Racing to calculus in high school so that you can repeat it in college?

Our high school, my daughter’s year: 3 students in Calc BC as 9th graders, all European-Americans. One Asian-American in Calc AB in 9th grade. A few years later, one Asian American 8th grader in Calc BC, but that did not go so well.

I think an issue that has not been discussed in connection with the “race to calculus,” is “What is the alternative, for a student who really understands math?” There may be few schools that have implemented the AoPS suggestion of better pre-calculus math. It is certainly possible, in principle. But it requires teachers who understand math pretty deeply, to be able to handle it.

My daughter was fortunate to have a really good 7th grade math teacher, who truly understood math. But he was rather atypical for the school system, even though it is a good school system (relative to our state).

Two of the 9th graders in Calc BC took AP Statistics the next year, rather than more advanced math at the university. They understood topics that the AP Statistics teacher really did not (chi-squared test, anyone?), and one of them wound up serving as a sort of “auxiliary AP Statistics teacher.”

My daughter took the university probability and statistics course that had multi-variable calculus as a pre-requisite, instead of AP Statistics, though she also took the AP Statistics test. If you look at some of the material that the College Board has posted on the free-response questions for AP Statistics, you will probably be able to see why my spouse refers to it as “Behavioral Compliance Math.” For example, suppose that you want to apply the chi-squared test to a set of data in “boxes.” You have to state that the data fit the requirements for applicability of the chi-squared test, or you are docked points on the free response. So far, okay. But apparently you have to note explicitly an inequality about the numbers in the boxes. If 7 is the smallest, in this example case, your answer has to include 7 > 5, to receive full credit. Really? (I am drawing on a memory of the CB posted, graded free-response questions from about a decade ago, so the details may not be quite correct, but the need for the trivial inequality is certainly correct.)

Now, imagine this situation, which has been set up by quite well-educated teachers of statistics, but translated into a typical high school classroom at a good-ish high school. It would drive a good young mathematician bonkers!