In a previous blog post I talked about some serious problems I had with questions on a standardized math test my son took recently. Apparently Reddit linked it, and both my blog and Reddit got a number of comments.
The interesting thing to me is the documentation the whole incident brought to the existence of two dramatically distinct views of what mathematics is—something I'd go as far as to call a mathematics "class divide"…
On the one side of the divide is what I'll call the "roties": folks who seem to think that math is a series of rote exercises designed to learn specific skills, something like rowing or piloting an airplane. I say "seem to" since I wouldn't count myself as part of this group, and so I probably can't represent their views accurately. Note that this characterization does not mean that these folks fail to embrace "hard" math: I've taken college multidimensional calculus and advanced geometry courses taught like this.
On the other side of the divide are what I'll call the "nerdies": folks like myself, who view math as an ultimately general tool for modeling problems and their solutions. We think that mathematics is an important discipline in its own right, that it exists independently of "practical" problem solving, and that it is fundamentally about creative answers within the bounds of strict and rigorous rules.
When it comes to the subject of math education, the roties seem to hate the nerdies…a lot. The nerdies aren't so fond of the roties, either.
In the recent flap, the roties stepped up big time with their complaints that I was nitpicking, that it should have been "obvious" what the questions were looking for, and that the test was perfectly fine given that it presumably covered material that had been previously heavily drilled into the students. There seemed to be a general sense of rotie outrage that someone like me could presume to question authority by suggesting the test had flaws—extending to accusing me of being outright incorrect in my critiques. (I'm certainly not infallible, but I do have 14 years of math-centric college education under my belt, and recently was co-advisor to a math student as she received her Ph.D. I think I'm capable of competently critiquing a third-grade math test.)
The nerdies shared my outrage that these defects, however trivial, would be in a third-grade math test. They shared my general feeling that any third-grade test that I and they couldn't get 100% on was a bad test indeed. The resentment extended to multiple-choice standardized tests in general—some of us recalled flawed tests we had personally experienced as children. (My math SAT score is lower than it probably should be because I had two "errors" on the exam that were later acknowledged to be mis-graded correct answers by the College Board.)
This is my blog, so I want to make my opinion clear here—the roties are wrong on this one, and the nerdies are right. One of the reasons for the struggle with elementary mathematics in this country that's inspiring this standardized testing mania is that students are turned off math at an early age because it seems to be an odd combination of verbal skills and mind reading.
That said, I'm not an early childhood education expert, and neither are most nerdies. I'm sure that a certain amount of controlled, rote practice is a necessary component of third grade math. I just wish that instead of multiple-choice standardized tests, students were given assistance in self-evaluation and allowed to proceed at their own pace. This is the approach used in reading instruction, as near as I can tell, and I think it works far better than the one normally used in mathematics.
I guess I'm just nerdy. (B)