what's the confidence level of THIS measurement? The Reference Frame's latest posting deals with the connection between students' levels of confidence and their actual performance in math. I read this article yesterday also, but I was not convinced at all by its arguments.
In case anyone had no idea, I really like math. And I have liked math since before I was in school. I even played with a calculator on just about every car trip I took as a toddler. Seriously. In eighth grade, I tried developing my own number systems, such as the "extreme number" system (a set of numbers that were all divisible by 0) along with another system based on the idea that for every number v, v + (any integer) = v. I also found a really unusual relation between the numbers pi and phi, which I have not seen written up anywhere. I've thought about turning it into a paper.
Anyway, the CNN article essentially states that American students don't perform as well in math because they're too confident. While that may seem like an oversimplification (it is), I will argue that American students don't perform as well because they don't see math as a language. A typical college-level calculus book could be 1000 pages or more, and last a student three semesters. Yet a lot of much older books are a lot smaller, and I've found them to be just as useful in explaining the material. (I have a fairly large collection of them.) One of my favorite old math books, Elements of the Differential and Integral Calculus, contains several topics one would RARELY see in a calc book these days, such as applications of the gudermannian function. In case anyone didn't know, it's the arctan of the hyperbolic sine. It's a powerful function, but how many people have heard of it?
Math textbooks rely too much on examples and illustrations, which are necessary to some extent, but not on every page. The Schaum's outlines, not regular textbooks, are better-suited for that purpose. Perhaps the enormous size of most textbooks is a push to increase the price of the books, which equals... more money for the authors and a lot less money for the students who have to pay $100+ for a book they're required to have. Or it's just an intimidation factor for not-so-mathematically-inclined students, who don't have much interest in epsilon-delta definitions or Riemann sums...
But calculus books aren't even the big problem. The multitude of courses for liberal arts majors- who are (falsely) presumed not to have as much interest in math as the science/engineering majors- are... frought with problems. "Modern Mathematical Concepts" or "Finite Math" are just euphemisms for "Liberal Arts, General Education Math Courses." I might be too demanding here, but I think everyone in college should have a working knowledge of some calculus at the end of their freshman year. Students aren't going to get much out of math if they learn "modern concepts" that aren't even as modern as calculus! The same goes for science courses; I'm appalled by the extremely qualitative (read: non-technical) nature of so many of them. You won't learn much about quantum physics or relativity if you can't do the calculations.
End of rant.
I've decided to change the layout of this site... to some extent. I removed my "I am Pro-Victory" banner, even though I am pro-victory, because it is somewhat of an ambiguous statement. I also can't make this site look too much like the Reference Frame, either. I'd experimented with the NeoCounter earlier, but when only 2 visitors showed up on it (even though there have been close to 200 visits since September 3), I got rid of that immediately.  ¶ 4:48 PM