I use Anki to learn French, Chess openings/tactics/techniques, to unscramble letters for scrabble, for Pub Trivia... The options are kind of limitless.
As a mid-30s guy who has well passed the neuroplasticity of his teen years, it's a godsend for me.
To echo the author's thoughts though, I can't prove empirically that I learn more effectively using Anki (or spaced repetition) than other methods... Only anecdotally. I have a shockingly poor memory, but now I'm B2 certified in French and an ~1800 Elo on chess.com .
Practicing your retrieval is actually one of the best ways to retain knowledge of something. Flashcard programs like Anki are really great because it identifies where you need more work and drills you on your weak points -- it feels awkward working constantly on your weak points, but you get quantifiably better results with the flashcard method it uses.
Some people criticize flashcards as optimizing for rote memorization and deemphasizing understanding, but you'll never achieve understanding or mastery in general without a solid platform of knowledge to work from.
I think deliberate practice is what's really core to improving any skill, including memory.
Spaced repetition is an effective way to review things but its biggest benefit is a process that's easy to be consistent with.
Somebody else can have equal or better performance with other technique but just like dieting, it doesnt matter as much what method you use as long as you stick with it.
Really curious exactly how you learn things like chess with flash cards. French makes sense as I would guess you just have a word or phrase in both languages.
When I was doing rote memorization and flashcards frequently (some years ago now) I observed that remembering things became a lot easier for me.
I also find my verbal fluency is directly affected by how much pure social time I have in my schedule. It makes me think its one of those 'use it or lose it' things and that I need to schedule more time with people.
I do a really lightweight version of flash cards. Everytime I'm learning a new tool or tech, I grab oversized notecards (my favorite are 8x5" dot-grid cards). I put a label at the top, and create bullet points of each item i want to remember. I then review. No individual cards for each item or anything. Just all the things grouped on one card as bullet points.
For example, I'll have a `sqlite` card, and put all the commands and everything on it, as I learn them. I'll use it as a cheatsheet, but then also a few minutes of mindful review. This for the toolings that I want to know well enough to not get slowed down googling the commands. I do this for a lot of CLI tools, but also things I need to remember about the business of my company and working across group, etc....
Eventually the five or six working cards I have, get put on a pile and new ones come in.....
> From this perspective, fields that require deep understanding, like math, require memory just as fields with a breadth of shallow knowledge do, though in different ways.
I'm interested in understanding how others use Anki for conceptual subjects like pure math or physics. I believe many fundamental rules in Spaced Repetition (e.g. like keeping cards concise) are thrown out the window for conceptual subjects.
I took my first real analysis course last semester, and I made flashcards with pen and paper for every single non trivial definition, theorem, lemma, and corollary that we covered in lecture.
Analysis definitions and theorems get really complicated with intricate and difficult to follow logical chains, and there are a lot to remember.
These definitions and results don’t mean much on their own without exploring their neighbourhoods by proving relevant things, and I could have learned these definitions and results by just doing proofs. But being absolutely sure I could recite every theorem and definition definitely helped me on the final exam.
I think if you’re learning algorithms (like find the area under a curve) in a calculus course for example, flashcards might have more limited value, as in that case problems are relatively short and you’re better off just running through your set of algorithms a ton of times by doing problems.
I also took a group theory course last semester and I memorized every definition and result from lecture via flashcard, but didn’t practice using them enough by writing proofs. I ended up with like 2 or 3 out of 10 complete proofs and the rest half finished on the final exam because I had the right starting points, but not enough practice using what I knew in unexpected ways. Still passed somehow.
Depends on how you use the flashcards. You can use them to memorize definitions and equalities, and you can also use them as quiz questions which excercise your reason and not simply your memory. For example, you make a flashcard for each excercise question in your textbook. Once you identify what you're struggling with, make more flashcards of that same problem type to avoid remembering the solutions. This will take you from a shaky understanding to much firmer ground pretty quickly.
Honestly just making the flashcards and elaborating on/modifying problems you're struggling with will take you a very long way.
Same caveat as in the article: Spaced repetition is just one (minor) part of learning math/physics. It alone won't get you anywhere.
For math - particularly higher level math, the most obvious use case is definitions. There are so many!
You can put theorems in there, but it is a bit challenging on how to phrase it. A single theorem could result in several smaller flash cards.
I think what works better is taking a theorem, finding a representative problem that is solved via that theorem, and make the problem statement the question. The downside of this approach is each card takes longer to process as this is not just plain recall, but actively solving a problem. For this reason, I keep such cards in a separate deck and review them only when I have time I can dedicate (e.g. spending well over a minute per card).
Yeah most of the advance assumes you have the data ready at hand and just need to phrase the cards right, get the number of words right. Whereas for conceptual domains the biggest problem is: how do I encode this as question-answer pairs at all? What I want to read more of is people sitting down and writing in the first-person perspective how they go about it, like Michael Nielsen does here: https://cognitivemedium.com/srs-mathematics
hey fernando, I read your article a lot and it's helped me a lot in my own spaced repetition so thanks from me!
a note on your request, have you seen this video before? Andy has some custom PDF reader he built with flashcards built-in, and it's two hours of tacit flashcard creation centered around quantum mechanics: https://www.youtube.com/watch?v=OFuu4pesKf0
Perhaps "Using spaced repetition systems to see through a piece of mathematics
" [1] might be of interest for you. I have read author's "Augmenting Long-term Memory" [2] and have incorporated a lot of his advice into my Anki practice.
For me, it's quick access recipes (breakfast pancakes for kids), what was the name of the glacier that we hiked to last year, behavioral prompts etc.
I actually tend to keep my cards super concise. I treat Anki as a way to practice fundamentals, like memorizing certain formulas. Anytime I try to add conceptual stuff to cards I feel like I'm only memorizing one specialized version of the thing and it doesn't feel super useful.
> IMO you want to be actively trying to map the new concepts to things you already understand, and constantly working to update your mental model.
It's not an either-or.
Where SRS comes in handy is when you have to take long breaks between your study sessions (due to job + family). Have you ever tried learning an advanced math topic where you get to work on it for a few days, then may have to stop for a few weeks (or even months), then resume, and repeat over and over?
Chances are, no matter how intense you study during those few days, you'll likely forget important definitions/theorems in the periods you don't.
SRS takes care of those gaps.
Case in point - many years ago I put a lot of my intro to statistics course in flashcards and actively reviewed them. I hadn't done actual statistics for over a year, and then made a (false) claim here on HN. Someone gave me a counterexample using the chi-squared distribution. And it was amazing that I could recall the basic properties of the chi-squared distribution, and enough other theorems to verify what he said without consulting any book.
I've never used the chi-squared distribution for anything before or after.
(Sadly, I stopped using those cards years ago so I've forgotten the material!)
I think of it like drills in a sport. If your practice is 100% drills, you'll be pretty bad. But drills give you an awesome foundation to do the really complex stuff intuitively.
I tried to make an auto flashcard generator but ran into the issue that one word can map to many senses. But most word frequency datasets don't disambiguate the sense. So if you want to include all the senses for a word while ranking words by frequency they all get the same starting position.
This is a big part of why language learners have largely moved toward sentence mining as the preferred way to build an Anki deck.
Getting your words from real-world contexts, and keeping that context on the front of the card, largely eliminates the ambiguity problem. If a word has multiple senses, it gets multiple cards with different example sentences to illustrate each one.
It also helps a bunch with words that don’t really have a concise translation to your native language. For example the French words “mur” and “paroi” both mean “wall” in English, but the contexts where you use them are quite different. An example sentence helps with that, and getting that sentence from an even richer context such as a book or article you’ve read helps even more.
It’s also, frankly, just more enjoyable. I’ve come to view frequency lists as an antiquated tool. I needed them in the 1990s when good authentic-context study materials were hard to come by, but the modern Internet has made so-called immersion-based learning methods so easy and inexpensive I’m frankly mystified that people still cling to the joyless, almost mechanistic methods we were stuck with in the previous century.
Thank you, its good to hear some of what the state of the art is. My natural language processing studies at university are around the vintage you mention. I will have a go at this...
Yeah, NLP is a different beast from human language learning.
The most salient difference here is that NLP wants to automate as much as possible for reasons that are specific to NLP.
But for human language learning a lot of automation is actually harmful because manual effort tends to be good for Ebbinghaus’s arguably more important but less popularly appreciated discovery: memory encoding quality.
The fun is in making the cards truly yours, by writing them yourself based on your experience. After experimenting with generated cards, I throw them away. They were semantically correct, but not relatable/memorable.
Used to use Anki for foreign language learning. Guessing it would have been useful to memorise calc, chem and physics equations if it had existed when I was young.
Flashcards are brilliant. Anki is finally usable after they ditched the hot garbage algorithm they were using. Previously I've used the Leitner method and I stil think that's the best one for me.
I use Anki to learn French, Chess openings/tactics/techniques, to unscramble letters for scrabble, for Pub Trivia... The options are kind of limitless.
As a mid-30s guy who has well passed the neuroplasticity of his teen years, it's a godsend for me.
To echo the author's thoughts though, I can't prove empirically that I learn more effectively using Anki (or spaced repetition) than other methods... Only anecdotally. I have a shockingly poor memory, but now I'm B2 certified in French and an ~1800 Elo on chess.com .
Do I still forget things all the time? Yes.
Practicing your retrieval is actually one of the best ways to retain knowledge of something. Flashcard programs like Anki are really great because it identifies where you need more work and drills you on your weak points -- it feels awkward working constantly on your weak points, but you get quantifiably better results with the flashcard method it uses.
Some people criticize flashcards as optimizing for rote memorization and deemphasizing understanding, but you'll never achieve understanding or mastery in general without a solid platform of knowledge to work from.
I think deliberate practice is what's really core to improving any skill, including memory.
Spaced repetition is an effective way to review things but its biggest benefit is a process that's easy to be consistent with.
Somebody else can have equal or better performance with other technique but just like dieting, it doesnt matter as much what method you use as long as you stick with it.
Really curious exactly how you learn things like chess with flash cards. French makes sense as I would guess you just have a word or phrase in both languages.
What do you do for topics like chess?
When I was doing rote memorization and flashcards frequently (some years ago now) I observed that remembering things became a lot easier for me.
I also find my verbal fluency is directly affected by how much pure social time I have in my schedule. It makes me think its one of those 'use it or lose it' things and that I need to schedule more time with people.
I do a really lightweight version of flash cards. Everytime I'm learning a new tool or tech, I grab oversized notecards (my favorite are 8x5" dot-grid cards). I put a label at the top, and create bullet points of each item i want to remember. I then review. No individual cards for each item or anything. Just all the things grouped on one card as bullet points.
For example, I'll have a `sqlite` card, and put all the commands and everything on it, as I learn them. I'll use it as a cheatsheet, but then also a few minutes of mindful review. This for the toolings that I want to know well enough to not get slowed down googling the commands. I do this for a lot of CLI tools, but also things I need to remember about the business of my company and working across group, etc....
Eventually the five or six working cards I have, get put on a pile and new ones come in.....
> From this perspective, fields that require deep understanding, like math, require memory just as fields with a breadth of shallow knowledge do, though in different ways.
I'm interested in understanding how others use Anki for conceptual subjects like pure math or physics. I believe many fundamental rules in Spaced Repetition (e.g. like keeping cards concise) are thrown out the window for conceptual subjects.
I took my first real analysis course last semester, and I made flashcards with pen and paper for every single non trivial definition, theorem, lemma, and corollary that we covered in lecture.
Analysis definitions and theorems get really complicated with intricate and difficult to follow logical chains, and there are a lot to remember.
These definitions and results don’t mean much on their own without exploring their neighbourhoods by proving relevant things, and I could have learned these definitions and results by just doing proofs. But being absolutely sure I could recite every theorem and definition definitely helped me on the final exam.
I think if you’re learning algorithms (like find the area under a curve) in a calculus course for example, flashcards might have more limited value, as in that case problems are relatively short and you’re better off just running through your set of algorithms a ton of times by doing problems.
I also took a group theory course last semester and I memorized every definition and result from lecture via flashcard, but didn’t practice using them enough by writing proofs. I ended up with like 2 or 3 out of 10 complete proofs and the rest half finished on the final exam because I had the right starting points, but not enough practice using what I knew in unexpected ways. Still passed somehow.
> I took my first real analysis course last semester,
> These definitions and results don’t mean much on their own without exploring their neighbourhoods
Were these epsilon-neighborhoods?
I couldn’t resist :)
Depends on how you use the flashcards. You can use them to memorize definitions and equalities, and you can also use them as quiz questions which excercise your reason and not simply your memory. For example, you make a flashcard for each excercise question in your textbook. Once you identify what you're struggling with, make more flashcards of that same problem type to avoid remembering the solutions. This will take you from a shaky understanding to much firmer ground pretty quickly.
Honestly just making the flashcards and elaborating on/modifying problems you're struggling with will take you a very long way.
It is a bit more challenging, but it is workable.
Same caveat as in the article: Spaced repetition is just one (minor) part of learning math/physics. It alone won't get you anywhere.
For math - particularly higher level math, the most obvious use case is definitions. There are so many!
You can put theorems in there, but it is a bit challenging on how to phrase it. A single theorem could result in several smaller flash cards.
I think what works better is taking a theorem, finding a representative problem that is solved via that theorem, and make the problem statement the question. The downside of this approach is each card takes longer to process as this is not just plain recall, but actively solving a problem. For this reason, I keep such cards in a separate deck and review them only when I have time I can dedicate (e.g. spending well over a minute per card).
Just put every definition, theorem, and exercise in a textbook into a card in an anki deck.
There are no "rules" for how flashcards should work.
Yeah most of the advance assumes you have the data ready at hand and just need to phrase the cards right, get the number of words right. Whereas for conceptual domains the biggest problem is: how do I encode this as question-answer pairs at all? What I want to read more of is people sitting down and writing in the first-person perspective how they go about it, like Michael Nielsen does here: https://cognitivemedium.com/srs-mathematics
I wrote a bit more about this problem here: https://borretti.me/article/the-applicability-of-spaced-repe...
hey fernando, I read your article a lot and it's helped me a lot in my own spaced repetition so thanks from me!
a note on your request, have you seen this video before? Andy has some custom PDF reader he built with flashcards built-in, and it's two hours of tacit flashcard creation centered around quantum mechanics: https://www.youtube.com/watch?v=OFuu4pesKf0
Perhaps "Using spaced repetition systems to see through a piece of mathematics " [1] might be of interest for you. I have read author's "Augmenting Long-term Memory" [2] and have incorporated a lot of his advice into my Anki practice.
For me, it's quick access recipes (breakfast pancakes for kids), what was the name of the glacier that we hiked to last year, behavioral prompts etc.
1: https://cognitivemedium.com/srs-mathematics
2: https://augmentingcognition.com/ltm.html
Great blog posts. Exactly on point.
I actually tend to keep my cards super concise. I treat Anki as a way to practice fundamentals, like memorizing certain formulas. Anytime I try to add conceptual stuff to cards I feel like I'm only memorizing one specialized version of the thing and it doesn't feel super useful.
I kinda feel like using memorization techniques for things that require deeper understanding probably isn't the most efficient way to learn.
IMO you want to be actively trying to map the new concepts to things you already understand, and constantly working to update your mental model.
> IMO you want to be actively trying to map the new concepts to things you already understand, and constantly working to update your mental model.
It's not an either-or.
Where SRS comes in handy is when you have to take long breaks between your study sessions (due to job + family). Have you ever tried learning an advanced math topic where you get to work on it for a few days, then may have to stop for a few weeks (or even months), then resume, and repeat over and over?
Chances are, no matter how intense you study during those few days, you'll likely forget important definitions/theorems in the periods you don't.
SRS takes care of those gaps.
Case in point - many years ago I put a lot of my intro to statistics course in flashcards and actively reviewed them. I hadn't done actual statistics for over a year, and then made a (false) claim here on HN. Someone gave me a counterexample using the chi-squared distribution. And it was amazing that I could recall the basic properties of the chi-squared distribution, and enough other theorems to verify what he said without consulting any book.
I've never used the chi-squared distribution for anything before or after.
(Sadly, I stopped using those cards years ago so I've forgotten the material!)
Familiarity through repetition is 95% of learning any subject. Mathematics isn't special.
I think of it like drills in a sport. If your practice is 100% drills, you'll be pretty bad. But drills give you an awesome foundation to do the really complex stuff intuitively.
I tried to make an auto flashcard generator but ran into the issue that one word can map to many senses. But most word frequency datasets don't disambiguate the sense. So if you want to include all the senses for a word while ranking words by frequency they all get the same starting position.
This is a big part of why language learners have largely moved toward sentence mining as the preferred way to build an Anki deck.
Getting your words from real-world contexts, and keeping that context on the front of the card, largely eliminates the ambiguity problem. If a word has multiple senses, it gets multiple cards with different example sentences to illustrate each one.
It also helps a bunch with words that don’t really have a concise translation to your native language. For example the French words “mur” and “paroi” both mean “wall” in English, but the contexts where you use them are quite different. An example sentence helps with that, and getting that sentence from an even richer context such as a book or article you’ve read helps even more.
It’s also, frankly, just more enjoyable. I’ve come to view frequency lists as an antiquated tool. I needed them in the 1990s when good authentic-context study materials were hard to come by, but the modern Internet has made so-called immersion-based learning methods so easy and inexpensive I’m frankly mystified that people still cling to the joyless, almost mechanistic methods we were stuck with in the previous century.
Thank you, its good to hear some of what the state of the art is. My natural language processing studies at university are around the vintage you mention. I will have a go at this...
Yeah, NLP is a different beast from human language learning.
The most salient difference here is that NLP wants to automate as much as possible for reasons that are specific to NLP.
But for human language learning a lot of automation is actually harmful because manual effort tends to be good for Ebbinghaus’s arguably more important but less popularly appreciated discovery: memory encoding quality.
The fun is in making the cards truly yours, by writing them yourself based on your experience. After experimenting with generated cards, I throw them away. They were semantically correct, but not relatable/memorable.
Used to use Anki for foreign language learning. Guessing it would have been useful to memorise calc, chem and physics equations if it had existed when I was young.
it is less useful for physics, math, and music since fluency is so much important.
It is important for language acquisition too, but the language involves a lot more rote memorization than the above.
>it is less useful for physics, math, and music since fluency is so much important.
I mean, you can put whatever you want on a flashcard. e.g "Derive the fundamental theorem of whatever", "Prove this theorem" etc.
Also music has a extreme level of "stuff you just need to memorise".
Flashcards are brilliant. Anki is finally usable after they ditched the hot garbage algorithm they were using. Previously I've used the Leitner method and I stil think that's the best one for me.
Which algorithm is the hot garbage one to you? SuperMemo 2?