Add all permutations of a card to prevent pattern-matching
One of the common problems when writing cards (especially cloze deletion cards) is that the brain just pattern-matches the "shape" of a card without really processing the information on it, so that you can give the correct answer without really thinking. This happens because your brain knows which cards are in your Anki deck vs what isn't in there. One way to prevent such pattern matching is to add all the "permutations" of a card so that your brain must do some extra work to distinguish which of the cards is the one that just showed up.
Here's an example:
- if E is an elementary matrix, then how are the column spaces of A and EA related?
- if E is an elementary matrix, then how are the row spaces of A and EA related?
- if E is an elementary matrix, then how are the column spaces of A and AE related?
- if E is an elementary matrix, then how are the row spaces of A and AE related?
(i think it's better to ask what's the strongest statement we can make: are the spaces always equal? are the dimensions always equal? or neither?)
So the general principle is: if you make all the permutations of a card, then your brain can't pattern-match the answer, which is a good thing. Because if you just added one of the cards like that, your brain would automatically go "they're the same!" or whatever whenever it just sees the "shape" of the card.
How would this work for a cloze deletion card? I don't think it would work in a case like that. I think you'd need to convert it to basic question-answer cards.
I've also been experimenting with this trick to be able to add yes/no questions into Tao Analysis Flashcards. I'm hoping that while standard yes/no questions are not that useful (because your brain just pattern-matches), that if I add all the permutations then your brain will have to do some work and it will work out fine.