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Proofs are indeed very practical. For example, I believe Leslie Lamport mentioned somewhere that he only came up with the final version of Paxos once he tried t

Proofs are indeed very practical. For example, I believe Leslie Lamport mentioned somewhere that he only came up with the final version of Paxos once he tried to prove it, and noticed that some condition he assumed wasn't necessary at all.

dhosek 5y ago
The reasoning behind having geometry be the standard high school sophomore math class is that that’s the age where kids would be ready to do proofs. Except that curriculum designers seem to have forgotten this and except in honors classes, most sophomores don’t get taught proofs in geometry and instead get a set of inert rules about shapes that they have no use for.
- whatshisface 5y ago
  Geometry uses a deduction-only basket of proof techniques that don't prepare students for proofs done afterwards. I would like to see it replaced by elementary number theory which naturally uses a lot of induction/recursion and has some uses for proof by contradiction.
  - auggierose 5y ago
    Geometry has really all that is needed for proofs: * Axioms * Substitution * Modus Ponens * Universal Quantification Induction or proof by contradiction are just special cases of this. But yeah, geometry for introducing proofs is difficult, because it is so easy to confuse visual intuition with proof. At the very least, you need a capable teacher who knows the difference. But nobody expects children to understand it all from the get go. A healthy struggle to disentangle intuition and proof, and then to entangle them again later on once you know the difference, that's the path to understanding mathematics.
    - whatshisface 5y ago
      The thing about geometry is that it does not take long before you've taught those four things, and then you start teaching stuff that is specific to plane geometry.
      - auggierose 5y ago
        There are worse things to learn than plane geometry. It's actually a good thing to have a fixed topic to really learn those 4 things. Because once you really understood those 4 things, you are done, and you know everything about proofs in general there is to know.
    - bick_nyers 5y ago
      I got a math degree, but I definitely failed at understanding that difference when learning geometry in high school. My teacher was good, but not good enough in separating that, and with classroom sizes getting larger by the decade, I think it's not the best approach to require that kind of tip-toeing. I'm not sure what would be better though, I've thought about maybe combinatorics could be a good replacement, but I also don't have the brain of a teenager anymore and I don't teach them either, so I don't know how far of a reach that would be.

dhosek 5y ago

The reasoning behind having geometry be the standard high school sophomore math class is that that’s the age where kids would be ready to do proofs. Except that curriculum designers seem to have forgotten this and except in honors classes, most sophomores don’t get taught proofs in geometry and instead get a set of inert rules about shapes that they have no use for.

whatshisface 5y ago
Geometry uses a deduction-only basket of proof techniques that don't prepare students for proofs done afterwards. I would like to see it replaced by elementary number theory which naturally uses a lot of induction/recursion and has some uses for proof by contradiction.
- auggierose 5y ago
  Geometry has really all that is needed for proofs: * Axioms * Substitution * Modus Ponens * Universal Quantification Induction or proof by contradiction are just special cases of this. But yeah, geometry for introducing proofs is difficult, because it is so easy to confuse visual intuition with proof. At the very least, you need a capable teacher who knows the difference. But nobody expects children to understand it all from the get go. A healthy struggle to disentangle intuition and proof, and then to entangle them again later on once you know the difference, that's the path to understanding mathematics.
  - whatshisface 5y ago
    The thing about geometry is that it does not take long before you've taught those four things, and then you start teaching stuff that is specific to plane geometry.
    - auggierose 5y ago
      There are worse things to learn than plane geometry. It's actually a good thing to have a fixed topic to really learn those 4 things. Because once you really understood those 4 things, you are done, and you know everything about proofs in general there is to know.
  - bick_nyers 5y ago
    I got a math degree, but I definitely failed at understanding that difference when learning geometry in high school. My teacher was good, but not good enough in separating that, and with classroom sizes getting larger by the decade, I think it's not the best approach to require that kind of tip-toeing. I'm not sure what would be better though, I've thought about maybe combinatorics could be a good replacement, but I also don't have the brain of a teenager anymore and I don't teach them either, so I don't know how far of a reach that would be.