Im asking because I noticed in America there is this definitive thing about teaching kids certain things by a certain age. I come from a place where kids can do advanced math and calculus in elementary school. Chemistry is hardcore by the 5th grade.
While I’m sympathetic to the first part, I call complete and utter bullshit on the second unless you have some serious hedging and qualifying to do.
I want you to explain what you mean by “advanced mathematics” and “calculus”. Generally when someone says advanced mathematics they are referring at least to various branches of mathematics that are heavily into proof theory and set theory–So stuff like group theory and modern algebra, algebraic and geometric topology, etc. You of course can throw things like analysis or analytic number theory in there too, even though in their introductory presentations they aren’t too set theoretic. As for “calculus”, when someone mentions this I assume they are talking about a more rigorous limit calculus where the normal definitions of derivative and integral are given along with techniques for finding these things and of course lots of applications–gradient, curl, etc.
Unless you take me to the classroom where your average 9-10 yr old 5th grader is sitting and doing these sorts of things, I will not believe it. I do think your average middle school child–12-15ish–is able to handle many proof concepts, and that there are even probably a good number of children in this age range who can handle set theoretic concepts. It’s certainly fairly common for younger high school students–15-16–to do good parts of calculus and advanced mathematics, as I have described above.
Your AVERAGE 9-10 year old doing these things? Bullshit… complete and utter. The occasional exceptional one who can? Sure, there are cases.
Now, as to why I say this… (I can’t believe I’m arguing this point.) I actually have a hard time believing that the average 9-10 yr old can even conceptually handle many algebraic concepts–let alone set theoretic concepts (Don’t get me started on “new math”). I say this both because the anecdotal evidence seems to support it–there are reasons why the average 5th grader doesn’t get much beyond fractions–and also because the neuroscience and psychology people seem to lend much support to the idea that the average 5th graders mind hasn’t developed enough to understand the sort of abstract concepts that are involved in advanced mathematics.
So, I have explained, now you explain.