[HN Gopher] Individualized Spaced Repetition in Hierarchical Kno...
       ___________________________________________________________________
        
       Individualized Spaced Repetition in Hierarchical Knowledge
       Structures
        
       Author : JustinSkycak
       Score  : 159 points
       Date   : 2024-07-13 15:13 UTC (4 days ago)
        
 (HTM) web link (www.justinmath.com)
 (TXT) w3m dump (www.justinmath.com)
        
       | hiAndrewQuinn wrote:
       | Now these are the insights I'm looking for when it comes to
       | "second generation" SRS software suites. When you focus your
       | attention on a specific niche, like mathematics here, you can get
       | some serious improvements in retention just by using the shape of
       | the subject to your advantage like this.
        
       | AlchemistCamp wrote:
       | Anki contributor here:
       | 
       | I've been using SRS on and off since 2006 and this post addresses
       | one of the key failure modes I've seen in SRS usage--they tend to
       | be fantastic for discrete pieces of information, like the names
       | of capital cities, the pronunciation of various symbols or
       | various physical constants.
       | 
       | Most my usage of SRS in the early days was languages. For that
       | domain, SRS is useful for learning an alphabet (or syllabary),
       | for scaffolding enough common words to start understanding graded
       | readers and for a few other tasks. They're terrible as a primary
       | learning strategy, though! Too much of language is highly nuanced
       | and context dependent and the only way to absorb all the
       | unwritten rules, the common collocations and the precise
       | boundaries of word meanings is through extensive input. This
       | means encountering the same words and structures in countless
       | different variations and contexts, not the same few sentences
       | drilled repeatedly (at least past the beginning stages).
       | 
       | By paying attention to the specifics of learning math and
       | tailoring the SRS to match it, it's possible to make a far more
       | efficient system than anyone could with an Anki deck. I'd love to
       | see similar efforts in other subjects!
        
         | dotancohen wrote:
         | Anki is great for building vocabulary. It's not suitable for
         | actually learning the language. I use it constantly, averaging
         | over 200 cards a day for over fifteen years.
        
           | kiba wrote:
           | I wish I have the same dedication, but alas Anki hadn't
           | sufficiently proven useful to me that I would use it on a day
           | to day basis.
        
             | dotancohen wrote:
             | If you have an Android device, go install Ankidroid. It's
             | absolutely terrific, letting you fill in those wasted
             | seconds when you're waiting in line, sitting on the toilet,
             | waiting for the pot to boil. Two or three cards at a time,
             | dozens of times per day, adds up.
             | 
             | You could treat yourself to three cards after every git
             | commit, for instance. Takes literally less than ten seconds
             | to review three cards.
        
               | kiba wrote:
               | The problem isn't the convenience but that the value in
               | my deck hasn't sufficiently manifested itself in real
               | world applications.
               | 
               | This is my own fault rather than the app's fault.
        
               | Bluestein wrote:
               | I both _second_ Ankidroid (oustanding) ...
               | 
               | ... and concur when failing (as of yet) to find a way to
               | use the system with other types of knowledge, sadly.-
        
         | gwd wrote:
         | A couple of problems I found with Anki for languages:
         | 
         | 1. The words aren't in context, which leads to "flashcard
         | blindness", where you see a word in context, know that you
         | recognize it, but can't remember what it means.
         | 
         | 2. The theory behind spaced repetition is that you learn most
         | efficiently when you try to remember something just when you're
         | about to forget it. But that means that if the algorithm is
         | working properly, every single card is hard. This makes
         | motivation a problem, because you know studying is going to be
         | a grind, not fun.
         | 
         | 3. While "being able to remember it after thinking a second or
         | two" might be fine when studying for an exam, or in many other
         | contexts where memorization might be important, that's too slow
         | for languages. What you want for a language is "know it
         | immediately without having to think about it".
         | 
         | 4. The "scheduled review" system is too inflexible. Some days
         | you get only a handful of cards to review, some days you get
         | dozens. It's hard to tell when you're starting out how many
         | cards you should be adding each day such that the number of
         | cards match the amount of time / effort you have to study.
         | Furthermore, if you skip a single day, you have twice as much
         | the next day; and if life happens and you end up missing a week
         | or a month, you come back with a giant jumble of cards, half of
         | which you've forgotten, and it's really difficult to dig your
         | way out of it.
         | 
         | By a strange coincidence, in 2019 I also started on an
         | alternate to Anki to help myself study Mandarin. It has some
         | similarities to his system, in that there's multi-level
         | knowledge; but it's different in that instead of having a fixed
         | schedule, it has the concept of "difficulty" and "study value"
         | for each word / grammar concept, and the algorithm tries to
         | give you a full "readunit" of "native input" which will balance
         | the two. "Spaced repetition" emerges naturally from the model,
         | and if you go away for a week (or 6 months), it knows you've
         | forgotten some things, so it gradually refreshes your memory.
         | And because you're reading actual native text, there's
         | something which pulls you in.
         | 
         | It's in closed beta now; the first public language (MVP) will
         | be in Biblical Greek, but the second one (if it happens, maybe
         | in a year or two) will be in Mandarin; and hopefully there will
         | be other ones after that. There's a sign-up form you can use to
         | be notified for updates.
         | 
         | https://www.laleolanguage.com
        
           | Bluestein wrote:
           | > But that means that if the algorithm is working properly,
           | every single card is hard.
           | 
           | Could the algo be tweaked so as to regulate the "closeness to
           | the edge", ergo, the difficulty?                 PS. Then
           | again, something tells me what makes SR so effective *might
           | just be* (or be related to) that "difficulty".-
        
             | gwd wrote:
             | So let's separate out "effective" from "efficient".
             | 
             | I'm perfectly happy to accept that the "every single card
             | is hard" is the most _efficient_ system for _memorizing
             | facts_ : i.e., that if you measure the number of facts you
             | can recite and divide it by the amount spent studying, that
             | SRS will come out on top.
             | 
             | But is that the most "effective" -- will it actually result
             | in you learning more facts at the end of some time frame?
             | 
             | For that you need to know not only the amount learned per
             | unit of studying, but the amount that you actually study;
             | and the amount you study depends in part on your
             | motivation; and your motivation depends on how hard /
             | engaging the study is.
             | 
             | Suppose that with every card being hard, you study on
             | average 20 cards a day; but that with every card being only
             | moderate, you average 60 cards a day. Even if the
             | "effectiveness" of moderate card study is only one half of
             | difficult card study, you still end up learning more,
             | because you've studied three times as much.
             | 
             | The idea that after seeing a given card 30 times over the
             | course of a year, you'd somehow end up knowing it _less_
             | well than if you 'd seen it only 10 times, because it
             | wasn't "hard enough" when you did see it, seems really
             | unlikely to me.
        
               | Bluestein wrote:
               | I tend to agree, but, perhaps "being hard enough" as a
               | function of "prevented forgetting" or likelihood of
               | forgetfulness might be an indicator.-
        
           | CuriouslyC wrote:
           | I've seen studies that show that the optimal learning rate
           | occurs when you are 70-75% likely to succeed in a challenge.
           | If it is much easier you tend to downgrade your effort, which
           | leads to learning to half ass at worst, and slow learning at
           | best. If it is much harder the stress of the challenge
           | actually inhibits learning. The exact optimum is thought to
           | be person dependent as a lot has to do with how you respond
           | to challenges, but for the average person 70% effort is the
           | sweet spot.
        
             | gwd wrote:
             | As I said in a parallel thread, if you're going for "most
             | number of facts you can recite per hour of time spent
             | studying", I can well believe flashcards with a 70% failure
             | rate are "optimum". But if you're trying to have a
             | conversation, watch a movie, or read a newspaper article,
             | and there's a 30% chance you're not going to recognize any
             | given word, you're going to have a hard time.
             | 
             | What you really want is an appropriate level of difficulty
             | _for an entire thing you 're trying to understand_. This
             | could be either because you have one completely new word
             | per paragraph, or because you have 5 moderately difficult
             | words, or 10 not-too-hard words. The fact that the rest of
             | the words might already be super easy for you doesn't mean
             | you aren't still reinforcing them.
             | 
             | That's basically what my algorithm is trying to do: hand
             | you something to read (a sentence, paragraph, section,
             | chapter, whatever) that's at the "right level" of effort
             | for you.
        
           | zozbot234 wrote:
           | > Furthermore, if you skip a single day, you have twice as
           | much the next day; and if life happens and you end up missing
           | a week or a month, you come back with a giant jumble of
           | cards, half of which you've forgotten, and it's really
           | difficult to dig your way out of it.
           | 
           | The Anki system is actually really good at dealing with
           | missed days. You end up recalling _most_ of the cards that
           | you skipped review for, and the system gives you extra credit
           | for the increased interval before review, in that subsequent
           | repeats for the same card will be spaced out even further.
           | Cards that you outright fail to recall due to the missed
           | reviews are a problem, but the best way to  'dig your way
           | out' of that hole is to keep reviewing on a regular schedule
           | and not to overwork or cram. The backlog gets cleared rather
           | quickly.
        
             | gwd wrote:
             | Sure, a single missed day isn't bad; but have you ever
             | skipped a month?
             | 
             | I'd been using Anki for Mandarin flash cards for a couple
             | of years, and decided I wanted to memorize the "outs"
             | (probabilities) of various hands for Texas Hold 'Em Poker.
             | So I made a separate Anki deck and used it for a few
             | months. Then I got busy, and stopped studying the poker
             | deck (while maintaining the Mandarin deck). When I tried to
             | pick it up again, it was just impossible -- I'd forgotten
             | so much, and the card list was so long, that if I said "I
             | forgot this", it would be _scheduled_ for the next day, but
             | because it was behind 100 other cards, I wouldn 't actually
             | be _shown_ it for a week or two. The system was just
             | completely broken.
             | 
             | Contrast that to the system of my own that I developed,
             | based on the "study value" (effect of studying now on the
             | difficulty) rather than fixed timeouts. After working on
             | and using my own system for about 4 years, I got a bit
             | tired of it (and I was also in the middle of redesigning
             | the database from the ground up), and so decided to give
             | Duolingo a go for a bit, just to see what it was like. Six
             | months later, I came back to my own system, and it was
             | great -- just slowly eased me back into the vocab I had
             | before. The same is true after missing a day, or a week:
             | it's always welcoming to get back into, rather than
             | terrifying to get behind.
        
               | zozbot234 wrote:
               | > The system was just completely broken.
               | 
               | It's not broken, it's just doing its best to cope with
               | your situation. Missing lots of days means that there
               | will be lots of cards where it's just not clear if you're
               | going to recall them or not. Figuring that out becomes
               | the priority, then the system is effectively back to
               | normal - possibly with some missed cards that will have
               | to be learned again. I'm not sure how one could do better
               | than that.
        
               | d110af5ccf wrote:
               | The comment you replied to described an edge case and
               | explained why it's broken in that particular case. You
               | haven't actually responded to the example provided.
               | 
               | > it's just not clear if you're going to recall them or
               | not. Figuring that out becomes the priority
               | 
               | Presumably the priority ought to be (re)starting with a
               | small subset of cards and gradually trickling the others
               | back in. The algorithm needs to account for time spent by
               | the given individual and adapt to changes in that over
               | time.
               | 
               | I haven't used Anki for about a decade so I'm not
               | familiar with the current state of things. At the time a
               | major factor in my dropping it was that I found the
               | algorithm to be more of a hindrance than a help.
        
           | yjftsjthsd-h wrote:
           | > 1. The words aren't in context, which leads to "flashcard
           | blindness", where you see a word in context, know that you
           | recognize it, but can't remember what it means.
           | 
           | Clozes should help with this. If anything, I sometimes find
           | it easier to remember words when they're presented in a
           | sentence, though obviously you have to be cautious of
           | overfitting.
        
             | gwd wrote:
             | In my experience, it's actually easier to memorize a
             | sentence than to actually learn the principles behind
             | something. (Turns out this is also true for neural
             | networks, and there are loads of techniques for
             | counteracting it.)
             | 
             | So OK, to counteract memorization and lack of
             | contextualization, you have 5-6 sentences with the same
             | word. But now Anki doesn't know that they're related, so
             | the SRS system can't actually space out the learning the
             | way it wants to.
             | 
             | With the system I developed, you're given a full phrase /
             | sentence / paragraph / section / chapter, and it separately
             | tracks the words or grammar elements you've seen, in a way
             | similar to that described by OP. So you're always actually
             | reading native content, of which much of the content will
             | be new even if the words are already known to you.
        
         | jwells89 wrote:
         | For this reason, I've seen it recommended in various language
         | learning guides to use Anki in a manner that's complementary to
         | consumption of media in the target language. The general idea
         | is to do Anki-only for the earliest bootstrapping stages (super
         | basic vocab) and switch to media+Anki as early as possible.
         | 
         | The media gives both context and real experience with the
         | language while Anki serves to commit the words you've
         | read/heard (even those not used quite as commonly) to memory.
         | I've only just dipped my toe into this method but have seen
         | many reports of success with it from others.
        
       | isaacfrond wrote:
       | There lots of knowledge types where Anki might not be the ideal
       | choice. For example,
       | 
       | - itemized lists of information. E.g. The 5 reasons for the civil
       | war, type of questions. What to do, if you miss one item? Your
       | card as a whole gets over exposed, while the missed item might
       | get underexposed.
       | 
       | - Related information, e.g., history dates. When using Anki the
       | students tends to latch on to incidental facts, e.g., Treaty of
       | Paris, ah I remember it has two repeating digits, yes, 1899.
       | While it would be more useful for a student to think, ah, that
       | was after the Cuban independence struggles in the 1890's.
       | 
       | Any user will recognize that this effect is very strong. You tend
       | to remember cards by the most trivial of things.
       | 
       | - Hierarchical knowledge. Things like chess openings. How do you
       | put that in Anki cards. It's all a kludge. Where to put the
       | variants, etc.
       | 
       | - Knowledge networks. Things like medical information (where Anki
       | is hugely popular). But typically, you get cards with massive
       | amounts of information because you have lots of linked
       | information, (symptoms, causes, treatment, pharmaceuticals, etc.
       | )
       | 
       | - Even in language learning. We have the useful fiction that
       | there is a 1-1 relationship between words in two languages, but
       | there almost never is.
       | 
       | - Learned knowledge tends to be linked to Anki. It happens often
       | that you can remember things when doing Anki, while being at a
       | loss when needing the information in the real world.
       | 
       | Add to that, that Anki does nothing for conceptual understanding.
       | You really need to learn a subject before memorizing it, but in
       | the learning phase Anki is not helpful.
       | 
       | So in short, yes, Anki is the best tool there is to help
       | learning, but I'm sure better tools can be made, especially when
       | targeted to a particular knowledge field.
        
         | gwervc wrote:
         | > - Even in language learning. We have the useful fiction that
         | there is a 1-1 relationship between words in two languages, but
         | there almost never is.
         | 
         | It's not really a problem: space repetition is a way to build
         | familiarity with vocabulary. Once it is done, more finer uses
         | can be inferred from context. The value lies in breadth not
         | depth.
        
           | gwd wrote:
           | A couple of problems I found with Anki for languages:
           | 
           | 1. The words aren't in context, which leads to "flashcard
           | blindness", where you see a word in context, know that you
           | recognize it, but can't remember what it means.
           | 
           | 2. The theory behind spaced repetition is that you learn most
           | _efficiently_ when you try to remember something just when
           | you 're about to forget it. But that means that if the
           | algorithm is working properly, _every single card is hard_.
           | This makes motivation a problem, because you know studying is
           | going to be a grind, not fun.
           | 
           | 3. While "being able to remember it after thinking a second
           | or two" might be fine when studying for an exam, or in many
           | other contexts where memorization might be important, that's
           | too slow for languages. What you want for a language is "know
           | it immediately without having to think about it".
           | 
           | 4. The "scheduled review" system is too inflexible. Some days
           | you get only a handful of cards to review, some days you get
           | dozens. It's hard to tell when you're starting out how many
           | cards you should be adding each day such that the number of
           | cards match the amount of time / effort you have to study.
           | Furthermore, if you skip a single day, you have twice as much
           | the next day; and if life happens and you end up missing a
           | week or a month, you come back with a giant jumble of cards,
           | half of which you've forgotten, and it's really difficult to
           | dig your way out of it.
           | 
           | By a strange coincidence, in 2019 I _also_ started on an
           | alternate to Anki to help myself study Mandarin. It has some
           | similarities to his system, in that there 's multi-level
           | knowledge; but it's different in that instead of having a
           | fixed schedule, it has the concept of "difficulty" and "study
           | value" for each word / grammar concept, and the algorithm
           | tries to give you a full "readunit" of "native input" which
           | will balance the two. "Spaced repetition" emerges naturally
           | from the model, and if you go away for a week (or 6 months),
           | it knows you've forgotten some things, so it gradually
           | refreshes your memory.
           | 
           | It's in closed beta now; the first public language (MVP) will
           | be in Biblical Greek, but the second one (if it happens,
           | maybe in a year or two) will be in Mandarin; and hopefully
           | there will be other ones after that. There's a sign-up form
           | you can use to be notified for updates.
           | 
           | https://www.laleolanguage.com
        
           | AlchemistCamp wrote:
           | It's a very bad way to build familiarity with vocabulary for
           | two reasons--it doesn't teach word boundaries and it doesn't
           | teach collocations.
           | 
           | For example, even simple words like "nose" differ a bit from
           | language to language. Can "nose" refer to the thing that
           | smells on a pig or an elephant? In English, no. In Chinese,
           | yes. In Malay, people and pigs have noses but an elephant's
           | trunk is a different word.
           | 
           | In English if someone asks you how you are, it's reasonable
           | to reply "absolutely fantastic" or "pretty good", while it
           | would be a bit odd to answer "pretty fantastic" and very
           | strange to answer "absolutely good". This isn't because of a
           | grammatical issue that can be memorized. It's just that
           | certain words tend to be used together and the only way to
           | really consistently get it right is to get a lot of input and
           | develop a feel for the language.
           | 
           | Extensive reading is a better way of building and maintaining
           | vocabulary than anything you can do with flash cards and at
           | the same time you'll be gaining understanding about the
           | common stories, beliefs and culture of the speakers of the
           | target language.
        
             | vlz wrote:
             | Hmm, sort of agree for the later stages of learning, but
             | learning by flashcards is incredibly helpful at the
             | beginning and to get started.
             | 
             | Referring badly to a nose on an elephant is better than not
             | having any word ready at all.
             | 
             | Saying ,,absolutely good" is totally fine for most people
             | if you are a beginner in the english language. (Also, you
             | can put phrases on flashcards)
             | 
             | And sure, reading extensively is a great way to build
             | vocabulary. But it takes a while (depending on the language
             | quite a long while) before you can begin to read
             | extensively.
        
               | AlchemistCamp wrote:
               | A lack of suitable resources is often a problem at the
               | lower levels. FWIW, I experienced this first hand as the
               | first foreign language I learned to a relatively fluent
               | (~B2 level) was Japanese and that was from 2000-2002.
               | 
               | Graded readers are ideal early on, but if the language
               | you're learning just doesn't have them, then going
               | through multiple textbooks aimed at your level (e.g. an
               | intro textbook from publisher A and another intro
               | textbook from publisher B) is a good strategy. Materials
               | aimed at 5 or 6 year-old native learners are also often a
               | decent path. It's not exciting but there's a lot of
               | repetition, there are a lot of pictures and if it's a
               | character-based language, there will be a syllabary like
               | hiragana/zhuyin/pinyin to help you.
        
               | csa wrote:
               | > Graded readers are ideal early on
               | 
               | Depends on learner. I've seen people really love graded
               | readers from an early stage. I personally can't stand
               | them until the 1000-2000 word or more range. Note that I
               | am a big fan of extensive reading, but the lower level
               | stuff just makes my eyes bleed, and in some cases is just
               | bad (e.g., graded English readers that use lower
               | frequency meanings of common words to meet a word limit).
               | 
               | > going through multiple textbooks aimed at your level
               | (e.g. an intro textbook from publisher A and another
               | intro textbook from publisher B) is a good strategy
               | 
               | Very underrated, imho. I wish more folks would do this.
               | 
               | > Materials aimed at 5 or 6 year-old native learners are
               | also often a decent path
               | 
               | Again, this makes my eyes bleed. There is often quite a
               | bit of words that are aimed at children that maybe aren't
               | the best for beginning learners. I can't remember what
               | they were with Japanese, but I'm pretty sure a lot of
               | them were onomatopoeic words that every Japanese kid
               | knows but non-native speakers do not... and probably
               | should not learn that early in the process.
               | 
               | Iirc, third grade is when the language becomes more
               | "standard" and less kids talk, middle school stuff is
               | godly for beginning mid-range fluency, and high school
               | content fleshes out mid-range fluency (as one might
               | expect).
               | 
               | Books and online content aimed at teenaged readers can be
               | surprisingly accessible, with the main challenge being to
               | find material with substance (imho).
        
             | csa wrote:
             | > Extensive reading is a better way of building and
             | maintaining vocabulary than anything you can do with flash
             | cards
             | 
             | Eh, I think that this is only true at certain ranges of
             | fluency development.
             | 
             | Note that I am a huge fan of extensive reading, and I don't
             | think folks use it enough, but...
             | 
             | 1. It's usually prudent to brute force the first few
             | hundred words, maybe up to 1000, depending on one's access
             | to quality graded readers. The theory says that you want
             | 95-98% lexical coverage for extensive reading to reach its
             | highest potential.
             | 
             | 2. To maintain general fluency, extensive reading just
             | can't be beat.
             | 
             | 3. That said, for domain specific vocabulary and/or low
             | frequency vocabulary, cards are almost necessary since the
             | space in between exposure can be incredibly wide. For
             | reference, as a native speaker of English, I still add new
             | words that I run across to a vocab memorization list --
             | recent additions are _petard_ and _malapert_. Frankly, I'm
             | not sure I will ever run across these words again in a
             | text, but I want to know them and (in the case of
             | _malapert_ ) use them. For specialists in a field, knowing
             | things like "nuclear non-proliferaiton treaty" or
             | "bilateral negotiations" might be worthy of flash card
             | study for folks in politics/political science.
        
         | keiferski wrote:
         | 1. The best card-creation practice is to divide these itemized
         | lists into separate cards. So ideally, you shouldn't have 5
         | items on one card anyway.
         | 
         | 2. Dates are pretty important to know, so I'm not sure what the
         | issue is here.
         | 
         | 3. With language learning, there is no reason why you need to
         | make cards word-word. Personally I use image-word much more
         | often, which correlates more to how we learn our first
         | language.
         | 
         |  _It happens often that you can remember things when doing
         | Anki, while being at a loss when needing the information in the
         | real world._
         | 
         | I haven't had that experience at all. But if you have, there is
         | a simple fix: create cards that mimic the situation you'd use
         | the phrase in. For example, have the phrase "a cappuccino,
         | please" matched with a photo of a barista in a coffee shop.
         | 
         |  _Anki does nothing for conceptual understanding. You really
         | need to learn a subject before memorizing it, but in the
         | learning phase Anki is not helpful._
         | 
         | I also don't agree with this. Learning the "foundational"
         | aspects of something is critique for understanding it
         | conceptually. For example, knowing the boring geographical
         | details of European borders circa 1900 is key to understanding
         | the subsequent 45 years of geopolitical conflicts.
         | 
         | In general, I think most of the critiques of Anki/spaced
         | repetition/flashcards are mostly just critiques of the
         | "typical" way people make cards and use the apps. If you get a
         | little more creative with creating cards, most of these issues
         | go away.
         | 
         | That all said, I do agree that Anki is definitely not perfect
         | and could be improved - but more in the sense of making better-
         | designed cards and better practices the default, not something
         | you have to implement manually yourself.
        
           | Bluestein wrote:
           | > In general, I think most of the critiques of Anki/spaced
           | repetition/flashcards are mostly just critiques of the
           | "typical" way people make cards and use the apps.In general,
           | I think most of the critiques of Anki/spaced
           | repetition/flashcards are mostly just critiques of the
           | "typical" way people make cards and use the apps.
           | 
           | Somwhere, _there 's gotta be_ an expert/course/training on
           | how to best _use_ SR, that is to say, how to best ingest
           | knowledge into the system and prepare the reptition items
           | themselves. Kind of like a best-practices approach ...
        
             | keiferski wrote:
             | Working on it myself, just give me some time... :)
        
               | Bluestein wrote:
               | Let me wish you all the best, and send you sincere
               | congrats.-
        
             | MichaelNolan wrote:
             | There are some really good guides on how to use SRS/Anki
             | out there. In order of most basic to more advanced:
             | 
             | http://super-memory.com/articles/20rules.htm
             | 
             | https://borretti.me/article/effective-spaced-repetition
             | 
             | https://andymatuschak.org/prompts/
        
               | Bluestein wrote:
               | Who knows, right, maybe AI-assisted SRS can become so
               | effective ...
               | 
               | ... that the "singularity" ends up being us :)
               | (we become the superhuman intelligence that we were
               | seeking to create ...       ... by "partnering" with
               | increasingly intelligent systems).-       In a sense it'd
               | make much sense: We are as good a starting point as any,
               | if not better.-
        
         | t_mann wrote:
         | ad 1: have you tried using Cloze cards for that? I like to
         | group eg 1-2 reasons, then I will see the list with 1 or 2
         | items missing
         | 
         | ad 3: I had success for similar problems by simply creating a
         | lot of cards that give enough context and just ask for the next
         | step. In chess openings, couldn't you just display the current
         | position and ask something like "In opening X, variant Y, what
         | are the next moves for white here"? In some cases I've written
         | scripts to create cards for all variations of a question I want
         | to ask
         | 
         | ad 4: I think Cloze deletions can help to some extent here
         | (I've basically made Cloze my new default card type), but you
         | are probably running into the limitations of Anki there
         | 
         | ad 5: language learning, specifically vocab lists, has always
         | baffled me as a use case for SRS. there is so much context that
         | you need in order to use words proficiently (in what kind of
         | medium was the word used? what register was used
         | (formal/scientific/informal/...)? was it used ironically,
         | empathetically,...?). the only way to learn language imho is to
         | immerse youself as much as possible, through ways where it gets
         | actually used, not such artificial environments
         | 
         | the one thing that I'd like to see changed about Anki would be
         | to have more options for changing the scheduler, or making it
         | easier to use custom schedulers on multiple device types. I
         | simply don't like the logic of SM2/FSRS of hiding a card from
         | you until a specified date and assuming that you'll be reading
         | it then. if you don't open the app for a while, the review
         | dates get completely messed up (I've had new cards scheduled
         | for review sometime in the 2040's). I love the interface and
         | that you can use HTML to enter cards, but I just want to put
         | knowledge in there and get exposed to it from time to time. I
         | wish there was a scheduler that just randomly shows you cards,
         | with probability roughly proportional to how urgently you need
         | to see them. and do not interpret too much into the fact if I
         | haven't opened the app for half a year but still remember some
         | of the cards well. I don't mind seeing those cards "too often",
         | but I do mind if Anki hides the knowledge that I put in there
         | from me, for years or decades even
        
         | pessimizer wrote:
         | > We have the useful fiction that there is a 1-1 relationship
         | between words in two languages, but there almost never is.
         | 
         | But you aren't forced to drill single word L1->L2/L2->L1 cards.
         | You can drill sentences; I've never found single vocabulary
         | word cards useful, or translation cards (before more advanced
         | stages - B2/C1 - rather than early on.) What I found useful
         | were full L2 sentences, often embedded in paragraphs, with
         | words missing ("clozes.") There's also an L1 version of the
         | complete sentence in small print on the front of the card, to
         | use as a prompt to figure out the L2 word being asked for, but
         | it may be phrased completely differently.
         | 
         | They allow you to just learn languages as they are. You can
         | also drill synonyms and antonyms: single L2 word on the front,
         | multiple L2 synonyms and antonyms on the back (and maybe a
         | terse _also L2_ definition.) When the card comes up, name as
         | many as you can out loud, say the definition if you can
         | remember it. If you got a lot of them, and /or could repeat the
         | definition you pass the card.
         | 
         | Also, an author (David Parlett) who studied the process of
         | language learning from written grammars and radio
         | broadcasts/ethnographic recordings (i.e. without an instructor
         | or specialized recordings, usually very small languages)
         | advised a long time ago that one tackle the hard part(s) first:
         | coming from one language to another there are features that
         | have no parallel in the languages one already speaks but are
         | very important to be able to use. For example, if you're going
         | from English to a Romance language, _verbs and their
         | conjugations._ Anki can just let you learn those by rote and
         | figure out how to use them later; if you separate each
         | conjugation onto its own card, it will eventually be
         | effortless. Then all you have left is vocabulary and set
         | phrases, and all of the vocabulary and set phrases you read
         | from native material will be sandwiching another verb that you
         | can conjugate, being reinforced in that conjugation.
         | 
         | What I'm saying is that you can't dismiss Anki because you
         | think that translating word by word between languages is a dead
         | end for learning languages. There are any number of ways to use
         | Anki; ingenuity doesn't stop at the existence of a spaced
         | repetition effect, you can subject that to a little further
         | engineering. People are doing all of the above, I certainly am.
         | 
         | > You really need to learn a subject before memorizing it, but
         | in the learning phase Anki is not helpful.
         | 
         | I disagree with this for similar reasons. A lot of the learning
         | phase is memorizing a bunch of vocabulary and units and
         | remembering basic checklists. Having that done before you show
         | up to do the learning will accelerate that learning
         | significantly.
         | 
         | I don't think spaced repetition and Anki are limited by not
         | being all-encompassing. It's a tool for remembering largely
         | atomic things, and we have to figure out how to apply it.
         | 
         | But overall I probably have to agree with you on some level,
         | because I think that Anki itself promotes a particular style of
         | usage that may not always be ideal. Anki encourages a usage
         | that reflects its simple model of spaced repetition, which is
         | largely borrowed from Supermemo, and they make it difficult or
         | impossible to change that behavior to the point of actively
         | discouraging users from experimenting. I find it annoying that
         | Anki is very opinionated, and I think that its decisions about
         | how it should work were partially shaped by the fact that it
         | started very amateurishly put together, and adjusting one's
         | opinions to match the interface is easier done than the
         | opposite. There's not a lot of good, exacting science around
         | spaced repetition, and all the papers people cite are old, of
         | very small size, and not very systematic or adventurous. It's
         | too early to be opinionated.
        
       | hereme888 wrote:
       | This is why my initial flashcards on a topic would be cover a
       | breadth of individual details, but later I'd start creating
       | concept based flashcards where I'd ask things like "how does it
       | make sense that....?"
       | 
       | After somewhat memorizing foundational knowledge, understanding
       | concepts and having frameworks of thinking for a topic will
       | further increase critical thinking while reducing the amount of
       | cognitive effort required for critical thinking about unfamiliar
       | situations.
       | 
       | I hope one day these more efficient models that "clean up" the
       | review schedule by linking/identifying related flashcards become
       | publicly available.
        
       | azeirah wrote:
       | I really hope to see more research like this. I feel like LLMs
       | have insanely high pedagogic value, and that's because I've been
       | using them to teach myself difficult subjects and review my
       | understanding.
       | 
       | The issue with the kind of system that the author is proposing
       | for curious self-driven learning is that the SRS is optimized for
       | a given curriculum.
       | 
       | Many people including myself use flashcards to guide (and sort of
       | "create") their own curriculum. Flashcards with SRS are really
       | good for many things, but it's difficult to generalize them for
       | thus usecase.
       | 
       | I'd really like to see some prototypes of people integrating LLM
       | intelligence in creating and adjusting cards on the fly. It's
       | clearly something LLMs excel at, especially the larger closed-
       | source ones like Claude 3.5 sonnet
        
         | kiba wrote:
         | _I really hope to see more research like this. I feel like LLMs
         | have insanely high pedagogic value, and that 's because I've
         | been using them to teach myself difficult subjects and review
         | my understanding._
         | 
         | How do you know if the LLM isn't hallucinating?
        
           | EnigmaFlare wrote:
           | For mathy subjects you usually have to verify things yourself
           | so you'd detect any mistakes as you try to work things out or
           | makes sense of the information. You can't learn math, physics
           | or theory for engineering by remembering and believing
           | things. It would be different for "bag of random facts"
           | subjects though.
        
           | knighthack wrote:
           | This fear that LLMs are hallucinating constantly, and
           | therefore entirely unreliable, is unfounded.
           | 
           | Sure, that'll happen if you're going into extreme limits of
           | areas of knowledge - but if you're dipping your foot into
           | superficial waters of known areas, it's reasonably fine (and
           | perhaps even more sound than the hotter areas of Wikipedia).
           | 
           | E.g. if you're programming in the most well-known languages
           | (say Python), and you're only asking beginner questions
           | (which is where high pedagogic value lies) it's unlikely that
           | the program will hallucinate all that deeply to mislead you.
           | Yes, you won't know, but simple/mid questions are easy to
           | check.
           | 
           | You shouldn't of course head to LLMs for the most arcane
           | scientific/mathematical knowledge and conclusions; if you do
           | that, that's on you, because offering expertise is not what
           | LLMs are designed for, and the disclaimers all warn against
           | it. But you shouldn't throw out the baby with the bathwater.
        
           | azeirah wrote:
           | I don't use an LLM in isolation. I use it alongside reading
           | material, books, papers etc.
           | 
           | Since I'm using it in involved studying sessions, it is
           | totally sensible to cross-check most of what the LLM outputs,
           | since that's part of the learning process anyway!
           | 
           | In my experience learning design, some math, basic android
           | dev with local and private models, they are very reliable if
           | you use them "in the loop" (ie, as part of a process).
           | 
           | During programming, it's extremely easy to verify what the
           | LLM says is correct by running code.
           | 
           | For math, this is a bit more difficult, but so far it's only
           | been surface level math. I know that LLMs are good at
           | teaching concepts and ideas in math, but not at _doing_ math.
           | I don't fully trust an LLM to teach me more advanced math
           | because I have no way of verifying what I learn is
           | 
           | * Correct
           | 
           | * Relevant
           | 
           | * The "right" way of learning it
           | 
           | For design, which I'm currently studying a lot for work and
           | personal projects, it does well. I'm using Claude to help me
           | solidify my understanding by asking it to critique my
           | summaries and quiz me on topics. I know Claude is correct
           | because I'm using it to solidify my understanding and how
           | topics interrelate, but not to learn new topics. I already
           | sort of "intuitively understand" these topics, but am
           | training myself to go a bit deeper.
           | 
           | They work really well, and I really do understand the
           | skepticism, but in practice it's unwarranted.
        
           | theptip wrote:
           | Hallucination isn't really a problem when you can verify the
           | ground truth. For example if you're using it as a companion
           | to a Khan Academy math problem with immediate feedback.
        
       | ofirg wrote:
       | Our company (Language Zen) has this patent
       | https://patents.google.com/patent/EP1891619A2/en and we have done
       | work to teach hierarchical knowledge for language learning
        
         | ofirg wrote:
         | sorry wrong patent link:
         | https://www.patentsencyclopedia.com/app/20160035249
        
         | AlchemistCamp wrote:
         | How revolting. Nothing in what was described in your updated
         | link below looks even remotely novel even years before the 2016
         | filing date.
         | 
         | I say this as someone who was deeply involved in the industry
         | in the late 2000s. I also contributed to Anki in that time
         | frame.
        
           | rmbyrro wrote:
           | This patent is just for the business owners vanity. It's
           | clearly not defensible in courts. Even if it was, they
           | probably don't have the money required to pursue court
           | enforcement of the patent. More so when any reasonable lawyer
           | will tell them they'll get their case dismissed anyway.
        
       | asoneth wrote:
       | More than a decade ago I worked as a research programmer on a
       | similar AI tutoring product for hierarchical skills like
       | mathematics at Carnegie Mellon (in conjunction with the
       | Pittsburgh Science of Learning Center and Carnegie Learning).
       | 
       | The system would prompt students with problems that incorporated
       | dozens of sub-skills, each of which incorporated other sub-skills
       | and so on. If the student gets the problem right, all requisite
       | sub-skills are marked as reasonably strong. If they get it wrong
       | then the statistical model concludes that at least one sub-skill
       | must be weak/faulty/missing, and when selecting subsequent
       | problems the system would incorporate problems with different
       | subsets of the original sub-skills to identify the missing sub-
       | skill(s), with the goal being to spend time reinforcing only
       | those skills that the student has not mastered.
       | 
       | I no longer work in that domain, but I recall it being amazingly
       | efficient -- it often only took a dozen questions to assess a
       | student's understanding of thousands of skills.
        
         | BenoitP wrote:
         | Seems quite close to the 'active learning' ML topic: let the
         | model choose the question that will bring the best information
         | return.
         | 
         | And this kind of decomposition using simple knowledge pieces
         | (logical axioms?) is IMHO what we have to do to bring LLMs to
         | senses. These pieces should light up in the intermediate
         | embeddings inside the LLM. It won't really be more intelligent,
         | but it'll model reality better.
        
       | iandanforth wrote:
       | While this article presents a system it doesn't present any
       | results. Does this modification to SRS help? Which type of
       | student does it help? How large is the effect if there is one?
       | 
       | I haven't read the larger pdf of which this is a part so perhaps
       | someone who has can provide a pointer to some results.
        
         | JustinSkycak wrote:
         | The main idea is that this approach makes spaced repetition
         | feasible in something like mathematics. Without this approach,
         | spaced repetition wouldn't even be feasible because after a
         | short while, you'd be continually overloaded with too many
         | reviews to really make any progress learning new material.
         | 
         | Moreover, in addition to making spaced repetition feasible, it
         | minimizes the amount of review (subject to the condition that
         | you're getting _sufficient_ review) which allows you to make
         | really fast progress.
         | 
         | We (Math Academy) don't have any official academic studies out
         | at the moment, but if you want some kind of more concrete
         | evidence of learning efficiency, you can read more online about
         | our original in-school program in Pasadena where we have 6th
         | graders start in Prealgebra, and then learn the entirety of
         | high school math (Algebra 1, Geometry, Algebra 2, Precalculus)
         | by 8th grade, and then in 8th grade they learn AP Calculus BC
         | and take the AP exam.
         | 
         | The AP scores started off decent while doing manual teaching,
         | but the year we started using our automated system (of which
         | the SRS described here is a component), the AP Calculus BC exam
         | scores rose, with most students passing the exam and most
         | students who passed receiving the maximum score possible (5 out
         | of 5). Four other students took AP Calculus BC on our system
         | that year, unaffiliated with our Pasadena school program,
         | completely independent of a classroom, and all but one of them
         | scored a perfect 5 on the AP exam (the other one received a 4).
         | 
         | Even some seemingly impossible things started happening like
         | some highly motivated 6th graders (who started midway through
         | Prealgebra) completing all of what is typically high school
         | math (Algebra I, Geometry, Algebra II, Precalculus) and
         | starting AP Calculus BC within a single school year. Funny
         | enough, the first time Jason & Sandy (MA founders) saw a 6th
         | grader receiving AP Calculus BC tasks, Jason's reaction was
         | "WTF is happening with the model, why is this kid getting
         | calculus tasks, he placed into Prealgebra last fall, this
         | doesn't make any sense," but I looked into it only to find that
         | it was legit -- this kid completed all of what is typically
         | high school math (Algebra I, Geometry, Algebra II, Precalculus)
         | within a single school year.
         | 
         | Anyway, some links if you're interested:
         | 
         | * https://www.mathacademy.us/press
         | 
         | *
         | https://www.reddit.com/r/homeschool/comments/16hn9f5/comment...
         | 
         | * https://x.com/justinskycak/status/1810482435940913502
         | 
         | * https://x.com/justinskycak/status/1812557234028839193
         | 
         | Again, I realize these are not official academic studies, but
         | we're completely overloaded in startup grind mode right now and
         | have so many fish to fry with the product that we just don't
         | have the time for academic pursuits at the moment, let alone
         | much sleep. Happy to answer any follow-up questions that you
         | might have, though.
        
           | wantsanagent wrote:
           | Thanks for the detailed response! Fwiw I bet you could get
           | some free academic labor just by offering to let a local PhD
           | student have access to your internal data. (Obviously still
           | not zero effort)
        
       | graboid wrote:
       | Say you have concepts/items/cards A, B and C, with
       | 
       | A -> B -> C (C encompasses B, B encompasses A, keeping the
       | notation from the article).
       | 
       | As I understand it, the article advocates for showing C first,
       | then you can assume that you also know B and A to at least some
       | part, and save yourself the repetitions for these.
       | 
       | Intuitively, I would have guessed the opposite approach to be the
       | best: Show A first, suspend B until A is learned (by some
       | measure), then show B, etc.
       | 
       | That means no repetitions to skip, but also you get less failures
       | (and thus additional repetitions) that occur as follows: you are
       | shown C, but don't know B anymore, and thus cannot answer and
       | have to repeat C.
       | 
       | If you are shown C before B, you kinda make C _less atomic_ (you
       | might have to actively recall both, B and C to answer it),
       | showing B before C makes C more atomic, as you will have B more
       | mentally present /internalized and can focus on what C adds to B.
        
         | JustinSkycak wrote:
         | Hey! Good questions. I'll try to clarify:
         | 
         | 1. First want to clarify that the learner is first introduced
         | to the topics through mastery learning (i.e., not given a topic
         | until they've seen and mastered the prereqs). So, they would
         | explicitly learn A before learning B, and explicitly learn B
         | before learning C. It's only in the review phase when we do all
         | this stuff with "knocking out" repetitions implicitly.
         | 
         | 2. When you say "then you can assume that you also know B and A
         | to at least some part," I want to emphasize that if C
         | encompasses B and B encompasses A in the sense of a full
         | encompassing that would account for a full repetition, then
         | doing C fully exercises B and A as component skills. Not just
         | exercises them "to some part." For instance, topic C might be
         | solving equations of the form "ax+b=cx+d," topic B might be
         | solving equations "ax+b=c," and topic A might be solving
         | equations "ax=b."
         | 
         | 3. This scenario should never happen: "you are shown C, but
         | don't know B anymore, and thus cannot answer and have to repeat
         | C." There are both theoretical and practical safeguards.
         | 
         | 3a-- Theoretical: if you are at risk of forgetting B in the
         | near future, then you'll have a repetition due on B right now,
         | which means you're going to review it right now (by "knocking
         | it out" with some more advanced topic if possible, but if
         | that's not possible, we're going to give you an explicit review
         | of B itself. In general, if a repetition is due, we're not
         | going to wait for an "implicit knock-out" opportunity to open
         | up and let you forget it while we wait. We'll just say "okay,
         | guess we can't knock this one out implicitly, so we'll give it
         | to you explicitly."
         | 
         | 3b-- Practical: suppose that for whatever reason, the review
         | timing is a little miscalibrated and a student ends up having
         | forgotten more of B than we'd like when they're shown C. Even
         | then, they haven't forgotten B completely, and they can refresh
         | on B pretty easily. Often, that refresher is within C itself:
         | for instance, if you're learning to solve equations of the form
         | "ax+b=cx+d," then the explanation is going to include a
         | thorough reminder of how to solve "ax+b=c." And even in other
         | cases where that reminder might not be as thorough, if you're
         | too fuzzy on B to follow the explanation in C, then you can
         | just refer back to the content where you learned B and freshen
         | up: "Huh, that thing in C is familiar but it involves B and I
         | forgot how you do some part of B... okay, look back at B's
         | lesson... ah yeah, that's right, that's how you do it. Okay,
         | back to C." And then the act of solving problems in C
         | solidifies your refreshed memory on B.
         | 
         | Anyway, I think I've clarified all your questions? But please
         | do let me know if you have any follow-up questions or I've
         | misinterpreted anything about what you're asking. Happy to
         | discuss further.
        
           | graboid wrote:
           | Thank you for clarifying!
           | 
           | I guess math is uniquely suited for this kind of strategy,
           | but would you say it translates to learning concepts in other
           | domains too?
           | 
           | I was thinking about whether something like "what is X?" ->
           | "What field is X used in?", which seems to form a hierarchy
           | for me, would benefit of this technique? Personally, I found
           | that for something like the preceding example, I could answer
           | the second question without thinking about what X is at all,
           | just by rote memorization of the wording. Happened to me
           | quite a lot when I was using Anki. And actually, I guess this
           | is even acceptable in some way, since the question is not
           | about activating "what X is", but "what X is used in". What I
           | am trying to express: I feel like I would not necessarily
           | activate a parent concept by answering a child concept, and I
           | think that might be true for a lot of questions outside math
           | problems, although they form a hierarchy. So I am wondering
           | what you think about the general applicability of this
           | technique...
           | 
           | Please don't take all of this questioning wrong, I think you
           | are doing pretty cool stuff, and I am grateful for everyone
           | trying to push the boundaries of current SRS approaches :-)!
        
             | JustinSkycak wrote:
             | Yeah, you're right that the power of this strategy comes
             | from leveraging the hierarchical / highly-encompassed
             | nature of the structure of mathematical knowledge. If you
             | have a knowledge domain that lacks a serious density of
             | encompassings, there's just a hard limit to how much review
             | you can "knock out" implicitly.
             | 
             | > I feel like I would not necessarily activate a parent
             | concept by answering a child concept, and I think that
             | might be true for a lot of questions outside math problems,
             | although they form a hierarchy.
             | 
             | This is where it's really important to distinguish between
             | "prerequisite" vs "encompassing." Admittedly I probably
             | should have explained this better in the article, but you
             | are right, prerequisites are not necessarily activated. If
             | you do FIRe on a prerequisite graph, pretending
             | prerequisites are the same as encompassings, then you're
             | going to get a lot of incorrect repetition credit trickling
             | down.
             | 
             | We actually faced that issue early on, and the solution was
             | that I just had to go through and manually construct an
             | "encompassing graph" by encoding my domain-expert
             | knowledge, which was a ton of work, just like manually
             | constructing the prerequisite graph. You can kind of think
             | of the prerequisite graph as a "forwards" graph, showing
             | what you're ready to learn next, and the encompassing graph
             | as a "backwards" graph, showing you how your work on later
             | topics should trickle back to award credit to earlier
             | topics.
             | 
             | Manually constructing the encompassing graph was a real
             | pain in the butt and I spent lots of time just looking at
             | topics asking myself "if a student solves problems in the
             | 'post'-requisite topic, does that mean we can be reasonably
             | sure they truly know the prerequisite topic? Like, sure, it
             | makes sense that a student needs to learn the prerequisite
             | beforehand in order for the learning experience to be
             | smooth, but is the prerequisite _really_ a component skill
             | here that we 're sure the student is practicing?" Turns out
             | there are many cases where the answer is "no" -- but there
             | are also many cases where the answer is "yes," and there
             | are enough of those cases to make a huge impact on learning
             | efficiency if you leverage them.
             | 
             | I still have to make updates to the encompassing graph
             | every time we roll out a new topic, or tweak an existing
             | topic. Having domain expertise about the knowledge
             | represented in the graph is absolutely vital to pull this
             | off. (In general, our curriculum director manages the
             | prerequisite graph, and I manage the encompassing graph.)
             | 
             | Happy to answer any more questions if you've got any! :)
        
       | jchanimal wrote:
       | Is anyone building a personal social friend graph / calendar
       | hangout maximizer with spaced repetition?
        
       | pessimizer wrote:
       | I've been wanting to request an Anki feature for a while that is
       | in this vein (and would enable this style): allowing cards within
       | a deck to be tagged with a trigger, which would activate when all
       | (or some portion of) cards within a deck also tagged with that
       | trigger reach "maturity." When activated, it can add a tagged
       | batch of cards from the deck as new cards for review, or more
       | generally it could change their state (from/to Young, Mature,
       | Suspended, etc.).
       | 
       | This would allow cards to be automatically introduced in groups,
       | rather than the "just give me 10 new cards every day" thing. It
       | could also allow a default suspended deck style, where all but a
       | few cards begin suspended, and they are unsuspended in an orderly
       | way based on one's progress with the active cards. That could be
       | a pattern that works for drilling hierarchies of knowledge.
       | 
       | There's a deck style called the KOFI (conjugation first) system
       | for learning Romance conjugations that would really benefit from
       | that, which now depends on people manipulating the decks manually
       | with the aid of an abused deck description field describing that
       | manipulation.
       | 
       | Anki is pretty hostile to order, because spaced repetition is all
       | about moving individual cards optimally and without regard to
       | other cards, but the order in which information is _introduced_
       | can be important. At this point you can only choose between
       | introducing cards in a linear order, or completely at random.
       | There 's no way to deviate from that without the user having to
       | learn to juggle things manually. A deck creator can't just
       | suggest a schedule programmatically, even if the deck was
       | designed around that schedule.
       | 
       | The other half of this, where cards that duplicate combinations
       | of other cards are automatically strengthened when their related
       | cards are strengthened (or vice versa) is interesting. Seems like
       | a neuron model.
        
         | AlexErrant wrote:
         | How do you feel about hierarchical tags? No, I don't mean in
         | the way that Anki has a "file tree/directory" kind of structure
         | for tags and decks, but like, a separate "concept" hierarchical
         | graph that organizes the tags.
         | 
         | For example, consider two tags, "Fractions" and "Prime
         | Numbers". One should know Fractions before they study Prime
         | Factors, and one could represent that using a drag/drop UI like
         | <insert generic mindmap tool>. This "concept hierarchy" would
         | organize _using_ tags. This way you could still syntactically
         | tag cards with, say,  "Prealgebra/Fractions" and
         | "Prealgebra/Prime Numbers". In this way one could have a
         | "syntax" tree and a "semantic" tree/graph. (File trees can't
         | represent graphs, as you may know.)
         | 
         | One problem with making cards directly hierarchical with each
         | other is that people have many cards, and organizing them
         | individually can be a pain (and questionable usage of time).
        
       | JuliusSu wrote:
       | Hi Jason, we had discussions at Caltech on some of these ideas
       | many years back. We do have a patent, now lapsed, on doing spaced
       | repetition on knowledge graphs:
       | https://patentimages.storage.googleapis.com/ff/ae/6d/3483859...
       | 
       | Math pedagogy in the US leans to understanding being more
       | important than practice. This is wrong. As you point out,
       | understanding more often comes from practice. To correct this
       | imbalance, software like your company is developing is useful, as
       | are platforms like ALEKS, iReady, etc.
       | 
       | The challenge is addressing the social aspect of learning -- the
       | benefits students get from working and learning together. Is it
       | still a classroom if all the students are doing different things?
       | 
       | Of course, students come in with different abilities and levels
       | of preparation. Differentiation that works in a class setting is
       | very hard. Software is the easier part. Students who are
       | motivated to learn and can grow with guidance from a computerized
       | tutoring environment -- helping them is also the easier part.
        
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