[quote]Dr.Matt581 wrote:
[quote]Headhunter wrote:
You are mostly incorrect. In Precalc, I teach them the structure of proof. In Calc, we do the proofs, such as of the Product Rule for derivatives, and so on. The black kids and asian kids can’t do it on their own. The white kids can. [/quote]
You are supposed to teach them very simplified versions of proofs in precalc and Calc 1, but do not pretend for a second that those are actual proofs. Precalc and calc 1 students just do not have the math skills to do or understand real proofs and the inability of precalc and calc 1 students to do even the watered down versions of proofs those classes require is no mark against them as far as mathematical ability. Learning general problem solving and basic mathematical techniques are way more important at that level. Developing those skills is not a priority or a requirement at that stage of their mathematical development. If you had to teach students beyond a very basic level you would understand that. Like I said, it is only after spending a couple years at the undergrad level learning mathematical techniques and problem solving skills in classes like calc 1-3 intro to differential equations and intro to linear algebra are their mathematical skills developed to the point where they should be able to understand proofs. It is only after completing these courses that the inability to grasp the concept of proofs means anything at all.
I am very familiar with the kinds of proofs provided in precalc and basic calc textbooks. Here is the textbook for the intro to theoretical math, usually referred to as basic analysis, course the university I teach at uses:
go to p. 106-107 and look at Proposition 4.1.8. This is the most basic proof of the chain rule that can be considered valid from a theoretical mathematics point of view. If you are trying to say that you consistently have students that are capable of producing that then you are just plain full of shit. I was considered a mathematical prodigy, entered university at age 14 and got a PhD in physics at 22 and I could not produce that proof until I was a junior in college.
Like I have said, these days the world of theoretical math and physics is dominated by Indians, Asians, and Arabs. Just look at prominent authors published in major journals. White people like me are a minority. Thinking back over my teaching career, most of the people who fail or drop my intro physics classes are white, and as I said earlier my upper level and especially graduate level classes are dominated by Indians, Arabs, and Asians which is the norm in this country. In fact, I have never had a white grad student and can count on one hand the number of white grad students in my department that I know of right now and I teach at a very large and well known university. That is the norm all over the country.
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I think you are a snob. I teach simple proofs that are several hundreds of years old, but they aren’t university level, so they aren’t…proofs…uh…okay…
As I also said, Asians are good mimics. This makes them very good at what they do best, replicate what others have done. They do so very well and thus dominate those fields. I also said that a small number of Asians (Chinese, never taught any Arabs) are creative though not to the degree of the white students IN MY CLASSES.
Finally, last time I looked, China and India had about 2.5 billion people between them. Both cultures also despised business until quite recently and put great store on education. Small wonder that those societies dominate math and science, they outnumber us 10 to 1.
When one of these mimics starts an Apple, Microsoft or Facebook, your argument will carry more weight.