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Geometry has really all that is needed for proofs: * Axioms * Substitution * Modus Ponens * Universal Quantification Induction or proof by contradiction ar
by 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 agoThe 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 agoThere 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 agoI 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.