My general practice with mathematics is and Anki is to:
1) Understand the material I'm learning.
2) Put explanations of any algebraic procedures (for instance, the dot product of two vectors) as a flip card.
3) Put a single example of doing the work in a flip card.
For important proofs, I put them in Anki using Cloze deletion. I just drop in the whole proof, and knock out portions. This has been extremely effective in remembering and understanding the proofs. I also do this for geometric explanations of procedure.
This is definitely not overkill, and creates cards that you can go over really quickly. Ever since I have begun doing so, I have found that it is far easier for me to apply what I have learned, and that I can more easily understand the options that I have for finding solutions to problems, because I have all of the options available without requiring me to look over old information. It's just there.
Ever since taking Barbara Oakley's classes (Learning How to Learn and Mindshift), I have been a more productive and emotionally stable human being, and my ability to learn and understand the information that I am learning has exploded. One of the most important things I remember mentioned in that class was that memorization and understanding are actually quite tightly linked.
There are things that I have dealt with in the real world that would have been solved by math lessons that I've forgotten since I left University twenty years ago. I was never very good at studying because of anxieties and procrastination. The simple fact that I know I'm going to put information into Anki allows me to concentrate and gives me procedure no matter what I'm trying to learn, regardless of source (readings, lectures, etc.). I wish I had this ages ago.
> For important proofs, I put them in Anki using Cloze deletion. I just drop in the whole proof, and knock out portions. This has been extremely effective in remembering and understanding the proofs.
Thanks - I still haven't used it for mathematics, but this is good to know. I do have a few proofs of theorems in statistics in my flashcards, but the whole point of the cards is to spend only a few minutes a day on them - and doing a few proofs requires a paper, pen, and time. So I keep those in a separate deck and do them only when I know I have time.
My concern with mere cloze deletion is that I'll likely get the illusion of understanding without real testing (being able to rederive something is a real test). I'll likely go for a hybrid approach - full proofs in a separate deck and either proof sketches or cloze deletion in the regular deck.
> One of the most important things I remember mentioned in that class was that memorization and understanding are actually quite tightly linked.
This stood out to me when I took the course, although my memory of it is different. I don't think she said memorization, but "covering it and reproducing it in your own words" - the latter requiring understanding. But yes, she claimed that the research showed this outperforms things like mind maps, and that nothing has so far been shown to outperform this.
I’ve done some cloze deletions for math and related things, but I generally feel like having almost the whole proof in the prompt gives me too many cues. It often leaves me thinking that I indeed wouldn’t be able to come with the answer with fewer hints.
What I’ve tried the last couple of attempts is to “chunk” the proof (also terminology touched on in Barbara Oakley’s course) so that I end up with a question that’s something like “what’s the high-level idea / approach in the proof for X?”. That card would likely require an understanding of some underlying concepts or “chunks”, so I add questions for these too until I get to something that’s less abstract and easier to rederive.
I’m still not 100% confident if this will work well when these particular cards get into the 6-month range or so, and they start showing up at completely unrelated times. My main concern is that if I’ve forgotten some idea from “the middle”, it would be hard to reason about cards that build up on top of that.
"Covering and reproducing in your own words" is a combination of recall and synthesis, both necessary for remembering. This was a different section, and it might have been the Mindshift class, where she mentioned in US schools, we focus too much on understanding and conceptualization, while in Chinese schools, it's mostly memorization. Unfortunately, the two ideas only really work optimally together. Either model produces extremely well educated on occasion, but if you use both, then anyone can not only educate themselves well, but retain it for a far longer time period. Further, understandings of subjects are compounded by the memorization process. In my own practice, I've found this to be true, but that's anecdotal. Some nation is going to get their act together and try this on a larger scale, and I can't wait to see the output.
1) Understand the material I'm learning. 2) Put explanations of any algebraic procedures (for instance, the dot product of two vectors) as a flip card. 3) Put a single example of doing the work in a flip card.
For important proofs, I put them in Anki using Cloze deletion. I just drop in the whole proof, and knock out portions. This has been extremely effective in remembering and understanding the proofs. I also do this for geometric explanations of procedure.
This is definitely not overkill, and creates cards that you can go over really quickly. Ever since I have begun doing so, I have found that it is far easier for me to apply what I have learned, and that I can more easily understand the options that I have for finding solutions to problems, because I have all of the options available without requiring me to look over old information. It's just there.
Ever since taking Barbara Oakley's classes (Learning How to Learn and Mindshift), I have been a more productive and emotionally stable human being, and my ability to learn and understand the information that I am learning has exploded. One of the most important things I remember mentioned in that class was that memorization and understanding are actually quite tightly linked.
There are things that I have dealt with in the real world that would have been solved by math lessons that I've forgotten since I left University twenty years ago. I was never very good at studying because of anxieties and procrastination. The simple fact that I know I'm going to put information into Anki allows me to concentrate and gives me procedure no matter what I'm trying to learn, regardless of source (readings, lectures, etc.). I wish I had this ages ago.