Very interesting tgat you mention bad math teachers. I agree. During my teaching assistant stint during graduate studies in applied and pure math, I had one student who was failing. Talking to her I learned that a math teacher in high school had made her feel very stupid - she stopped learning. This happens more often than is recognized especially to girls but not just to girls.
I told her to come to office hours and I gave her problem sets to solve, first easy then progressively harder. As she got confidence that she could do this her demeanor in class changed and in the space of a month she went from failing to a B-
After this I started asking anyone who said they had math anxiety or did not like math if they had a bad math teacher they remembered. I have asked close to a hundred people this over the last 30+ years and invariably they not only remembered the name of said bad math teacher but also relived how they were told they were dumb and would never be good at math. They stopped learning at that point.
Nonetheless math is hard because it is not an evolutionary survival skill we developed. I say jokingly that math is an unnatural act. I am not a gifted math student but I like solving problems and I would just solve every problem in the book ploddingly and stubbornly. So I dont hate math and I am not in love with it either. It is a very powerful tool for problem solving and also gives you powerful analytical capability you can use in other places in life.
> I like solving problems and I would just solve every problem in the book ploddingly and stubbornly.
Maybe that is all it takes to be a "gifted" math student?
Tangental:
I have always hated the term gifted. I will not deny there are some absolute phenoms out there in regards to any domain. Those individuals are few and far between and should be celebrated because of it. Maybe I am being semantical, but being "slightly better" does not make one gifted.
Learning a subject that is being taught to someone quicker than their peers does not make them gifted. Show me what they have created or discovered with their alleged "gift," and then we will see.
Von Neumann is not remembered because of how much quicker he learned math than others or how easy the subjects were for him. He is remembered for what he discovered and what he created -- that is what makes one truly gifted in my opinion.
I told her to come to office hours and I gave her problem sets to solve, first easy then progressively harder. As she got confidence that she could do this her demeanor in class changed and in the space of a month she went from failing to a B-
After this I started asking anyone who said they had math anxiety or did not like math if they had a bad math teacher they remembered. I have asked close to a hundred people this over the last 30+ years and invariably they not only remembered the name of said bad math teacher but also relived how they were told they were dumb and would never be good at math. They stopped learning at that point.
Nonetheless math is hard because it is not an evolutionary survival skill we developed. I say jokingly that math is an unnatural act. I am not a gifted math student but I like solving problems and I would just solve every problem in the book ploddingly and stubbornly. So I dont hate math and I am not in love with it either. It is a very powerful tool for problem solving and also gives you powerful analytical capability you can use in other places in life.