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> If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better.

> If they would teach kids to play with math (or any form of knowledge, for that matter), and not just run through 10,000 rote problems, maybe we'd rank better. Don't the countries that rank better use the rote method even more?

saint_fiasco 10y ago
From the article: >Though lesson study is pervasive in elementary and middle school, it is less so in high school, where the emphasis is on cramming for college entrance exams I think the implication is that kids are supposed to be taught to play with math in addition to the rote memorization, not that rote memorization is evil. Many of the more "fun" math techniques rely on knowledge acquired through rote memorization, just like dynamic programming uses the results of inefficient calculations to speed up subsequent calculations.
- Frogolocalypse 10y ago
  I think rote learning is a really really important thing, perhaps the most important thing, in math. Math is like any sport... you get good at it by practice practice practice. Check check check check. You have to train your brain to be good at it, and it can be hard, just like anything you train at. > Many of the more "fun" math techniques rely on knowledge acquired through rote memorization I wasn't aware of this. I have a nine-year-old. Are there any examples of this?
  - saint_fiasco 10y ago
    Most of the new fancy techniques for learning multiplication and so on assume the student knows the tables. For example, take a look at this lesson: http://www.homeschoolmath.net/teaching/md/distributive.php http://www.homeschoolmath.net/teaching/md/distributive.php Ignore the stupid rectangles, and ignore the part where it says "They actually use the distributive property, but we do not need to explain that to 4th grade students." (seriously, wtf) A child who practices lots of sums, such that she knows how to add 420 and 56 without counting with their fingers or writing things down, will be able to learn this kind of multiplication with ease. Once they learn that and practice a lot, they will be able to generalize the method to multiply any two two-digit numbers. Memorizing things is important because if you have to count with your fingers to calculate 3x3, you will never be able to calculate, for example, 23 squared in your head. But if you know the times tables your thought process might look like this: 20x20 = 400 23x20 = 400 + 60 23x23 = 460 + 23x3 = 460 + 69 = 529 (23 times 3 is "the hard part" where most kids who know all the theory (distributive property) but are out of practice (not enough rote memorization) will lose track) A more advanced example is what engineers used to do a lot before they had calculators: They memorized log tables, so when they wanted to multiply big numbers they just added their logs together, because log(a x b) = log(a) + log(b). An unrelated example is converting miles to kilometers. The official relationship is that a mile equals 1.609 kilometers, an ugly number that doesn't work well with mental arithmetic. But that number is kinda close to the golden ratio, don't you think? So if you are the kind of weirdo who memorizes the Fibonacci sequence, you can quickly calculate that 13 miles should be about 21 kilometers (and 21 miles is about 34km, and so on), because the ratio between a Fibonacci number and the next approaches phi.
    - Frogolocalypse 10y ago
      Thanks so much for that link.
  - tomc1985 10y ago
    But the whole point of play is to run through all those rote learning steps while simultaneously learning about the system and environment they live in. Sure you can cram, and then you'll test well on standardized entrance exams, but then how many of these people are able to effectively apply that knowledge to real-world problems? If you play, or tinker, or experiment, as part of your learning, then you already have this experience. It's not about "fun", it's about experimentation. Free-form intellectual play.

saint_fiasco 10y ago

From the article: >Though lesson study is pervasive in elementary and middle school, it is less so in high school, where the emphasis is on cramming for college entrance exams I think the implication is that kids are supposed to be taught to play with math in addition to the rote memorization, not that rote memorization is evil. Many of the more "fun" math techniques rely on knowledge acquired through rote memorization, just like dynamic programming uses the results of inefficient calculations to speed up subsequent calculations.

Frogolocalypse 10y ago
I think rote learning is a really really important thing, perhaps the most important thing, in math. Math is like any sport... you get good at it by practice practice practice. Check check check check. You have to train your brain to be good at it, and it can be hard, just like anything you train at. > Many of the more "fun" math techniques rely on knowledge acquired through rote memorization I wasn't aware of this. I have a nine-year-old. Are there any examples of this?
- saint_fiasco 10y ago
  Most of the new fancy techniques for learning multiplication and so on assume the student knows the tables. For example, take a look at this lesson: http://www.homeschoolmath.net/teaching/md/distributive.php http://www.homeschoolmath.net/teaching/md/distributive.php Ignore the stupid rectangles, and ignore the part where it says "They actually use the distributive property, but we do not need to explain that to 4th grade students." (seriously, wtf) A child who practices lots of sums, such that she knows how to add 420 and 56 without counting with their fingers or writing things down, will be able to learn this kind of multiplication with ease. Once they learn that and practice a lot, they will be able to generalize the method to multiply any two two-digit numbers. Memorizing things is important because if you have to count with your fingers to calculate 3x3, you will never be able to calculate, for example, 23 squared in your head. But if you know the times tables your thought process might look like this: 20x20 = 400 23x20 = 400 + 60 23x23 = 460 + 23x3 = 460 + 69 = 529 (23 times 3 is "the hard part" where most kids who know all the theory (distributive property) but are out of practice (not enough rote memorization) will lose track) A more advanced example is what engineers used to do a lot before they had calculators: They memorized log tables, so when they wanted to multiply big numbers they just added their logs together, because log(a x b) = log(a) + log(b). An unrelated example is converting miles to kilometers. The official relationship is that a mile equals 1.609 kilometers, an ugly number that doesn't work well with mental arithmetic. But that number is kinda close to the golden ratio, don't you think? So if you are the kind of weirdo who memorizes the Fibonacci sequence, you can quickly calculate that 13 miles should be about 21 kilometers (and 21 miles is about 34km, and so on), because the ratio between a Fibonacci number and the next approaches phi.
  - Frogolocalypse 10y ago
    Thanks so much for that link.
- tomc1985 10y ago
  But the whole point of play is to run through all those rote learning steps while simultaneously learning about the system and environment they live in. Sure you can cram, and then you'll test well on standardized entrance exams, but then how many of these people are able to effectively apply that knowledge to real-world problems? If you play, or tinker, or experiment, as part of your learning, then you already have this experience. It's not about "fun", it's about experimentation. Free-form intellectual play.