5 ms·

Memorization is so underrated. Memorizing the fundamentals and having them available for instant recall is hugely valuable, especially when trying to grok a ne

by cle 9y ago

Memorization is so underrated. Memorizing the fundamentals and having them available for instant recall is hugely valuable, especially when trying to grok a new concept. I generally buck the standard advice and memorize first, before trying to understand. Understanding is much easier for me if I can easily hold everything in my working memory.

Philipp__ 9y ago
I agree, but I still haven’t found a way to make that process more enjoyable or less fatiguing.
newman8r 9y ago
I think people tend to conflate "memorization" with "cramming". You're right that memorization is underrated. Are you familiar with the 'method of loci' (i.e. memory palace). It's an amazing technique.
fooker 9y ago
Proper mental indexing is even more so. You can not memorize everything, but you can certainly index almost everything. That is why we can have databases that do not fit in 'memory'. Do you see the analogy here?
- goldenkey 9y ago
  Luckily we have brains that expose this interface quite readily with intuition. Learn the logic, and the partial indexes, the foreign keys, etc..they all follow. Reason before RAM. It is often much faster to derive data than to store it, and look it up. This applies to CPUs and to our brains. Our brains have instruction cache, and often instructions are better use of memory than their final executed output.
joe_the_user 9y ago
I wouldn't personally find advice like this useful for me. I suspect it varies with "personal style". I grasped mathematical concept easily from an early age and I never made an effort to memorize things. If anything, I saw those coming from less-advanced math founder on advanced math (arithmetic to algebra, algebra to calculus, calculus to advanced subjects) because they attempted to deal with the subject based on memorization rather than grasping the basic point. Generally, I did wind-up committing a lot of content to memory but it was and is much easier, even "effortless", when I knew the reason for each part of the content. Of course, language is slippery and we might be talking about exactly the same thing. So I wouldn't give blanket advise - each person has to find their own learning style (or styles, if it varies by discipline).
- gowld 9y ago
  Rote Memorization is awful. Memorizing by practicing so much that the details become "muscle memory" is the foundation of progress in learning. A basketball player has memorized how to shoot a free throw, not by cramming by rote, but by practicing.
  - jacobolus 9y ago
    The best basketball players start by spending years and years just playing the game all the time, as recreation. The equivalent for mathematics is solving problems that you find personally relevant and interesting and which are at the limits of your current abilities. NOT just doing piles of rote calculation. Often solving a hard problem requires a big pile of intermediate calculations, but those a tool in service to some meaningful purpose, not an end in themselves. Forcing students to work through thousands and thousands of trivial calculation exercises is horrible pedagogy (and a very inefficient use of time). It’s like doing nothing but shooting drills and getting quizzed on the NBA rule book for years before ever trying to play a game.
    - mamon 9y ago
      >> The best basketball players start by spending years and years just playing the game all the time, as recreation. No, they start by joining a club where they get professional training, from a very young age. Just playing the game all the time won't make you any better at it. There are millions of children that spent significant part of their childhood playing basketball for fun, and never went past amateur level. This is just a conclusion from Ericsson famous paper[1]: you need DELIBERATE practice, not just recreational playing. Playing for fun will just develop bad habits, which you then will have to unlearn, so recreational playing might actually be an obstacle to learning. [1] http://www.nytimes.com/images/blogs/freakonomics/pdf/DeliberatePractice(PsychologicalReview).pdf http://www.nytimes.com/images/blogs/freakonomics/pdf/Deliber...
      - jacobolus 9y ago
        As you say, the key to skill improvement is playing deliberately and getting meaningful feedback in a tight loop, ideally at the edge of your abilities. But there are many aspects to any complicated skill, including tiny subskills, combination of various subskills, and at a higher-level meta skills like knowing when to change strategies, etc. The problem with only sport games as a mechanism for feedback is that (a) there’s not necessarily a good way to correct and try again right away if you want to practice one particular thing, (b) situations that arise are not homogeneous enough to compare feedback across trials, (c) there are periods of waiting in between direct practice, (etc.?). As a result, people who are training to be basketball players spend only like half their time playing realistic games, and the rest of their time on a variety of drills and workouts including general aerobic and strength training, practice running sideways and jumping, shooting / passing / dribbling drills, practice setting screens / rebounding / driving / inbounding the ball, larger-scale coordination drills, and so on. These let the players focus their conscious attention at one level at a time, and repeat a situation with analytical feedback in between. But those who improve fastest are the ones who figure out what they need to work on (or have a mentor/coach to figure out what they need to work on) and then get lots of feedback about that particular area, in an intentional way. This can even be done within the context of a realistic full game by choosing what to direct attention/focus to. But you’re missing my basic point, which is that all the skills in basketball are situated within a context. It’s obvious how they fit into playing a game. Students start with the high-level context (by watching / playing full games), and then break it down into small pieces they can work on separately or jointly, and then frequently practice putting those pieces fully back together in the context of the game. I doubt you’ll find anyone seriously training to play basketball who doesn’t play in a semi-realistic game-like situation at least once per week. In classroom education, often the high-level context is completely missing, and students end up memorizing / drilling on a pile of atomized facts and trivial very low level skills without ever practicing combining those in larger settings, without ever getting a very fast or effective feedback loop going, and without ever having any motivation for going through the practice. In the case of mathematics education, someone being taught 1-on-1 by a skilled tutor can move I’d say about 4–10 times faster than a student only watching lectures, doing completely independent book reading / trivial homework exercises / quizzes, and then getting back graded homework/quizzes a week afterward. That student can be assigned dramatically harder problems, can be helped along by limited (but well placed) hints, and can be given direct feedback/corrections at every level (from basic arithmetic computations through higher-level strategy to meta skills like strategy selection/evaluation). This is something that can’t be done in basketball because basketball is a group activity; you can’t watch a single player go through the game, and pause/backtrack everyone to the beginning of a situation whenever that player makes a mistake or suboptimal play.
trentmb 9y ago
I always found 'memorization' incidental- after step 1 and 2 in What should you do with a definition?, step 3 was already done.
AnimalMuppet 9y ago
I did that approach, too... up until my real analysis class. Then we'd have something like 50 theorems [edit: per test], and I couldn't remember them all. But I noticed that two or three theorems were used to prove the other 47, and so I memorized those. They gave me enough to survive the tests.
analog31 9y ago
I found that grinding through the problems, over and over again, while using the textbook as a reference, resulted in the facts becoming committed to memory. I think it worked in two ways. First was the obvious repetition. Second, it created "slots" in my brain that were receptive to related material. There may have been an emotional factor as well: Feeling "on top" of the material made it easier to learn.

by cle 9y ago

Philipp__ 9y ago

I agree, but I still haven’t found a way to make that process more enjoyable or less fatiguing.

newman8r 9y ago

I think people tend to conflate "memorization" with "cramming". You're right that memorization is underrated. Are you familiar with the 'method of loci' (i.e. memory palace). It's an amazing technique.

fooker 9y ago

Proper mental indexing is even more so. You can not memorize everything, but you can certainly index almost everything. That is why we can have databases that do not fit in 'memory'. Do you see the analogy here?

goldenkey 9y ago
Luckily we have brains that expose this interface quite readily with intuition. Learn the logic, and the partial indexes, the foreign keys, etc..they all follow. Reason before RAM. It is often much faster to derive data than to store it, and look it up. This applies to CPUs and to our brains. Our brains have instruction cache, and often instructions are better use of memory than their final executed output.

joe_the_user 9y ago

I wouldn't personally find advice like this useful for me. I suspect it varies with "personal style". I grasped mathematical concept easily from an early age and I never made an effort to memorize things. If anything, I saw those coming from less-advanced math founder on advanced math (arithmetic to algebra, algebra to calculus, calculus to advanced subjects) because they attempted to deal with the subject based on memorization rather than grasping the basic point. Generally, I did wind-up committing a lot of content to memory but it was and is much easier, even "effortless", when I knew the reason for each part of the content. Of course, language is slippery and we might be talking about exactly the same thing. So I wouldn't give blanket advise - each person has to find their own learning style (or styles, if it varies by discipline).

gowld 9y ago
Rote Memorization is awful. Memorizing by practicing so much that the details become "muscle memory" is the foundation of progress in learning. A basketball player has memorized how to shoot a free throw, not by cramming by rote, but by practicing.
- jacobolus 9y ago
  The best basketball players start by spending years and years just playing the game all the time, as recreation. The equivalent for mathematics is solving problems that you find personally relevant and interesting and which are at the limits of your current abilities. NOT just doing piles of rote calculation. Often solving a hard problem requires a big pile of intermediate calculations, but those a tool in service to some meaningful purpose, not an end in themselves. Forcing students to work through thousands and thousands of trivial calculation exercises is horrible pedagogy (and a very inefficient use of time). It’s like doing nothing but shooting drills and getting quizzed on the NBA rule book for years before ever trying to play a game.
  - mamon 9y ago
    >> The best basketball players start by spending years and years just playing the game all the time, as recreation. No, they start by joining a club where they get professional training, from a very young age. Just playing the game all the time won't make you any better at it. There are millions of children that spent significant part of their childhood playing basketball for fun, and never went past amateur level. This is just a conclusion from Ericsson famous paper[1]: you need DELIBERATE practice, not just recreational playing. Playing for fun will just develop bad habits, which you then will have to unlearn, so recreational playing might actually be an obstacle to learning. [1] http://www.nytimes.com/images/blogs/freakonomics/pdf/DeliberatePractice(PsychologicalReview).pdf http://www.nytimes.com/images/blogs/freakonomics/pdf/Deliber...
    - jacobolus 9y ago
      As you say, the key to skill improvement is playing deliberately and getting meaningful feedback in a tight loop, ideally at the edge of your abilities. But there are many aspects to any complicated skill, including tiny subskills, combination of various subskills, and at a higher-level meta skills like knowing when to change strategies, etc. The problem with only sport games as a mechanism for feedback is that (a) there’s not necessarily a good way to correct and try again right away if you want to practice one particular thing, (b) situations that arise are not homogeneous enough to compare feedback across trials, (c) there are periods of waiting in between direct practice, (etc.?). As a result, people who are training to be basketball players spend only like half their time playing realistic games, and the rest of their time on a variety of drills and workouts including general aerobic and strength training, practice running sideways and jumping, shooting / passing / dribbling drills, practice setting screens / rebounding / driving / inbounding the ball, larger-scale coordination drills, and so on. These let the players focus their conscious attention at one level at a time, and repeat a situation with analytical feedback in between. But those who improve fastest are the ones who figure out what they need to work on (or have a mentor/coach to figure out what they need to work on) and then get lots of feedback about that particular area, in an intentional way. This can even be done within the context of a realistic full game by choosing what to direct attention/focus to. But you’re missing my basic point, which is that all the skills in basketball are situated within a context. It’s obvious how they fit into playing a game. Students start with the high-level context (by watching / playing full games), and then break it down into small pieces they can work on separately or jointly, and then frequently practice putting those pieces fully back together in the context of the game. I doubt you’ll find anyone seriously training to play basketball who doesn’t play in a semi-realistic game-like situation at least once per week. In classroom education, often the high-level context is completely missing, and students end up memorizing / drilling on a pile of atomized facts and trivial very low level skills without ever practicing combining those in larger settings, without ever getting a very fast or effective feedback loop going, and without ever having any motivation for going through the practice. In the case of mathematics education, someone being taught 1-on-1 by a skilled tutor can move I’d say about 4–10 times faster than a student only watching lectures, doing completely independent book reading / trivial homework exercises / quizzes, and then getting back graded homework/quizzes a week afterward. That student can be assigned dramatically harder problems, can be helped along by limited (but well placed) hints, and can be given direct feedback/corrections at every level (from basic arithmetic computations through higher-level strategy to meta skills like strategy selection/evaluation). This is something that can’t be done in basketball because basketball is a group activity; you can’t watch a single player go through the game, and pause/backtrack everyone to the beginning of a situation whenever that player makes a mistake or suboptimal play.

trentmb 9y ago

I always found 'memorization' incidental- after step 1 and 2 in What should you do with a definition?, step 3 was already done.

AnimalMuppet 9y ago

I did that approach, too... up until my real analysis class. Then we'd have something like 50 theorems [edit: per test], and I couldn't remember them all. But I noticed that two or three theorems were used to prove the other 47, and so I memorized those. They gave me enough to survive the tests.

analog31 9y ago

I found that grinding through the problems, over and over again, while using the textbook as a reference, resulted in the facts becoming committed to memory. I think it worked in two ways. First was the obvious repetition. Second, it created "slots" in my brain that were receptive to related material. There may have been an emotional factor as well: Feeling "on top" of the material made it easier to learn.