Monday, December 24, 2012

US - declining standards in mathematics

The proof of falling standards comes from looking at the best schools:
The transition from high school to college presents problems for all students, but for some students it is particularly challenging. At Caltech, many newly admitted students lack the background in mathematics that is necessary to succeed in Ma 1a. Unfortunately, few of them are even aware that their background in mathematics is deficient. This is not their fault. The mathematics curriculum in high schools is less rigorous than it was even a few decades ago. In conversations with Caltech students who have struggled with freshman mathematics, most report that they were star math students in high school, which of course is a major reason why they were offered admission to Caltech in the first place. Many of them, however, have never seen mathematics as it is taught at Caltech.

Those who struggle in Ma 1a usually continue to struggle in the rest of the core mathematics classes. They earn relatively low GPA’s during their first two years or so at Caltech, and when they graduate their GPA’s are significantly lower than those of other students. And not all who struggle with freshman mathematics succeed; such students are also less likely than their counterparts to graduate from Caltech. The students often report that, in the end, they have also not learned very much math, as too much of the material was beyond their ability to comprehend at the time it was presented. Currently Caltech attempts to assist such students in a number of ways but this assistance may be too little, too late.

In order to understand the specific reasons why many of our freshman struggle in Ma 1a, the undergraduate Academics and Research Committee conducted an online survey that asked a series of specific questions about the difficulties they encountered in Ma1a. From the survey results, the most common area of weakness that students identified was that of formal reasoning, writing proofs, and common proof techniques. The results thus corroborate what most people connected with Ma 1a have known anecdotally—that many Caltech freshmen, though computationally skilled, struggle with basic proof concepts. Moreover, a corollary obstacle to students thriving in Ma1a is that, because it is a “calculus” course, students feel like they should be mastering the topic with ease. They are thus reluctant to go to classmates, TA’s, or professors when they encounter difficulties. 
CIP pointed out the the Caltech core curriculum is revised down from five terms each of math. and physics, to three terms each. There appear to be a variety of reasons.

Anyway, for all the IQmetricians' (idiotic) claims that we are getting smarter, what with the Flynn Effect, and such, our high school achievement level is dropping. The higher IQ (supposedly) best students of today come out of high school knowing less math than their counterparts from a generation ago.