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> The last attempt to fix it (common core) mostly emphasized memorizing arithmetic facts. Memorizing facts is the foundation of all learning. When you add 7+7

> The last attempt to fix it (common core) mostly emphasized memorizing arithmetic facts. Memorizing facts is the foundation of all learning. When you add 7+7 in your head do you instantly know the answer is 14 because of "understanding" or because you memorized over all the years. Also the current US education system strictly deemphasizes memorization. Instead it pushes for "understanding" (conveniently a concept that is not measurable). > Like anybody doesn't have multiple calculators in their pockets. Ok and? China and India are producing the smartest people in the world and their education systems strongly emphasize memorization. Understanding comes when you've memorized enough information that you can connect the dots. Once you get to advanced math it's basically impossible to understand from the start and you can only rely on memorization until you've memorized enough and experienced enough that it finally clicks.

yummypaint 4y ago
People really underestimate the importance of creativity to advanced technical problem solving. That has been the key human ingredient pushing the frontiers of STEM forward, especially in the most recent decades with better computational tools. The best mathematicians aren't the ones just proving theorems anymore, they're discovering interesting conjectures through exploration and then handing the grunt work off to a computer. Engineers aren't calculating anything remotely complex by hand anymore, nor should they. The best scientists also tend not to be people who were problem set whizzes in school.
- anon291 4y ago
  > The best mathematicians aren't the ones just proving theorems anymore, they're discovering interesting conjectures through exploration and then handing the grunt work off to a computer. I'm sorry no. This is simply wrong. Computer proofs are not there yet, and plus, a lot of the interesting theorems (including many of the well-known ones) are non-constructive which are difficult to prove on a computer. In fact, many theorem provers cannot prove 'basic' facts about math due to how constructive proof theory works. Indeed it is not clear what truth means at that level, but considering we regularly use non-constructive proofs to build things, I'm not sure that matters. I think what is most undervalued is the utility of sheer competence and technical skill to creativity. Without the former, there is no latter. If someone who never studied piano told you they had a beautiful piano solo in their head, would you believe them? More importantly, would you trust them to execute on the creative impulse?
  - yummypaint 4y ago
    Ask the mathematicians you know whether they do all their work on paper or use maple/octave/mathematica/python. 6/6 that i know do. If a person who doesn't play piano told me they have a piano solo in their head, i would set them up with a midi sequencer so they can bring it to life. My preconceptions about their capabilities are irrelevant.
    - i-use-nixos-btw 4y ago
      > maple/octave/mathematica/python I’m no mathematician, but I’d be very surprised if the overlap these tools have with mathematical research is very large.
    - anon291 4y ago
      > Ask the mathematicians you know whether they do all their work on paper or use maple/octave/mathematica/python. 6/6 that i know do. If a person who doesn't play piano told me they have a piano solo in their head, i would set them up with a midi sequencer so they can bring it to life. My preconceptions about their capabilities are irrelevant. A MIDI sequencer is not a piano, and mathematicians typically don't use maple/mathematica/octave/python (unless they're in applied maths, which is a subset of mathematics as a whole). The most important breakthroughs in mathematics, the kinds of things that push you over the edge as a society and that expand the scope of humanity's knowledge, are at the proof level, which those programs cannot achieve. Your MIDI sequencer analogy is very apt, because while someone may be able to bang something out on the MIDI sequencer and have the computer play it, a MIDI sequencing is not a human piano performance. But you're right, if you want a hollow fascimile of the real thing, then yes, those tools could work to impress someone.

yummypaint 4y ago

People really underestimate the importance of creativity to advanced technical problem solving. That has been the key human ingredient pushing the frontiers of STEM forward, especially in the most recent decades with better computational tools. The best mathematicians aren't the ones just proving theorems anymore, they're discovering interesting conjectures through exploration and then handing the grunt work off to a computer. Engineers aren't calculating anything remotely complex by hand anymore, nor should they. The best scientists also tend not to be people who were problem set whizzes in school.

anon291 4y ago
> The best mathematicians aren't the ones just proving theorems anymore, they're discovering interesting conjectures through exploration and then handing the grunt work off to a computer. I'm sorry no. This is simply wrong. Computer proofs are not there yet, and plus, a lot of the interesting theorems (including many of the well-known ones) are non-constructive which are difficult to prove on a computer. In fact, many theorem provers cannot prove 'basic' facts about math due to how constructive proof theory works. Indeed it is not clear what truth means at that level, but considering we regularly use non-constructive proofs to build things, I'm not sure that matters. I think what is most undervalued is the utility of sheer competence and technical skill to creativity. Without the former, there is no latter. If someone who never studied piano told you they had a beautiful piano solo in their head, would you believe them? More importantly, would you trust them to execute on the creative impulse?
- yummypaint 4y ago
  Ask the mathematicians you know whether they do all their work on paper or use maple/octave/mathematica/python. 6/6 that i know do. If a person who doesn't play piano told me they have a piano solo in their head, i would set them up with a midi sequencer so they can bring it to life. My preconceptions about their capabilities are irrelevant.
  - i-use-nixos-btw 4y ago
    > maple/octave/mathematica/python I’m no mathematician, but I’d be very surprised if the overlap these tools have with mathematical research is very large.
  - anon291 4y ago
    > Ask the mathematicians you know whether they do all their work on paper or use maple/octave/mathematica/python. 6/6 that i know do. If a person who doesn't play piano told me they have a piano solo in their head, i would set them up with a midi sequencer so they can bring it to life. My preconceptions about their capabilities are irrelevant. A MIDI sequencer is not a piano, and mathematicians typically don't use maple/mathematica/octave/python (unless they're in applied maths, which is a subset of mathematics as a whole). The most important breakthroughs in mathematics, the kinds of things that push you over the edge as a society and that expand the scope of humanity's knowledge, are at the proof level, which those programs cannot achieve. Your MIDI sequencer analogy is very apt, because while someone may be able to bang something out on the MIDI sequencer and have the computer play it, a MIDI sequencing is not a human piano performance. But you're right, if you want a hollow fascimile of the real thing, then yes, those tools could work to impress someone.