18 ms·

I was anti-memorization until I went back to graduate school for mathematics. I had forgotten (or never learned) a lot of things needed to pass qualifying exams

by dls2016 4y ago

I was anti-memorization until I went back to graduate school for mathematics. I had forgotten (or never learned) a lot of things needed to pass qualifying exams. At some point I ran across the spaced repetition idea (maybe from the Wired SuperMemo article [0]) and I gave it a try. I ended up using it to memorize large portions of baby Rudin and Munkres' Topology, as well as some algebra and a bunch of qualifying exam questions. The qualifying exams were difficult until I reached some "critical mass" of knowledge. Then I could regurgitate proofs and even attack novel problems easily. There's an analogy here somewhere to the "leetcode" style of software engineer interview. On one hand qualifying exams and leetcode questions are a stupid gatekeeping mechanism, but on the other hand the best researchers/engineers I know have a huge number of facts and examples memorized and ready at their fingertips. I didn't think I needed to do so, but perhaps there is something to suffering through the rote memorization phase to make what comes next that much easier. [0] https://www.wired.com/2008/04/ff-wozniak/ https://www.wired.com/2008/04/ff-wozniak/

rg111 4y ago
Hi, can you please show me some of your cards? Do you create cards with full proofs or do you write parts of proof? Or do you write down definitions? Can you please give me an idea how you used spaced repeatition for grad school math? Thanks.
Silverback_VII 4y ago
Memorization is powerful only if you memorize the right stuff like Machiavelli's Prince instead of a phone book. Incremental reading (supermemo 18) to dissect books is even better I think.
kazinator 4y ago
I remember the exact point in my life when I realized how much difference rote memorization makes. I had the opportunity to write some MC68000 assembly code, at a time which was not too long after having written a complete emulator for it in C. Writing the emulator required me becoming familiar with every single instruction in all of its nuances, and exactly what they all do. So, having that behind me, I sat down to write this code and it was like wow ... I could just spew the code without having to look anything up. It was so easy!
- therein 4y ago
  > I remember the exact point in my life when I realized how much difference rote memorization makes. I suspect this might have something to do with neurological development. At least in my experience. Something about memory and recollection "clicked" (not a skill but more a capacity) at a really adult age for me. Almost similar to being taught calculus after not knowing how most physics formula are derived and then looking back in confusion how you struggled with a straightforward thing.
xkfm 4y ago
That Supermemo article in Wired hooked me. I still remember where I was when I read it and the feeling of reading it. I still use Supermemo daily, and it's one of the programs keeping on Windows. Anki (and every other SRS program I've tried) just doesn't compare as soon as you move beyond a list of flashcards. That said, having used Supermemo for over a decade at this point, the hardest thing about SRS is deciding what's actually worth reviewing for a long period of time. I delete (really remove from repetitions) cards from my collection almost on a daily basis. There's a lot of stuff that seems really important that I just didn't care about after even three months. Supermemo's incremental reading basically lets you schedule chunks of text or images (alleged video too) like a flashcard from Anki. So, instead of bookmarking articles and never reading them, I can put them into Supermemo and know I'll eventually review it. It basically counts as a separate type of flashcard, but all your reviews are mixed by default. So on a typical day, I'll have maybe 20 flashcards to review, and then another 10-20 articles. Supermemo saves where you last were reading, so when I get bored of an article, I just hit next and go to the next one. Eventually, you'll process an article down to individual flashcards like you'd put in Anki, or remove it from your review process altogether. Also, you can just leave the entire article in there if you like rereading it.
- TeeMassive 4y ago
  Is Supermemo only available as a SaaS?
  - orangepurple 4y ago
    No it's primarily an awful Delphi for Windows desktop application that is extremely fragile. But once you know how to "hold it correctly" it will be your companion for life. I run it in a virtual machine with all its legacy dependencies like IE. Forget about running it on Wine, it barely works on any version of Windows (lol)
    - TremendousJudge 4y ago
      If actually using it has this huge friction, how do you manage to use it every day? I always have a hard time creating habits out things that are hard to "start" doing every time.
snowpiercer 4y ago
Don't you think you actually did well in your exams because you really understood it and not because you blindly memorized it ?
- nomel 4y ago
  I imagine it's possible that they are related. In my life, I've only witnessed it as a required for being an expert at any topic: experience and memorized knowledge, of a topic.
- ozim 4y ago
  That is false dichotomy that is running around. To really understand something first you blindly memorize - but that is not enough, once you do examples and exercises using what you blindly memorized you get to understand things quicker, a lot quicker. Not memorizing stuff and figuring things as you go is mostly recipe for disappointment. Like in chess - people think that chess players are somehow super intelligent - but being super intelligent without rote memorization of loads of chess settings will not help winning grand master title.
  - Silverback_VII 4y ago
    >"To really understand something first you blindly memorize" Because of this sort of advice ppl equate memorization with "not understanding" and cramming. Never memorize things you don't understand.
    - orangepurple 4y ago
      They must be performed in lock step. Fully agree.
  - borroka 4y ago
    It similar to the question, "if you could do just one exercise, what would you do?" And you have all these answers, it is the squat, no, it is the deadlift, please guys it is the power clean. It is not a useful question because you will never be in the position of choosing just one exercise to be done for the next month, year or decade. Memorization is important and understanding is important, and the two are not in any conflict whatsoever.
k__ 4y ago
Oh, could you go into more detail about math and memoizantion? What did you do? I had the impression, these techniques only work well for languages, but I really would love to get better at math.
- mkl 4y ago
  Have a look at this article by Michael Nielsen: https://cognitivemedium.com/srs-mathematics https://cognitivemedium.com/srs-mathematics Old HN discussion: https://news.ycombinator.com/item?id=18895613 https://news.ycombinator.com/item?id=18895613 Or this one: https://cronokirby.com/posts/2021/02/spaced-repetition-for-mathematics/ https://cronokirby.com/posts/2021/02/spaced-repetition-for-m... Hasn't been on HN before so I just posted it: https://news.ycombinator.com/item?id=32390730 https://news.ycombinator.com/item?id=32390730
- dls2016 4y ago
  See my other comment.
ren_engineer 4y ago
I'd be really interested to see some research into integrating spaced repetition into our actual education system. Almost everything I see about it is adults learning, I wonder how much we could speed up primary school education considering so much of the "base" stuff needed to advance is rote memorization anyway seems like countries should be investing money in this, potentially trillions in unlocked economic potential by improving and speeding up education. I think I read something like 20-30% of medical school students use SRS, yet only a fraction of the general population uses it. Insane to me that we have a tool like this and almost nothing is being done to improve adoption.
- pessimizer 4y ago
  Hundreds of millions of the world's kids were remote learning for up to a year and a half. If there was any opportunity to develop real tools to help with remote learning, it was then, but we ended up with nothing, and remote learning still sucks. If anybody is going to integrate memory techniques into a curriculum, it'll probably be some Silicon Valley charter.
- lemming 4y ago
  No research here, but I use the great Fresh Cards app (by allenu here on HN) with my daughter's homeschooling, and it works great. We've used it for phonics and all sorts of basic math facts, and I use it for scheduling spelling word review as well. We're about to start teaching science and I anticipate using it a lot there as well.
- Denzel 4y ago
  Do you have a link to that research that claimed 20-30% of medical school students use SRS?
- zozbot234 4y ago
  Given that so much of modern education happens in large-group settings, it seems hard to apply SRS principles to it. A group of students will be a lot farther from 100% recall of all items than any individual student might be, and the items that require review will correspondingly differ.
ok_dad 4y ago
Do you have any notes on how you studied? I’m interested in going back to math grad school but forgot everything from undergrad, basically.
- dls2016 4y ago
  Two articles I wrote at the time which hold up surprisingly well: https://blogs.ams.org/mathgradblog/2010/12/28/spaced-math-repetition/ https://blogs.ams.org/mathgradblog/2010/12/28/spaced-math-re... https://blogs.ams.org/mathgradblog/2011/03/10/space-math-repetition-repetition/ https://blogs.ams.org/mathgradblog/2011/03/10/space-math-rep... And an example of some of my cards: https://www.dropbox.com/s/z714xpq36nvn3o1/rudin.pdf?dl=0 https://www.dropbox.com/s/z714xpq36nvn3o1/rudin.pdf?dl=0 If I'm being honest, I went overboard. Like I said, I literally memorized entire books. Entering cards into the system was the most difficult part. But it absolutely works! Had I stayed in academia, I would have loved to developed a set of flash cards to go along with course material.
  - ok_dad 4y ago
    Thank you
  - k__ 4y ago
    Okay, so the idea is to get a math book and convert the definitions in it to flash cards?
zinclozenge 4y ago
> but on the other hand the best researchers/engineers I know have a huge number of facts and examples memorized and ready at their fingertips The US is staunchly anti-memorization. It wasn't until I did a year abroad in a French university where the power of memorization was so obvious. One of the math students I spent time with told me it's the French tradition to "carry everything around in your head". They were studying symplectic geometry in their sophomore year of their bachelor's!
- deleted 4y ago
  [deleted]
- CogitoCogito 4y ago
  > The US is staunchly anti-memorization. I don't understand where this coming from. In my experience learning and teaching math in the US, I've found it's almost _entirely_ about memorization. Calculus students are usually able to regurgitate algorithms for differentiation/integration, but can't answer the most basic questions about what they're doing really means. This is just an aside. I'm not against memorization. I think memorization is the first step necessary for deeper internalized understanding since it lets you take the basic stuff and put it on autopilot so you can think about the rest that isn't as basic. That said my main complaint about US teaching of math is that that second step seems rarely to be taken and instead focus entirely on the memorization. I guess our experiences are both anecdotal, but I'm having trouble wrapping my head around your idea that the US is anti-memorization.
  - zinclozenge 4y ago
    This might be the case for k-12 and maybe lower level courses, but this was _definitely_ not the case for when I was taking group theory, real analysis, etc. With that said, someone else in the comments mentioned that while it might seem there's an emphasis "regurgitation" it's mainly because going beyond that and really digging into the why of things is vastly out of scope for the class.
ctchocula 4y ago
I found this post fascinating. It makes me wonder is there an equivalent superpower that's more software engineering focused rather than coding focused like leetcode questions? I know everyone here likes to dump on Gang of Four, but perhaps design patterns and their usecases?
t_mann 4y ago
In grad school it seems obvious what you want to retain, after that it can become a bit trickier to make the choice. General question for everyone using this approach: how do you go about selecting topics to put into your SR schedule? I mean there are so many things that would be good to remember: math problems and leetcode are actually continuously relevant if you're in employment and ever thinking about moving jobs, software engineering tools that are important for daily work (those are changing so fast in some cases that I'm wondering again how much is worth committing to long-term memory), maybe there are some academic fields where you want to stay up-to-date on the research, all sorts of life hacks in the household / cooking / DIY space, literally everything about your family life, maybe some strategies in hobbies (just recently got into speedcubing, which is a lot about algorithm memorization),... Maybe the problem is just that I have too much of a "finite memory" mindset and we can easily remember all of those, lol.
- borroka 4y ago
  The problem is quickly solved, and it is important not to fall into " paralysis by analysis." Sometimes, while writing a card, we tell ourselves that it is not so important to remember that information and discard it, other times we discard it when during the review process we sense or realize that we are not interested in remembering that information . Assuming that there is some sort of logic behind the decisions made, I recommend using the same strategy that Napoleon is said to have used in his campaigns: first we start, then we will see.
  - t_mann 4y ago
    Yeah, the whole thing is probably easy to overoptimize. Any recommendations wrt to the software? My preference for these sort of things are maximally compatible/portable solutions based on simplistic file formats (I keep a lot of personal tracking data in csv, eg). Here I'm thinking something along the lines of local markdown files for the cards, a database for the sampling info and a web app that does the sampling.
    - borroka 4y ago

rg111 4y ago

Hi, can you please show me some of your cards? Do you create cards with full proofs or do you write parts of proof? Or do you write down definitions? Can you please give me an idea how you used spaced repeatition for grad school math? Thanks.

Silverback_VII 4y ago

Memorization is powerful only if you memorize the right stuff like Machiavelli's Prince instead of a phone book. Incremental reading (supermemo 18) to dissect books is even better I think.

kazinator 4y ago

I remember the exact point in my life when I realized how much difference rote memorization makes. I had the opportunity to write some MC68000 assembly code, at a time which was not too long after having written a complete emulator for it in C. Writing the emulator required me becoming familiar with every single instruction in all of its nuances, and exactly what they all do. So, having that behind me, I sat down to write this code and it was like wow ... I could just spew the code without having to look anything up. It was so easy!

therein 4y ago
> I remember the exact point in my life when I realized how much difference rote memorization makes. I suspect this might have something to do with neurological development. At least in my experience. Something about memory and recollection "clicked" (not a skill but more a capacity) at a really adult age for me. Almost similar to being taught calculus after not knowing how most physics formula are derived and then looking back in confusion how you struggled with a straightforward thing.

xkfm 4y ago

That Supermemo article in Wired hooked me. I still remember where I was when I read it and the feeling of reading it. I still use Supermemo daily, and it's one of the programs keeping on Windows. Anki (and every other SRS program I've tried) just doesn't compare as soon as you move beyond a list of flashcards. That said, having used Supermemo for over a decade at this point, the hardest thing about SRS is deciding what's actually worth reviewing for a long period of time. I delete (really remove from repetitions) cards from my collection almost on a daily basis. There's a lot of stuff that seems really important that I just didn't care about after even three months. Supermemo's incremental reading basically lets you schedule chunks of text or images (alleged video too) like a flashcard from Anki. So, instead of bookmarking articles and never reading them, I can put them into Supermemo and know I'll eventually review it. It basically counts as a separate type of flashcard, but all your reviews are mixed by default. So on a typical day, I'll have maybe 20 flashcards to review, and then another 10-20 articles. Supermemo saves where you last were reading, so when I get bored of an article, I just hit next and go to the next one. Eventually, you'll process an article down to individual flashcards like you'd put in Anki, or remove it from your review process altogether. Also, you can just leave the entire article in there if you like rereading it.

TeeMassive 4y ago
Is Supermemo only available as a SaaS?
- orangepurple 4y ago
  No it's primarily an awful Delphi for Windows desktop application that is extremely fragile. But once you know how to "hold it correctly" it will be your companion for life. I run it in a virtual machine with all its legacy dependencies like IE. Forget about running it on Wine, it barely works on any version of Windows (lol)
  - TremendousJudge 4y ago
    If actually using it has this huge friction, how do you manage to use it every day? I always have a hard time creating habits out things that are hard to "start" doing every time.

snowpiercer 4y ago

Don't you think you actually did well in your exams because you really understood it and not because you blindly memorized it ?

nomel 4y ago
I imagine it's possible that they are related. In my life, I've only witnessed it as a required for being an expert at any topic: experience and memorized knowledge, of a topic.
ozim 4y ago
That is false dichotomy that is running around. To really understand something first you blindly memorize - but that is not enough, once you do examples and exercises using what you blindly memorized you get to understand things quicker, a lot quicker. Not memorizing stuff and figuring things as you go is mostly recipe for disappointment. Like in chess - people think that chess players are somehow super intelligent - but being super intelligent without rote memorization of loads of chess settings will not help winning grand master title.
- Silverback_VII 4y ago
  >"To really understand something first you blindly memorize" Because of this sort of advice ppl equate memorization with "not understanding" and cramming. Never memorize things you don't understand.
  - orangepurple 4y ago
    They must be performed in lock step. Fully agree.
- borroka 4y ago
  It similar to the question, "if you could do just one exercise, what would you do?" And you have all these answers, it is the squat, no, it is the deadlift, please guys it is the power clean. It is not a useful question because you will never be in the position of choosing just one exercise to be done for the next month, year or decade. Memorization is important and understanding is important, and the two are not in any conflict whatsoever.

k__ 4y ago

Oh, could you go into more detail about math and memoizantion? What did you do? I had the impression, these techniques only work well for languages, but I really would love to get better at math.

mkl 4y ago
Have a look at this article by Michael Nielsen: https://cognitivemedium.com/srs-mathematics https://cognitivemedium.com/srs-mathematics Old HN discussion: https://news.ycombinator.com/item?id=18895613 https://news.ycombinator.com/item?id=18895613 Or this one: https://cronokirby.com/posts/2021/02/spaced-repetition-for-mathematics/ https://cronokirby.com/posts/2021/02/spaced-repetition-for-m... Hasn't been on HN before so I just posted it: https://news.ycombinator.com/item?id=32390730 https://news.ycombinator.com/item?id=32390730
dls2016 4y ago
See my other comment.

ren_engineer 4y ago

I'd be really interested to see some research into integrating spaced repetition into our actual education system. Almost everything I see about it is adults learning, I wonder how much we could speed up primary school education considering so much of the "base" stuff needed to advance is rote memorization anyway seems like countries should be investing money in this, potentially trillions in unlocked economic potential by improving and speeding up education. I think I read something like 20-30% of medical school students use SRS, yet only a fraction of the general population uses it. Insane to me that we have a tool like this and almost nothing is being done to improve adoption.

pessimizer 4y ago
Hundreds of millions of the world's kids were remote learning for up to a year and a half. If there was any opportunity to develop real tools to help with remote learning, it was then, but we ended up with nothing, and remote learning still sucks. If anybody is going to integrate memory techniques into a curriculum, it'll probably be some Silicon Valley charter.
lemming 4y ago
No research here, but I use the great Fresh Cards app (by allenu here on HN) with my daughter's homeschooling, and it works great. We've used it for phonics and all sorts of basic math facts, and I use it for scheduling spelling word review as well. We're about to start teaching science and I anticipate using it a lot there as well.
Denzel 4y ago
Do you have a link to that research that claimed 20-30% of medical school students use SRS?
zozbot234 4y ago
Given that so much of modern education happens in large-group settings, it seems hard to apply SRS principles to it. A group of students will be a lot farther from 100% recall of all items than any individual student might be, and the items that require review will correspondingly differ.

ok_dad 4y ago

Do you have any notes on how you studied? I’m interested in going back to math grad school but forgot everything from undergrad, basically.

dls2016 4y ago
Two articles I wrote at the time which hold up surprisingly well: https://blogs.ams.org/mathgradblog/2010/12/28/spaced-math-repetition/ https://blogs.ams.org/mathgradblog/2010/12/28/spaced-math-re... https://blogs.ams.org/mathgradblog/2011/03/10/space-math-repetition-repetition/ https://blogs.ams.org/mathgradblog/2011/03/10/space-math-rep... And an example of some of my cards: https://www.dropbox.com/s/z714xpq36nvn3o1/rudin.pdf?dl=0 https://www.dropbox.com/s/z714xpq36nvn3o1/rudin.pdf?dl=0 If I'm being honest, I went overboard. Like I said, I literally memorized entire books. Entering cards into the system was the most difficult part. But it absolutely works! Had I stayed in academia, I would have loved to developed a set of flash cards to go along with course material.
- ok_dad 4y ago
  Thank you
- k__ 4y ago
  Okay, so the idea is to get a math book and convert the definitions in it to flash cards?

zinclozenge 4y ago

> but on the other hand the best researchers/engineers I know have a huge number of facts and examples memorized and ready at their fingertips The US is staunchly anti-memorization. It wasn't until I did a year abroad in a French university where the power of memorization was so obvious. One of the math students I spent time with told me it's the French tradition to "carry everything around in your head". They were studying symplectic geometry in their sophomore year of their bachelor's!

deleted 4y ago
[deleted]
CogitoCogito 4y ago
> The US is staunchly anti-memorization. I don't understand where this coming from. In my experience learning and teaching math in the US, I've found it's almost _entirely_ about memorization. Calculus students are usually able to regurgitate algorithms for differentiation/integration, but can't answer the most basic questions about what they're doing really means. This is just an aside. I'm not against memorization. I think memorization is the first step necessary for deeper internalized understanding since it lets you take the basic stuff and put it on autopilot so you can think about the rest that isn't as basic. That said my main complaint about US teaching of math is that that second step seems rarely to be taken and instead focus entirely on the memorization. I guess our experiences are both anecdotal, but I'm having trouble wrapping my head around your idea that the US is anti-memorization.
- zinclozenge 4y ago
  This might be the case for k-12 and maybe lower level courses, but this was _definitely_ not the case for when I was taking group theory, real analysis, etc. With that said, someone else in the comments mentioned that while it might seem there's an emphasis "regurgitation" it's mainly because going beyond that and really digging into the why of things is vastly out of scope for the class.

ctchocula 4y ago

I found this post fascinating. It makes me wonder is there an equivalent superpower that's more software engineering focused rather than coding focused like leetcode questions? I know everyone here likes to dump on Gang of Four, but perhaps design patterns and their usecases?

t_mann 4y ago

In grad school it seems obvious what you want to retain, after that it can become a bit trickier to make the choice. General question for everyone using this approach: how do you go about selecting topics to put into your SR schedule? I mean there are so many things that would be good to remember: math problems and leetcode are actually continuously relevant if you're in employment and ever thinking about moving jobs, software engineering tools that are important for daily work (those are changing so fast in some cases that I'm wondering again how much is worth committing to long-term memory), maybe there are some academic fields where you want to stay up-to-date on the research, all sorts of life hacks in the household / cooking / DIY space, literally everything about your family life, maybe some strategies in hobbies (just recently got into speedcubing, which is a lot about algorithm memorization),... Maybe the problem is just that I have too much of a "finite memory" mindset and we can easily remember all of those, lol.

borroka 4y ago
The problem is quickly solved, and it is important not to fall into " paralysis by analysis." Sometimes, while writing a card, we tell ourselves that it is not so important to remember that information and discard it, other times we discard it when during the review process we sense or realize that we are not interested in remembering that information . Assuming that there is some sort of logic behind the decisions made, I recommend using the same strategy that Napoleon is said to have used in his campaigns: first we start, then we will see.
- t_mann 4y ago
  Yeah, the whole thing is probably easy to overoptimize. Any recommendations wrt to the software? My preference for these sort of things are maximally compatible/portable solutions based on simplistic file formats (I keep a lot of personal tracking data in csv, eg). Here I'm thinking something along the lines of local markdown files for the cards, a database for the sampling info and a web app that does the sampling.
  - borroka 4y ago