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This is not a critique of the (nice) study, but what seems to me the overall context that should be kept in mind, especially once we are talking about "optimizi

This is not a critique of the (nice) study, but what seems to me the overall context that should be kept in mind, especially once we are talking about "optimizing". Optimizing "study, retention phase, test" for greatest knowledge retention at a delayed test time, is very different from optimizing for greatest value of knowledge learned. To optimize learning value, learn things that are immediately useful, you can immediately incorporate into learning something else, and ideally both. The sooner and more you use something, the greater its value AND the greater your retention will be. If you have to learn something valuable but with no short term use (how to handle a rare brain surgery complication), find a way to use it. Create an ongoing useful project that will revisit that knowledge during the "retention interval" (e.g. a concise summary of rare situations you need to handle, for you and others, that you can revisit and improve with additional and updated knowledge). So optimize "topic choice", "topic progression", and "study, (optionally) test, use, use, use", for total value of learning. "Use" is motivation, test, study review, and value realization put together.

zeroCalories 2y ago
I think a lot of topics are much less sequential the further you go. As an adult I spend most of my time repeating the fundamentals of my field, and learning a topic deeply as needed. For children it probably makes sense to cram the multiplication tables.
- Nevermark 2y ago
  I would think that the opportunities to immediately "use" multiplication, instead of just practice it for tests, or some future numerate citizenship, would be omnipresent. If you don't use something after you learned it, you miss out on: 1. Learning how it is actually applied 2. Discovering how the knowledge is useful for you personally, in ways you may not expect if you don't actually experience using it 3. Deeper understanding and mastery of the knowledge 4. Much much much better retention It is worth creating some immediate use for new knowledge, even the smallest possible useful or creative project, for better retention alone. > learning a topic deeply as needed That is the ultimate use-driven learning model. As for non-sequential, I agree. The more we manage our own learning, the more it is a directed graph (i.e. prerequisites translate to many follow up paths), and eventually just graphs (many ways to order topics, and alternate combinations of prerequisites for each topic, in any complex area).
  - zeroCalories 2y ago
    To be clear, in the context of this article, the alternative to drilling multiplication until you've memorized it is to space out the learning over a period of time. It's probably good to study for the test, because next week we're learning PEMDAS, so you better be solid on your multiplication.
- formerly_proven 2y ago
  Basically all undergrad stuff is fundamentals and "optimized cramming" (we call it bulimic learning, because you stuff knowledge into you just in time to throw it back up in the test) means tons of people "achieve" degrees without being even dimly aware of the existence of the fundamentals afterwards. If you have a bachelor's degree in e.g. computer science, the idea of encoding data shouldn't be an unknown unknown to you.
- shortrounddev2 2y ago
  They don't teach multiplication tables anymore as far as I know. I didn't learn them and I was born in 1995
  - Brybry 2y ago
    Wouldn't that be weird given that it's part of common core? > By the end of Grade 3, know from memory all products of two one-digit numbers. [1] https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Math.Content.3.OA.C.7 https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Mat...
    - lupire 2y ago
      Knowing the products is not the same as using or cramming the tables. It is quite sufficient (and probably superior) to learn the facts through use, for that makes them robust.
    - shortrounddev2 2y ago
      I learned that through brute force. They just had us multiply numbers over and over again rather than memorizing the table
  - Tempest1981 2y ago
    Interesting, in the US? What state?
    - shortrounddev2 2y ago
      Virginia
  - gumby 2y ago
    They still teach them in Germany, though I think maybe only up to 10x10 these days. In the US AFAIK they are called "times tables"; in Germany "one times one" („Einmaleins‟). It's funny what people emphasize for the same thing.
    - 2y ago
michaelt 2y ago
I sure hope my brain surgeon isn’t trying to create an opportunity to practice dealing with rare complications!
- Nevermark 2y ago
  The brain you lose in the name of practice, may save millions!
wahnfrieden 2y ago
That’s why I made Manabi Reader for language learning (currently only Japanese): https://news.ycombinator.com/item?id=41275227 https://news.ycombinator.com/item?id=41275227 It encourages finding content from native sources, learning new words in context from materials that interest you rather than textbook content, and helps you build your own personal corpus of sentences as you encounter them in the wild. Will soon expand to more media types than just web and epub, to include YouTube/comics/HDMI input/game emulators etc If you find flashcards from others, you also get easy tools for discovering more sentences from source materials that might interest you or from your own corpus. More coming for this and other word/kanji-level tracking analytics. Offline-first and privacy friendly.
- andai 2y ago
  This is great. Reminds me of the writings of Khatzumoto (All Japanese All The Time). On that note, do you know how to contact him? His site got deleted recently and I have an idea for restoring a static version.
  - wahnfrieden 2y ago
    Thanks! Yes I've read his stuff and basically all discourse online since ~2005 when I wrote my first web app version of Manabi. I was also heavily influenced by the Breaking into Japanese Literature book and similar ones which had translations of words and pages, sometimes additional explanations, for short stories from Akutagawa etc. (as I've included in the Rashomon EPUB in Manabi Reader) I don't know how to contact Khaz sorry I've never talked w/ him. There's a subreddit dedicated to his approach r/ajatt so you might find leads there. I'd also check archive.org of course If you try out my apps pls drop any feedback, easiest is Discord (chat or issue tracker) https://discord.gg/4aF9yuASzb https://discord.gg/4aF9yuASzb Thanks - recently went full-time on this so looking to grow it quickly and have lots more on deck

zeroCalories 2y ago

I think a lot of topics are much less sequential the further you go. As an adult I spend most of my time repeating the fundamentals of my field, and learning a topic deeply as needed. For children it probably makes sense to cram the multiplication tables.

Nevermark 2y ago
I would think that the opportunities to immediately "use" multiplication, instead of just practice it for tests, or some future numerate citizenship, would be omnipresent. If you don't use something after you learned it, you miss out on: 1. Learning how it is actually applied 2. Discovering how the knowledge is useful for you personally, in ways you may not expect if you don't actually experience using it 3. Deeper understanding and mastery of the knowledge 4. Much much much better retention It is worth creating some immediate use for new knowledge, even the smallest possible useful or creative project, for better retention alone. > learning a topic deeply as needed That is the ultimate use-driven learning model. As for non-sequential, I agree. The more we manage our own learning, the more it is a directed graph (i.e. prerequisites translate to many follow up paths), and eventually just graphs (many ways to order topics, and alternate combinations of prerequisites for each topic, in any complex area).
- zeroCalories 2y ago
  To be clear, in the context of this article, the alternative to drilling multiplication until you've memorized it is to space out the learning over a period of time. It's probably good to study for the test, because next week we're learning PEMDAS, so you better be solid on your multiplication.
formerly_proven 2y ago
Basically all undergrad stuff is fundamentals and "optimized cramming" (we call it bulimic learning, because you stuff knowledge into you just in time to throw it back up in the test) means tons of people "achieve" degrees without being even dimly aware of the existence of the fundamentals afterwards. If you have a bachelor's degree in e.g. computer science, the idea of encoding data shouldn't be an unknown unknown to you.
shortrounddev2 2y ago
They don't teach multiplication tables anymore as far as I know. I didn't learn them and I was born in 1995
- Brybry 2y ago
  Wouldn't that be weird given that it's part of common core? > By the end of Grade 3, know from memory all products of two one-digit numbers. [1] https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Math.Content.3.OA.C.7 https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Mat...
  - lupire 2y ago
    Knowing the products is not the same as using or cramming the tables. It is quite sufficient (and probably superior) to learn the facts through use, for that makes them robust.
  - shortrounddev2 2y ago
    I learned that through brute force. They just had us multiply numbers over and over again rather than memorizing the table
- Tempest1981 2y ago
  Interesting, in the US? What state?
  - shortrounddev2 2y ago
    Virginia
- gumby 2y ago
  They still teach them in Germany, though I think maybe only up to 10x10 these days. In the US AFAIK they are called "times tables"; in Germany "one times one" („Einmaleins‟). It's funny what people emphasize for the same thing.
  - 2y ago

michaelt 2y ago

I sure hope my brain surgeon isn’t trying to create an opportunity to practice dealing with rare complications!

Nevermark 2y ago
The brain you lose in the name of practice, may save millions!

wahnfrieden 2y ago

That’s why I made Manabi Reader for language learning (currently only Japanese): https://news.ycombinator.com/item?id=41275227 https://news.ycombinator.com/item?id=41275227 It encourages finding content from native sources, learning new words in context from materials that interest you rather than textbook content, and helps you build your own personal corpus of sentences as you encounter them in the wild. Will soon expand to more media types than just web and epub, to include YouTube/comics/HDMI input/game emulators etc If you find flashcards from others, you also get easy tools for discovering more sentences from source materials that might interest you or from your own corpus. More coming for this and other word/kanji-level tracking analytics. Offline-first and privacy friendly.

andai 2y ago
This is great. Reminds me of the writings of Khatzumoto (All Japanese All The Time). On that note, do you know how to contact him? His site got deleted recently and I have an idea for restoring a static version.
- wahnfrieden 2y ago
  Thanks! Yes I've read his stuff and basically all discourse online since ~2005 when I wrote my first web app version of Manabi. I was also heavily influenced by the Breaking into Japanese Literature book and similar ones which had translations of words and pages, sometimes additional explanations, for short stories from Akutagawa etc. (as I've included in the Rashomon EPUB in Manabi Reader) I don't know how to contact Khaz sorry I've never talked w/ him. There's a subreddit dedicated to his approach r/ajatt so you might find leads there. I'd also check archive.org of course If you try out my apps pls drop any feedback, easiest is Discord (chat or issue tracker) https://discord.gg/4aF9yuASzb https://discord.gg/4aF9yuASzb Thanks - recently went full-time on this so looking to grow it quickly and have lots more on deck