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> (Just makes the process faster) So the opposite of irrelevant. You need 10 minutes before you can start to think about the question that was likely a premise

> (Just makes the process faster) So the opposite of irrelevant. You need 10 minutes before you can start to think about the question that was likely a premise for a larger argument. "To be a surgeon, knowing surgery techniques from memory is irrelevant. When called upon to do surgery, I can simply leave, attend medical school, then come back and do the surgery. What's really important is knowing where the medical school is located."

viraptor 2y ago
The ability of critical thinking in abstract is different than a combination knowledge/physical skill which requires practice and is time sensitive. Your example is of an entirely different class than the concept of "critical thinking". The claim was "you need memorization as a starting point". And that's the part I disagree with. Ability - it's irrelevant. Speed of doing it in specific cases - relevant.
- tialaramex 2y ago
  Yeah, I know a bunch more of my times table from memory today than I did when I was tested on it forty years ago. But I passed all those tests because of course all you need is know that multiplication is repeated addition and do the addition fast. Today I can tell you that 7 x 7 = 49 but back then I'd have just gone 7, 14, 21, 28, 35, 42, 49 quickly and said "49" for the same answer but a slight delay. Parents who were taught times tables and didn't do much later mathematics are often confused by the way we teach kids today, because they expect we'd try to cram the tables in there, but that's not actually useful, what's useful is seeing the pattern and we'd prefer a child who maybe doesn't know off by heart what 9x8 is but sees the pattern, and whose first question when the teacher finally explains exponentiation and shows how it relates to multiplication, is, "Does this keep going forever?" which yes, it does, there are more hyperoperations and they do keep going like this forever. That child understood the pattern, 9x8 is a problem a calculator can solve, understanding the pattern is something else.

viraptor 2y ago

The ability of critical thinking in abstract is different than a combination knowledge/physical skill which requires practice and is time sensitive. Your example is of an entirely different class than the concept of "critical thinking". The claim was "you need memorization as a starting point". And that's the part I disagree with. Ability - it's irrelevant. Speed of doing it in specific cases - relevant.

tialaramex 2y ago
Yeah, I know a bunch more of my times table from memory today than I did when I was tested on it forty years ago. But I passed all those tests because of course all you need is know that multiplication is repeated addition and do the addition fast. Today I can tell you that 7 x 7 = 49 but back then I'd have just gone 7, 14, 21, 28, 35, 42, 49 quickly and said "49" for the same answer but a slight delay. Parents who were taught times tables and didn't do much later mathematics are often confused by the way we teach kids today, because they expect we'd try to cram the tables in there, but that's not actually useful, what's useful is seeing the pattern and we'd prefer a child who maybe doesn't know off by heart what 9x8 is but sees the pattern, and whose first question when the teacher finally explains exponentiation and shows how it relates to multiplication, is, "Does this keep going forever?" which yes, it does, there are more hyperoperations and they do keep going like this forever. That child understood the pattern, 9x8 is a problem a calculator can solve, understanding the pattern is something else.