The Declining Quality of Mathematics Education in the US

http://www.kuro5hin.org/story/2007/1/25/174426/953
"Mathematics education seems to be very subject to passing trends - surprisingly more so than many other subjects. The most notorious are, of course, the rise of New Math in the 60s and 70s, and the corresponding backlash against it in the late 70s and 80s. It turns out that mathematics education, at least in the US, is now subject to a new trend, and it doesn't appear to be a good one.

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A couple of prime examples, in terms of textbooks and material for instructors, are brought up and suitably lampooned in a YouTube video by a Washington state weather presenter who encountered, and was appalled by, these particular teaching programs. The material in question is the TERC Investigations "Investigations in Number, Data, and Space", and the University of Chicago School Mathematics Project "Everyday Mathematics".

The focus of the YouTube video is on these math programs complete aversion to teaching students the classic methods for performing multi-digit multiplication and division. Indeed, these programs not only fail to teach such a method, they go so far as to actively discourage the method ever being taught, preferring that students didn't learn it outside class either.

What sort of methods do they teach? Well, for example, to solve the problem 26×31, a student might use the following approach: we can write 26×31 as 20×31 + 5×31 + 1×31 since 20+5+1=26; Now we know that 10×31=310, and 20×31 should be twice that (620) and 5×31 should be half that (155); so the solution is 620+155+31=806.

Note that the student could break the problem up differently, and thus there is no single approach that consistently works on all problems; each new multiplication is an entirely new problem. To be fair the methods they do teach, such as the above, are interesting, and I myself tend to use them (or variations thereon) for quick mental calculation. My complaint is not so much to the methods taught, but to the failure to first provide a solid grounding in traditional systematic algorithms for performing multiplication and division. Indeed, in my view, the real problems run much deeper than this particular symptom."