[grovulent]

I disagree with this in part. I'm using spaced repetition to learn maths - and without it I just wouldn't progress at all. My natural aptitude isn't great.

Can you say a little bit more about what you mean by immersion? Do you mean - say, having a teacher who can show you a problem from multiple angles, allowing you to triangulate your understanding by asking numerous questions... etc? Things like this?

I do agree that in terms of developing immediate understanding - having access to this environment allows you to obtain understanding quicker. And I agree that it doesn't cohere well with spaced repetition learning.

However, the problematic thing with learning with this way is that unless you go on to use it daily, you lose almost all of it. So all you manage to do is pass tests throughout your life - never developing a full suite of knowledge that you can deploy. What an enormous waste of time!

Given that the energy needed to learn/recall an individual card drops exponentially over time, over the long term this is a vastly more efficient process for retaining information.

The only question is whether it can be used to learn complex and abstract ideas. I believe it can.

Here's how I typically progress with learning a difficult, abstract mathematical concept or problem.

First pass - I'll rote memorise a solution.

Then after a couple of weeks - I'll typically forget various parts of the solution. More often than not these will be sub-problems that I don't completely understand. So I'll create new cards that will provide training on these smaller sub-tasks. In the meantime, I'll rote learn the solution to the larger problem again.

What I find is that no matter how many times I rote learn a complex solution, eventually I typically forget it. But the smaller, easier concepts stick. Eventually my rote knowledge gets swapped out progressively by the smaller units of understanding and I end up being able to work through the solution without remembering it as a whole at all.

This is a frustratingly slow process in the beginning - particularly if you are starting at the very beginning of a new field (as I am with maths). But in my experience it's worth it. For the first time in my life I feel I'm actually really learning a topic in a way that I'll truly own.

[voltagex_]

Do you have an example of some cards you're using? Was there an existing set or did you develop them yourself?

[grovulent]

I developed them myself.

Mostly this doesn't add much overhead to the learning process. As I'm working through a math's text book (in ebook or pdf form) I use the windows 7 snipping tool to create two images - one of the question and solution. And then I just insert these into my card program. This takes about 15-30 seconds at the most.

I use mnemosyne as my repetition software which allows me to insert images - and I can also annotate my cards with latex. I have a number of latex macros set up on my keyboard so that I've become pretty quick at inputting latex.

I continue to annotate my cards as I progress. For a complex problem, what starts out as a simple cut and paste from a text book grows into a voluminous set of notes covering every aspect of the problem that I've had trouble with on different repetitions of the problem. These notes become what I use to create the smaller cards.

For abstract and complex material - there is no substitute for creating your own cards imo. You need to read through a text book anyway to ensure that there is no important context that you've missed. And it isn't much overhead to create your base set of cards, cutting and pasting as you go. But your gaps in understanding are your own - and only you can identify those and fill them.