4 ms·

Oh man I could not disagree more. “Math facts” don’t require any sort of conjuring, in fact cease to seem mystical at all, once you have a deep understanding of

Oh man I could not disagree more. “Math facts” don’t require any sort of conjuring, in fact cease to seem mystical at all, once you have a deep understanding of the material. Take your favorite math textbook—do you seriously think the author wrote all that down by rote memorization? Of course not: it came naturally as a byproduct of study. Memorization for the sake of memorizing is the worst possible way to learn mathematics.

yCombLinks 4y ago
The 2 aren't mutually exclusive. If you give 2 middle schoolers a test and one knows all of his time tables by rote, he's going to fly circles around the "kid with deep understanding" that's writing out the multiples manually.
- tomjen3 4y ago
  If you give them a typical school tests designed to test a typical school scenario, then the kid best at school will get the highest score. But the question is, if school tests are at all related to reality. I don't think so.
- i2ksbu2b 4y ago
  Is what you are measuring actually meaningful? Also you dont need to write them out, you can still calculate it in your head "manually". I think second student may have easier time to apply knowledge on things like 4 * 2,75.
- watwut 4y ago
  If the test is purely about multiplying small numbers and the other kid don't know multiply, maybe. If the test is designed to test understanding, then the kid with deep understanding will win. By your definition, multiplying kid is faster at multiplying, but don't really know what he is doing outside of memorized situation. And at other is better at everything else.
  - yCombLinks 4y ago
    This applies to lots of areas though, the multiples is just one tiny example. Like rote memorization of an api for a language. It's far easier to see and plan ahead when you don't have to constantly stop to figure out something else. More of your mental energy can go toward higher level thinking when you don't have to continually downshift to figure out the low level pieces.
- hyperbovine 4y ago
  Now let’s ask both of those kids to multiply 226*148, and see who comes out on top.
emodendroket 4y ago
How do you have a "deep understanding of the material" without committing any of it to memory?

yCombLinks 4y ago

The 2 aren't mutually exclusive. If you give 2 middle schoolers a test and one knows all of his time tables by rote, he's going to fly circles around the "kid with deep understanding" that's writing out the multiples manually.

tomjen3 4y ago
If you give them a typical school tests designed to test a typical school scenario, then the kid best at school will get the highest score. But the question is, if school tests are at all related to reality. I don't think so.
i2ksbu2b 4y ago
Is what you are measuring actually meaningful? Also you dont need to write them out, you can still calculate it in your head "manually". I think second student may have easier time to apply knowledge on things like 4 * 2,75.
watwut 4y ago
If the test is purely about multiplying small numbers and the other kid don't know multiply, maybe. If the test is designed to test understanding, then the kid with deep understanding will win. By your definition, multiplying kid is faster at multiplying, but don't really know what he is doing outside of memorized situation. And at other is better at everything else.
- yCombLinks 4y ago
  This applies to lots of areas though, the multiples is just one tiny example. Like rote memorization of an api for a language. It's far easier to see and plan ahead when you don't have to constantly stop to figure out something else. More of your mental energy can go toward higher level thinking when you don't have to continually downshift to figure out the low level pieces.
hyperbovine 4y ago
Now let’s ask both of those kids to multiply 226*148, and see who comes out on top.

emodendroket 4y ago

How do you have a "deep understanding of the material" without committing any of it to memory?