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> The risk is that students think they’re bad at math, while in fact they’re bad at mindlessly memorizing and applying formulas. I'm skeptical that the kids wh

by raydev 3y ago

> The risk is that students think they’re bad at math, while in fact they’re bad at mindlessly memorizing and applying formulas. I'm skeptical that the kids who struggle with memorization will suddenly be able to write proofs with ease. I'd argue proof-writing is much harder to wrap one's head around than being forced to remember when to apply a2+b2=c2.

edanm 3y ago
I think this is a false dichotomy of what it means to be "smart" or "good at math/studies". Someone can jbe bad at arithmetic, but good at writing proofs. Hell, plenty of mathematicians say they are bad at arithmetic! More importantly in the context of education, someone can be completely unmotivated by arithmetic, but be more motivated by something else, leading to different amounts that they apply themselves, leading to different outcomes.
- raydev 3y ago
  > Someone can jbe bad at arithmetic, but good at writing proofs I'm not saying it's impossible, just that the median child/teen isn't going to demonstrate this. I don't think it's debatable that proofwriting is harder to teach, and requires more time and effort from both students and teachers.
strikelaserclaw 3y ago
proofs are actually what made me get interested in math, proofs allowed for such a range of self expression and creativity that i was hooked even though they usually required more thought. Compare this to the studying the myriad of integration techniques which i found very boring. My wife on the other hand seemed to enjoy rote mechanical memorization. I guess the fundamental question is, long after most students graduate high school or college and forget most of the math they learned, what are they supposed to keep from the many years of mathematical education? If you ask me, it is the ability to reason that they should keep and proof based math teaches you exactly that.
- raydev 3y ago
  I agree it should be an option for the children who are capable, but as I mentioned in another thread, I don't think the median child is capable... or they may be capable after far more effort from the institution than is acceptable. I'd imagine you'd have to start kids writing extremely basic baby proofs in elementary school, and then continue to hammer it in every single year until they graduate high school to get basic competency in proofwriting. That's a long time commitment for little visible gain.

by raydev 3y ago

edanm 3y ago

I think this is a false dichotomy of what it means to be "smart" or "good at math/studies". Someone can jbe bad at arithmetic, but good at writing proofs. Hell, plenty of mathematicians say they are bad at arithmetic! More importantly in the context of education, someone can be completely unmotivated by arithmetic, but be more motivated by something else, leading to different amounts that they apply themselves, leading to different outcomes.

raydev 3y ago
> Someone can jbe bad at arithmetic, but good at writing proofs I'm not saying it's impossible, just that the median child/teen isn't going to demonstrate this. I don't think it's debatable that proofwriting is harder to teach, and requires more time and effort from both students and teachers.

strikelaserclaw 3y ago

proofs are actually what made me get interested in math, proofs allowed for such a range of self expression and creativity that i was hooked even though they usually required more thought. Compare this to the studying the myriad of integration techniques which i found very boring. My wife on the other hand seemed to enjoy rote mechanical memorization. I guess the fundamental question is, long after most students graduate high school or college and forget most of the math they learned, what are they supposed to keep from the many years of mathematical education? If you ask me, it is the ability to reason that they should keep and proof based math teaches you exactly that.

raydev 3y ago
I agree it should be an option for the children who are capable, but as I mentioned in another thread, I don't think the median child is capable... or they may be capable after far more effort from the institution than is acceptable. I'd imagine you'd have to start kids writing extremely basic baby proofs in elementary school, and then continue to hammer it in every single year until they graduate high school to get basic competency in proofwriting. That's a long time commitment for little visible gain.