I use Anki a few times a week. When I've used it for math (as I work my way through Gilbert Strang's book "Linear Algebra and its applications"), I add full problems that seemed to be key to the topic, or surprised me in some way. These take longer to review, but I find it's been really helpful. And once it sticks, I don't have to review it again for months.
I also find it can be helpful to have a single card that prompts review of related definitions, for instance:
"What are the four subspaces of a matrix A? What are their dimensions with respect to the rank r of A? What are they subspaces of? (Fundamental theorem of Linear Algebra part 1)"
Remembering these things together is easier for me than breaking this down into multiple cards as one piece of this in isolation doesn't make as much sense as a part of the whole.
This is all to say that I disagree with the author on the point that it's important to find ways to break up cards to be bite sized. Otherwise great post IMO!
But by keeping those things together you're essentially cheating. You won't be able to remember these things in isolation as well. Also if it's easy for you to remember the rank of the matrix, but not the subspaces, you will be asked about the rank too often, since you connected it to subspaces.
In the example of the fundamental theorem of LA, the key point is the relationship between the subspaces (there are other ones just about the definition of a nullspace for example) - agree if every card was like this it would not be ideal.
I think my more important point was about problem sets, for instance:
Construct a matrix with the required property, or explain why you can't.
- left nullspace contains [1 3]^T
- rowspace contains [3 1]^T
breaks down into a few steps, and trying to break that down into bite sized flashcards such as, "what's the key idea in constructing a matrix with left nullspace [1 3]^T" and "given a matrix that is the product of L with row [1 3] can you choose a U so that combined they form a matrix with row space [3 1]?" seems like it could risk in resulting in me not being able to figure out the entire problem together. But maybe not?
Bringing it back to the post's proof example, what if you had completely nailed every step of the proof such that Anki doesn't ask you about it for a while, and then 6 months later, one of the harder steps comes up in isolation:
"What is the second adjustment we make in the proof of the ratio test, a < 1?"
what if you can't remember the first steps? Would having the rest of the context help? I guess it's a tradeoff.
Sure - for me, the cards slightly don't match the mental structure that is actually stored in my mind. In fact I remember the two steps "together", as this spatial move-and-squash. Perhaps I should rejig the cards.
I also find it can be helpful to have a single card that prompts review of related definitions, for instance:
"What are the four subspaces of a matrix A? What are their dimensions with respect to the rank r of A? What are they subspaces of? (Fundamental theorem of Linear Algebra part 1)"
Remembering these things together is easier for me than breaking this down into multiple cards as one piece of this in isolation doesn't make as much sense as a part of the whole.
This is all to say that I disagree with the author on the point that it's important to find ways to break up cards to be bite sized. Otherwise great post IMO!