subject. Though i've only gone up to level 2 mathematics in university so i don't know how things are up in 3rd year +

I've experimented with using SRS for high level math grad courses. This last quarter, I made a 127-card deck of model theory definitions and theorems. In the past, I made a deck for a very difficult number theory class, but I no longer review it.

Basically, it's good for memorizing the facts, but not so good for giving you the ability to use them, e.g. for doing proofs.

That said, I'm also a calculus teacher, and basic calculus would lend itself much better. I've been wondering whether one could teach, say, differentiation rules, in a manner similar to 10k sentences. Cards would have a function on the question side, and the derivative on the answer side. Do a bunch of those, and you'd be really good at differentiating (I think? I have not tested it out yet)

The biggest obstacle to testing it is getting it so everyone can see the LaTeX rendered stuff, since Mnemosyne requires LaTeX already be installed, and it's a bitch to install. But I noticed earlier that Anki has a LaTeX button, maybe you don't need to install it separate for Anki...

My personal opinion of math is that understanding is key. Learning 200 formulas is completely useless if you don't understand them and know why they exist. If you understand them and why they exist, you won't need to memorize them, you will use them naturally when they are needed.

Are you just adding mathematical terms and formulas? What about math problems?

snispilbor Wrote:That said, I'm also a calculus teacher, and basic calculus would lend itself much better. I've been wondering whether one could teach, say, differentiation rules, in a manner similar to 10k sentences. Cards would have a function on the question side, and the derivative on the answer side. Do a bunch of those, and you'd be really good at differentiating (I think? I have not tested it out yet)

You might end up with a bunch of students that on a test would answer the question"What is the derivative of π^2" with "2π". Knowing something without knowing how to use it can be useless or even dangerous.

I could memorize an Arabic history textbook word for word if I spend years and years doing it, but it'd be enormously easier and more useful if I learned Arabic first.

Tobberoth Wrote:My personal opinion of math is that understanding is key. Learning 200 formulas is completely useless if you don't understand them and know why they exist. If you understand them and why they exist, you won't need to memorize them, you will use them naturally when they are needed.

The Supermemo website has convinced me that learning math with the support of an SRS is feasible, if only because they make a very convincing argument that spaced repetition software is more about retaining knowledge than memorizing facts. Obviously, you have to already understand what you're putting in to the deck for it to be of much use. I know for a fact, though, that implicit understanding can fade just like any other knowledge. Several years of "math neglect" brought upon by an incredibly liberal-arts focused Gen Ed syllabus and lots of concept-based business courses have proven that to me.

I've been toying with the idea of simply re-learning the concepts of math through reading, since I was pretty good at picking them up that way in high school, then dumping all of the example problems and exercises I can find into an SRS and just using it to schedule what problems I practice when.

A bit of history: I used to be able to just read and understand stuff - I barely ever bothered to revise. However, that seemed to stop working when I got to uni: there just seemed to be too much stuff to process. SRS was the only way I could think of to get around this, although it took me a while to work out a way of using it. The current system is actually my second attempt at a mathematics SRS - the first one failed because it seemed to take up far too much of my time. This time round, I've been much more pragmatic, and have only bothered putting in stuff I deem interesting (hoping that this is a good enough criterion). Even so, it still seems to be a bit of a time drain, and I was worried that I had been making unnecessary work for myself. I'm intensely jealous of people that were able to make the transition from school to uni without much trouble.

Here is an example theorem card (note: I make cards using HTML, not Latex, as I found Latex on Mnemosyne a pain to set up).

FRONT:

Morera's theorem:

Let f: D &rarr; <b>C</b> be continuous and satisfy
&int;_&gamma; f(z)dz = 0
for any closed curve &gamma; in D. Then f is holomorphic.

BACK:

Fix a point a &isin; D. Define:

F(b) = &int;_&mu; f(z)dz

where &mu; is any path connecting a and b. This is well defined, since the difference between two integrals over two different paths is the integral over a closed curve and hence zero. By applying the real FTC to the real and imaginary parts, get

F'(z) = f(z)

i.e. F is holomorphic &rArr; f is holomorphic

Actually, the vast majority aren't theorems, like this one:

FRONT:

Let F be a field, and det: (Fⁿ)ⁿ &rarr; F, then det is uniquely determined by:

BACK:

1. it is multilinear
2. it is anti-symmetric
3. det(I) = 1

Ah cellophane, such beautiful poetry you've written.

You have to be careful that the flash card is consise. However, I think it's feasible if you have three example problems per formula. This can be akin to 3 example sentences per grammar point.

The question side would be the equation to be solved. The answer side is the full solution, with the generic formula for the solution as a reminder.

For lengthy theories, I'm not sure. It'd be akin to using an SRS to memorize the script to a play or song. Guess you can break it up, giving one part as the question and asking for the next part. I think there was a thread on this subject but no follow up as to if it worked.

Ugh...math--*violently convulses and vomits*...

obviously memorizing a bunch of math things isn't intrinsically helpful. but if your goal is long term retention, i say go for it. i'd do it if i had the time. it's a shame how quickly we can forget things without reviewing them, and we all know we never review them after the class is over, but it comes back to haunt us one day if we're serious. i wish i had done it.

Nukemarine Wrote:You have to be careful that the flash card is consise. However, I think it's feasible if you have three example problems per formula. This can be akin to 3 example sentences per grammar point.

I think that this is the most important point. Probably the reason it feels as if it takes such a long time is because some the cards I've got are beastly long. But I think you've reassured me that this is at least a reasonable idea. I hope other people will be willing to give it a shot as well. Anyway, I suppose we'd better get back to kanji eh.

I use it for my Chemistry but I've never tried it for Math before.

When I began studying university level maths about 8 years ago now I learned proofs verbatim for exams. Personally I had always been against verbatim learning, but because I was new to the subject I was unable to actually prove the theorems independently so I had no choice. However as time went by the chunks that I needed to memorize became less and less because I became able to fill in the gaps (probably from the time spent with the theorems themselves), finally ending I suppose in being able to reproduce a proof from just it's key ideas.

Maybe my point is that mathematics lends itself very well to wrote memorization, and in fact at all levels, since knowing theorems is very useful (if you are doing maths, otherwise its totally useless). But, like doing 10k sentences in language X won't make you able to speak X, learning facts alone in mathematics wont make you a 数学者 (number study person!). So you need to practice on real problems.

I think a balanced approach between learning facts and applying them sounds like an excellent way to approach the subject. But yes, all that latex would be a swine.

Not really about srs, but I found one thing that has helped me.

counting the amount of pages I have to read or amount of exercise pages I have to do and make small boxes, a box for every page. And after completing one page, color the next box and so on.

Making small milestones while learning.

To support this necromancy I was going to post some links I had gathered, specific to mathematics, related to distributed practice and the spacing effect and how they work beneficially for procedural/implicit memory as well as declarative/explicit (and scaffolding the continuum between).

Then I found this article which summarizes things very neatly and uses many of the same links I'd gathered, specific to maths: Desirable Difficulties in Math Teaching

Also, I guess the science-related SRS veterans know this already, but for equations and suchlike, LaTeX functions in Anki are a must.

The previous posts on that site on the topic also seem like nice overviews (one general, one on induction and spacing):

Desirable Difficulties in the Classroom

Desirable Difficulties and Inductive Learning

It's lower level math, but i used anki to study the math for the gmat and found it effective. Of course you quickly memorize the answers, but by continuing to work out each problem, I memorized the "tricks" of a certain problem set.

This is something I'm really interested in. I'm a high school math teacher and fully intend to incorporate SRS into my curriculum once I get some time to properly do this.

I think the main thing about SRSing is that the cards have to be as small as possible. Basically any information displayed on a flash card has to either be atomic or single step of the problem.

----------------------
E.g.
Front of card
2x-7=5

Back of card
2x-7=5
+7=+7
-----------------------

Hopefully the above shows up well, but the point is to just do a single step rather than solve a whole problem on a card. Unfortunately I don't remember any university math off the top of my head, but if the problem takes seven steps to solve, make seven different cards for that problem. Each card should just ask what the next step in the problem is.

Here's a possible calculus card for which integration method to use:

front
(intergral of) sin^2x(cos2x^2-1)

back
the sin^2x term implies them it would probably be a good idea to use the _____ identity to simplify first then use the trig method


^-- the information in the above card is completely wrong (I don't remember my and integrals sorry , but I think you get the point. Seeing the above integral should give you a hint about what to do next. That information can be placed on the back of the card.

http://www.khanacademy.org has a mathematics study page where you need to get 10 problems correct in a row to finish that section. In addition, it occasionly reactivates an old section for review purposes.

So, it's a variant of spaced repetition.

Khan Academy Mathematics Study Page

Does anyone know any good Anki shared MATH EQUATION/FORMULA DECKS for high school level?



I need it really fast!
Thanks in advance.

Ugh, I've gotta take the freakin' maths exam for the 文部省 scholarship, I suppose this is something I should consider. I tried doing it in the last year of high school but could never be bothered, as someone else said the latex code is a pain in the arse.

I really don't understand one thing: Why is math so much ***ing harder than learning Jap?

I would like to find a proper logical i+1 method of learning it.

But well...I don't have time for that in the next few months anyway.

It seems like:

1)I need to know formulas to do problems

2) BUT I need to do problems to memorize formulas. What the hell? So which one first?

I can't do 2 things at once.

And it's so hard to find the right formula for a problem if I don't know the formula well (if it isn't very well memorized)

But it doesn't stick without doing a problem.

how do you handle it?