There are as many opinions on issues with math education as there are mathematicians (I think the only consensus is We Are Doing It Wrong).
My view is math education needs to spend a long time at the start (e.g. before calculus, maybe even before trig) talking about what a proof is, and teaching students how to prove things. That is “here is a simple statement and a sequence of steps that form a proof. Now try to prove a similar statement.”
A lot of math education is subject-oriented (e.g. here is an analysis class, here is an algebra class, a topology class, etc.) And very few math programs, at least last I looked, really offer students fresh out of calculus a primer on proving things. They just immediately throw them in the pool and expect them to start showing things about a particular subject.
If I were Math-Emperor of Earth, I would start math education by first administering a test to figure out if a person is more visual or more algebraic, and in the former case start them on learning-what-a-proof-is via geometry (a modern Euclid take, basically), and in the latter case start them on learning-what-a-proof-is via a suitably algebraic subject, maybe even abstract algebra directly, or maybe some subject with an algebraic flavor but not too abstract (physics? number theory? I am not sure.)
Old school Russian math education used to start on geometry proofs very early (6th grade I think). Now I think they are copying Western education more, more’s the pity.
There are as many opinions on issues with math education as there are mathematicians (I think the only consensus is We Are Doing It Wrong).
My view is math education needs to spend a long time at the start (e.g. before calculus, maybe even before trig) talking about what a proof is, and teaching students how to prove things. That is “here is a simple statement and a sequence of steps that form a proof. Now try to prove a similar statement.”
A lot of math education is subject-oriented (e.g. here is an analysis class, here is an algebra class, a topology class, etc.) And very few math programs, at least last I looked, really offer students fresh out of calculus a primer on proving things. They just immediately throw them in the pool and expect them to start showing things about a particular subject.
If I were Math-Emperor of Earth, I would start math education by first administering a test to figure out if a person is more visual or more algebraic, and in the former case start them on learning-what-a-proof-is via geometry (a modern Euclid take, basically), and in the latter case start them on learning-what-a-proof-is via a suitably algebraic subject, maybe even abstract algebra directly, or maybe some subject with an algebraic flavor but not too abstract (physics? number theory? I am not sure.)
Old school Russian math education used to start on geometry proofs very early (6th grade I think). Now I think they are copying Western education more, more’s the pity.