[HN Gopher] Increasing Retention Without Increasing Study Time [...
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       Increasing Retention Without Increasing Study Time [pdf]
        
       Author : JustinSkycak
       Score  : 227 points
       Date   : 2024-08-17 13:53 UTC (9 hours ago)
        
 (HTM) web link (files.eric.ed.gov)
 (TXT) w3m dump (files.eric.ed.gov)
        
       | ngetchell wrote:
       | [2007]
        
       | Almondsetat wrote:
       | It's only a four page article about a particular spaced study
       | strategy. Nothing really groundbreaking nor a comprehensive
       | collection of techniques
        
         | boredemployee wrote:
         | any other recommendation for articles regarding techniques that
         | works for most people?
        
           | sva_ wrote:
           | The default algorithm in Anki, in case you don't know it
        
             | oehtXRwMkIs wrote:
             | Or not, since they recently added FSRS as an alternative.
        
             | watwut wrote:
             | It is super unlikely that an algorithm that was made based
             | on feels would turn out to be the most effective.
             | Especially since it requires some learning and errors to
             | even learn how to use it.
        
           | CuriouslyC wrote:
           | This is pretty much the current state of the art in learning
           | research: https://bjorklab.psych.ucla.edu/research/
        
             | closed wrote:
             | From a more applied angle, a book like "10 steps to complex
             | learning" might be helpful.
             | 
             | I come from a similar cog psych background as the Bjork
             | Lab, so am a big fan of their research, but books like 10
             | steps come from instructional design, which is a bit more
             | focused on the big picture (designing a whole course vs
             | individual mechanisms).
        
               | jimhefferon wrote:
               | Thanks for the tip.
        
             | uolmir wrote:
             | This is good stuff but I'll say that it isn't as
             | comprehensive as all that. These studies and findings are
             | almost entirely focused on simple recall knowledge
             | (isolated facts, vocabulary). That's an important part of
             | learning certainly and it informs research on learning
             | higher order concepts but it's not the full story.
             | 
             | Just to name one example, folks might look into research on
             | conceptual change theory (eg Chi or Posner). This theory
             | helps explain why a concept like electricity is so
             | challenging to learn. The reason, in brief, being that
             | naive conceptions make a category error and think of
             | electricity as a thing rather than a process. And this
             | theory then informs instructional practice. Specifically,
             | teachers should be aware of difficult concepts and should
             | design activities that force students to confront the
             | contradictions between their naive models and more
             | accurate/complete ones.
             | 
             | Mickie Chi also has fascinations research on active
             | learning (ICAP) and related work on the effectiveness of
             | peer learning.
        
           | kqr wrote:
           | The comment I wrote below is weird. What I mean to say is
           | google for articles on writing good prompts. The rest matters
           | less.
           | 
           | -----
           | 
           | Ignore this:
           | 
           | Spaced repetition, if you can stick with it, works. The
           | details around schedules etc. don't matter as much as doing
           | it in a way that you can keep up.
           | 
           | Also writing good prompts is important. I have yet to write
           | more extensively about this but here is a start:
           | https://news.ycombinator.com/item?id=41126734
        
           | wahnfrieden wrote:
           | FSRS v5 is state of the art
        
           | lxm wrote:
           | https://www.goodreads.com/book/show/19288640-how-we-learn
        
           | david_allison wrote:
           | Dunlosky J, Rawson KA, Marsh EJ, Nathan MJ, Willingham DT.
           | Improving Students' Learning With Effective Learning
           | Techniques: Promising Directions From Cognitive and
           | Educational Psychology. Psychol Sci Public Interest. 2013
           | Jan;14(1):4-58. doi: 10.1177/1529100612453266. PMID:
           | 26173288.
        
           | adamgordonbell wrote:
           | Scott Young has a lot on this, including going deep on the
           | literature and explaining it to populist student audience:
           | 
           | https://www.scotthyoung.com/blog/the-best-articles-on-
           | learni...
           | 
           | For instance, on memory:
           | 
           | https://www.scotthyoung.com/blog/2019/02/15/memory/
        
         | highcountess wrote:
         | It's just typical learning "science" fluff
        
       | trwhite wrote:
       | I recently read and enjoyed "A Mind for Numbers" by Barbara
       | Oakley, full of lots of techniques for learning maths and science
        
         | consf wrote:
         | Does the book offer practical strategies?
        
       | bdjsiqoocwk wrote:
       | The simplest way of increasing retention is being interested in
       | the subject.
        
         | rmbyrro wrote:
         | The topic isn't about simplicity, but performance and
         | efficiency.
        
         | Jtsummers wrote:
         | Simple, but not sufficient since you still need to pair your
         | interest with some methods of study and practice. Which methods
         | of studying are more effective or efficient is the question
         | they're researching.
        
         | IncreasePosts wrote:
         | You can just make yourself interested in whatever you want? If
         | not, then it probably isn't the simplest way.
        
           | bdjsiqoocwk wrote:
           | I would counter, why are you spending time learning something
           | you're not interested in?
        
         | consf wrote:
         | Passion and curiosity are powerful tools in learning. But not
         | always can be there for you
        
       | wahnfrieden wrote:
       | I'll mention that I've gone full-time on an iOS/macOS tool for
       | learning Japanese through reading called Manabi Reader:
       | https://reader.manabi.io
       | 
       | It combines reading and flashcards, such that it tracks every
       | word and kanji you read and learn in order to show you analytics
       | on what you need to learn to be able to read something or achieve
       | JLPT goals, and highlights unknown/learning words in texts. Next
       | up for the flashcard part is to replace the SM2 algorithm with
       | FSRS for the flashcards, as well as having flashcards get
       | passively reviewed simply by reading content.
       | 
       | I also suspect people are missing out on speed of learning when
       | reviewing flashcards one at a time for hours. Besides actively
       | recalling reviewing flashcards passively while reading, I'll
       | experiment with other review techniques like seeing a page at a
       | time of vocab / revealable answers. Our minds absorb at the
       | periphery of our vision and scanning/inputting a bunch of
       | information at once, too. I'm unconvinced flashcard UI is the
       | final expression of forgetting curve research based learning apps
       | 
       | Also working on Reader features such as manga/pdf/youtube/game
       | emulators, plus expanding to all languages.
        
       | shahzaibmushtaq wrote:
       | "Teach others what are you trying to teach yourself better" is
       | the best long-term retention strategy in my personal experience.
        
         | wahnfrieden wrote:
         | For language acquisition?
        
           | jakderrida wrote:
           | Si
        
           | shahzaibmushtaq wrote:
           | Also try for other things that are difficult to grasp.
        
         | kqr wrote:
         | Also possibly the most time consuming. Best and efficient with
         | time are two different metrics.
        
           | practicemaths wrote:
           | What is consider efficient if it yields less best results?
           | 
           | I understand time constraints and end goals may prohibit the
           | 'best' approach.
           | 
           | What I do not understand is how can you say something is more
           | 'efficient' if the yield in understanding is less than what
           | you would get with another method.
           | 
           | Hopefully this will clarify my thought process here:
           | 
           | If 'Best' is to teach others and requires 10,000 hours to
           | yield 90-99% understanding.
           | 
           | In contrast, 'Efficient' method requires 2,500 hours to yield
           | 30-40% understanding. However, there is diminishing returns
           | meaning that doubling your hours to 5,000 does not return you
           | with 60-80% understanding, rather maybe closer to 50-60%
           | understanding. With 7,500 hours closer to 65-70% and 10,000
           | hours may around 75-89% understanding.
           | 
           | Here you've spent the same amount of time but did not achieve
           | the same level of understanding. I think you may have a
           | dynamic 'Best' vs 'Efficient' curve and to switch between
           | those options to optimize maximizing your level of
           | understanding in the least amount of time.
        
             | fn-mote wrote:
             | The problem I have with this argument is that you cannot
             | consider "efficiency" in a vacuum. You need to have a
             | metric against which to measure it.
             | 
             | Consider these two scenarios -
             | 
             | Goal: remember where to look up information when it comes
             | up in $JOB Metric: how much you remember, how quickly you
             | find the info
             | 
             | Goal: discover new hyper-efficient method of training an AI
             | (or insert popular ML topic here). Metric: percent
             | improvement vs current pubished best practice (deliberately
             | vague) Required understanding to make progress: "like a
             | Ph.D. from Stanford"
             | 
             | Now you can possibly measure something.
             | 
             | The idea achievement of "90% understanding" is VERY topic
             | dependent. Simple topic? Sure 100% understanding, I
             | remembered the Latin names of all of the plants in my
             | house. Complicated topic? The information for "100%
             | understanding" might not even be written in the textbook -
             | it probably includes things like seeing the
             | interconnections between the topics and being able to apply
             | them in slightly different contexts.
             | 
             | Make sure you read the studies so you know what they're
             | talking about. In this area, I think summaries are
             | frequently misleading. You have to know what the real
             | evidence is that substantiates the claims. (I cannot tell
             | you how many times I have looked at the evidence and just
             | rolled my eyes - obviously not applicable in settings where
             | I wanted it to be.)
             | 
             | Edit: See this comment (not me) -
             | https://news.ycombinator.com/item?id=41275869
        
               | Swizec wrote:
               | > Complicated topic? The information for "100%
               | understanding" might not even be written
               | 
               | Bjarne Stroustop, creator of C, famously rates his C
               | knowledge as 7/10
        
               | Jtsummers wrote:
               | I suspect you mean C++, not C.
        
               | chrisweekly wrote:
               | Tangent: efficiency nearly always comes at the expense of
               | flexibility.
        
           | shahzaibmushtaq wrote:
           | Yes, possibly the most time consuming if you are thinking of
           | writing a book.
           | 
           | How effective something is comes with what is best and
           | compromise effectiveness for efficiency.
        
           | consf wrote:
           | Efficiency and effectiveness are indeed different metrics.
           | And I think balancing time and retention needs is key
        
             | shahzaibmushtaq wrote:
             | Different metrics can be interdependent, efficiency and
             | effectiveness are among them.
        
           | hinkley wrote:
           | Someday you will die. Then you will die again when people
           | forget you. Only the effect you've had on the world,
           | including teaching others, who pass that along, outlives that
           | second death.
           | 
           | So what's this about efficiency? You should be more worried
           | about effectiveness, not efficiency. Particularly in this
           | profession.
        
             | shahzaibmushtaq wrote:
             | Best thing I have read after a long time. Thank you!
        
             | maksimur wrote:
             | > Someday you will die. Then you will die again when people
             | forget you.
             | 
             | I've already heard that line somewhere but can't remember
             | where and who said it.
        
               | zoogeny wrote:
               | It's one of those quotes that gets attributed to a lot of
               | different people. Here is goodreads claiming it was
               | Ernest Hemingway [1].
               | 
               | "Every man has two deaths, when he is buried in the
               | ground and the last time someone says his name. In some
               | ways men can be immortal."
               | 
               | 1. https://www.goodreads.com/quotes/9556005-every-man-
               | has-two-d...
        
         | cainxinth wrote:
         | "See one, do one, teach one"
        
           | shahzaibmushtaq wrote:
           | Yes, monotasking is the way to go.
        
         | cyberax wrote:
         | > "Teach others what are you trying to teach yourself better"
         | 
         | A joke in Russian universities:
         | 
         | - A teaching assistant tells a student: "Look, I've been
         | explaining it to you for so long, that I myself understood it!"
        
           | hinkley wrote:
           | I tried to help some dude understand integration by parts,
           | which I'm not sure I'd understood myself. I warned him. But
           | it was late, he was desperate, and I was just going to go
           | play computer games anyway.
           | 
           | I figured it out, but I've no idea if I got him sorted out
           | for his final.
        
         | consf wrote:
         | 100%! Teaching others reinforces your understanding
        
         | huhtenberg wrote:
         | The expression goes "to know is to be able to explain".
        
           | riiii wrote:
           | Yes, but there are plenty of exceptions. I know brilliantly
           | knowledgeable and extraordinary clever people that are so
           | socially awkward that they can't explain virtually anything.
        
             | simonw wrote:
             | How are they at writing?
        
               | riiii wrote:
               | Good question and I think you're making a valid point.
               | 
               | I think overall on average they would do a decent job of
               | explaining it in writing to equally brilliant people. Not
               | so sure about "dumbing it down" for the "others".
        
         | hinkley wrote:
         | I push the new guys to fix project documentation once they've
         | figured out a tricky bit. It helps solidify their knowledge,
         | and helps us double check that they understood, and it's
         | something they can contribute when they still haven't become
         | part of the bus number on anything yet.
         | 
         | That all sounds reasonable and smart, but the real reason I do
         | it is the Curse of Knowledge. People in a system can't see it
         | from the outside. They make assumptions, use opaque or even
         | misleading jargon, and employ circular logic. The new guy
         | doesn't know the lingo, or the circular logic. Their
         | explanation will make more sense to the next hire than anything
         | I can say. And having it written down this way can also give me
         | new perspective on the system. Maybe it doesn't have to work
         | this way.
        
           | zoogeny wrote:
           | Adding a new smart person to the team is one of those golden
           | moments for a team, IMO. You get a tiny window of watching
           | them struggle until the tribal team knowledge seeps into them
           | by osmosis. During that time they don't yet know who to ask
           | the questions to directly so they will post to team slack
           | channels or the lead directly.
           | 
           | One must capitalize on this brief period because smart
           | programmers are flexible and adaptable. Very quickly they
           | will acclimatize themselves to the mess that surrounds them
           | and they will become as blind to the deficiencies as the rest
           | of the team.
        
             | hinkley wrote:
             | Adjacent to this: ignore criticism as feedback, but treat
             | questions as feedback.
             | 
             | People who don't "get" the code ask questions that contain
             | feedback they often don't even register as feedback. By the
             | time they distill it to an actual criticism, they're often
             | so wrapped up in the problem they can't be constructive, or
             | they present an XY problem. But if three people ask you the
             | same question about your code? You have a design issue. Fix
             | it. Fix it now.
             | 
             | That puts me in a weird relationship with FAQs. FAQs aren't
             | informational, they're confessional. Here's all the times I
             | fucked up and won't admit it. Let me explain why I am right
             | and you are wrong.
        
           | specialist wrote:
           | Nice. Somewhere I picked up the phrase "problem of assumed
           | knowledge" for the phenomenon you describe.
           | 
           | But your phrase is spot on, well defined, and the subject of
           | ongoing research.
           | 
           | https://en.wikipedia.org/wiki/Curse_of_knowledge
           | 
           | Cheers.
        
       | godelshalt wrote:
       | Sounds great but I was expecting more evidence. They talk about
       | this shuffling method, which interleaves material as a way to
       | provide spacing and reintroduce material. But it appears to just
       | be their opinion that it will help improve retention. Also what
       | is the deal with this "hypothetical interaction between ISI and
       | RI"? Why not do enough experiments to actually plot it out?
       | Anyone can graph out a hypothetical interaction.
        
         | kqr wrote:
         | I think _Accelerated Expertise_ comes to the same conclusion
         | and references the studies to back it up. It 's a good book!
        
         | abecedarius wrote:
         | Years ago there was a great extended comment here on HN about
         | teaching a linear algebra course using, among other tactics, a
         | similar spacing of the homework problems. He reported excellent
         | results. I wish I remembered the username. Ben something?
        
           | ExciteByte wrote:
           | I think it was Ben Tilly and I think his user name is btilly.
           | I also remember that comment you're referring too.
        
             | Jtsummers wrote:
             | https://news.ycombinator.com/item?id=818367
        
             | abecedarius wrote:
             | That's the one, thank you.
        
           | BJones12 wrote:
           | https://news.ycombinator.com/item?id=818367 ?
        
             | abecedarius wrote:
             | Yes, thanks!
        
           | mrandish wrote:
           | I really appreciate HN. There aren't many public online
           | forums were one could ask about a user comment made on a
           | related post posted years ago and in less than 20 minutes get
           | two different responses linking to the comment from 15 years
           | earlier.
           | 
           | Perhaps it helps the topic was "increasing retention". :-)
        
       | jppope wrote:
       | Real question. Does this count as a published paper?
        
         | david_allison wrote:
         | Yes, with 263 citations
         | 
         | Rohrer, D., & Pashler, H. (2007). Increasing Retention Without
         | Increasing Study Time. Current Directions in Psychological
         | Science, 16(4), 183-186.
         | https://doi.org/10.1111/j.1467-8721.2007.00500.x
        
         | layer8 wrote:
         | It was published in a scientific journal, so yes.
        
       | moffkalast wrote:
       | > Because people forget much of what they learn, students could
       | benefit from learning strategies that provide long-lasting
       | knowledge. Yet surprisingly little is known about how long-term
       | retention is most efficiently achieved.
       | 
       | I've always thought that the real problem is information
       | relevancy. People need practical uses for remembering something
       | beyond synthetic bullshit exams. Efficient techniques are great,
       | but nothing demotivates more than not having a reason to learn
       | beyond being told that you have to.
       | 
       | Nobody has to reach for flashcards, extensive notes, or advanced
       | techniques when trying to learn something they're actually
       | interested in, it's retained almost immediately and effortlessly.
       | There has to be some kind of subconscious gauge of information
       | relevancy that physically controls the level of absorption, a
       | sort of "learning rate" if you will.
        
         | larsrc wrote:
         | I disagree. Motivation will keep you reading the material, but
         | that alone will not make you remember it that much better.
         | 
         | When you're motivated about something you can practice, you may
         | remember more by doing it (which also acts a spaced
         | repetition). But good luck trying that with, say, astrophysics
         | or macroeconomics.
         | 
         | When motivated, you're also more likely to pick up other books
         | on the subject, which is another form of spaced repetition.
        
         | james-revisoai wrote:
         | I agree motivation to learn and maintaining interest is key, to
         | effect the learning rate you mention. The enjoyment itself,
         | although a crucifying word to use in discussions when teaching
         | students considered the "best of the best", still matters and
         | predominates over the effectiveness factor for most of the
         | semester for students, at least. Because of just being "told to
         | learn" it.
         | 
         | Basically 70% of the semester most students are not studying 40
         | hours - they are doing 30 hours of real work, and perhaps only
         | 15 hours effectively. And for good reason: Nothing is bridging
         | or rewarding them in a way that interests/motivates them, for
         | courses where the interest isn't natural.
         | 
         | A bridge to motivate them would be ideal. In 2021 I started
         | using GPT-3 to generate motivational "reasons to learn a
         | concept" cards for my flashcard app, - Revision.ai - which you
         | can read about here in the 3rd item:
         | https://www.revision.ai/articles/20ThingsRevisionAIDoesForBe...
         | - the reason we disabled them was simple: we could never quite
         | time the cards right to help the student when they needed it.
         | When the app is closed, they aren't motivated - they don't see
         | them. Mid study session? Showing such cards (or AI generated
         | examples) interrupted the flow
         | [https://www.instagram.com/p/CVVlIuVg31W/] We have also tried
         | recommending relevant short/mid length youtube videos for
         | visual/"breaks" from overwhelming learning. That did not boost
         | student success either. I guess it doesn't address that you are
         | still being told to do it, not naturally flowing into learning.
         | 
         | I welcome any technical or conceptual ideas you have to improve
         | this and help increase interest amongst students. We have found
         | that turning lecture slideshows into sets of exercises with
         | clear visuals[https://www.instagram.com/p/C5ByftwiJ00/],
         | breaking content up, and showing progress does motivate
         | students to study more(and in a semi-related dissertation I
         | wrote, possibly reduce Test Anxiety and tension). Please let me
         | know of any ideas you have!
        
       | WaitWaitWha wrote:
       | From the abstract (emphasis added):
       | 
       | > Because people forget much of what they learn, _students could
       | benefit from learning strategies_ that provide long-lasting
       | knowledge.
       | 
       | What learning strategies were taught in your secondary
       | educational years?
        
       | tnvmadhav wrote:
       | spaced repetition
        
       | aflukasz wrote:
       | If you are interested in similar research, take a look at
       | https://supermemo.guru (somewhat hidden "about" page:
       | https://supermemo.guru/wiki/SuperMemo_Guru:About). Author spent
       | quite some time on the topic and its history, including writing
       | applications.
        
         | light_hue_1 wrote:
         | A lot of what's on that page is just nonsense. The page has a
         | very clear bias toward one method and writes all sorts of
         | unscientific drivel as a result.
         | 
         | https://supermemo.guru/wiki/School_damages_your_brain
         | 
         | As someone who also publishes in neuroscience I can tell you
         | this is total and utter trash.
        
           | aflukasz wrote:
           | I'm not in a position to judge this author's work as a whole,
           | as this is not my area of expertise.
           | 
           | I know this person as an author of "super memo" algorithms
           | for spaced repetition learning, so yes, he most likely have a
           | bias, probably even financial stake to some degree, although
           | not sure, I don't follow him in any way, so don't know if
           | this ever was or still is the case.
           | 
           | In the past, I've used some of his algorithms in particular,
           | with quite interesting results - subjectively speaking, not
           | in any scientific regime, And, obviously, those are just one
           | of many. I also remembered this was his area of interest in
           | general, so assumed his wiki to be of some interest in the
           | context of discussed article.
           | 
           | Thanks for your critical opinion, it will contribute to my
           | priors about his writing.
        
       | aledalgrande wrote:
       | Why do researchers need to use acronyms for a 2 pager article?
        
       | cod1r wrote:
       | Sometimes I feel like I know nothing because information goes in
       | one ear, stays for a bit, then just runs out the other ear.
       | 
       | Then I have to go back and review.
       | 
       | Repeat.
        
         | consf wrote:
         | Our brains are constantly filtering and processing a massive
         | amount of information. That's why this sometimes happens
        
       | Modified3019 wrote:
       | One thing I've found when I spend most of a day trying to learn
       | things, is that having a ~1.5 hour nap is pretty important. Not
       | sure what goes on, but it feels like it turns the disconnected
       | "fog" of information in my head into something that is a least
       | loosely linked and can be vaguely recalled upon rather than
       | completely forgotten.
       | 
       | Unfortunately I kinda need to plan these sorts of days ahead,
       | because trying to nap past 2PM is a good way to fuck my nighttime
       | sleep.
        
       | mrlase wrote:
       | I'd highly encourage anyone interested in the contents of this
       | article/learning about learning to read through the submitter's
       | blog: https://www.justinmath.com/blog/
        
         | james-revisoai wrote:
         | I also recommend https://www.learningscientists.org/posters
         | from scientists in the field, which covers additional
         | scientifically-effective approaches that a course designer or
         | more long term approach might take. For example, not only
         | applying Spaced Repetition, Interleaving and Active Recall (all
         | possible through automated spaced repetition apps based on
         | simply input), but elements like Dual coding (related to
         | "Varied practise") - mixing visual and other elements when
         | learning (which requires effort to create them), and
         | elaboration practise (like free recall). To the end of applying
         | these - and other critical elements like focusing on the
         | motivation of the learner and enabling them to understand what
         | they are missing with progress & identified "blindspot"
         | misconceptions (on their own incredibly powerful), I've been
         | developing Revision.ai since before GPT-3, through a Psychology
         | MSc.
        
         | hnthrow12390 wrote:
         | Content is good but he is part of a paid math program and some
         | articles and submissions appear to be indirect
         | advertising/marketing if you think about it. (but it's
         | effective and less forceful) https://www.justinmath.com/why-is-
         | the-edtech-industry-so-dam...
        
         | chrisweekly wrote:
         | See also the wonderful https://betterexplained.com
        
       | paulpauper wrote:
       | High IQ. A component of IQ is memory--working and long-term
       | memory. There is a reason why doctors are smarter than average--
       | you got to be smart to memorize all that stuff. I am skeptical
       | that hacks make much of a difference. There is also a difference
       | between recall and understanding. This is why speed reading
       | courses are dubious because you're not really understanding
       | things, but just recalling items in the text.
        
       | westcort wrote:
       | The time between study and testing (retention interval) is the
       | most salient factor for students. Repeating material at intervals
       | attenuates the forgetting curve somewhat, but not enough to
       | generate passing scores. Cumulative exams only force students to
       | study all material in a massed study session prior to a final
       | exam.
       | 
       | I say this as someone who works on education and as a lifelong
       | learner who has tried many ways of improving retention.
        
       | Nevermark wrote:
       | 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 wrote:
         | 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 wrote:
           | 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-oriented 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 learning of subtopics in any
           | complex area).
        
         | michaelt wrote:
         | I sure hope _my_ brain surgeon isn't trying to create an
         | opportunity to practice dealing with rare complications!
        
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