Some thoughts on math
[T]there is no evidence whatsoever, that accumulation of facts and background knowledge are the same thing. In fact, there is plenty of evidence to the contrary. Facts learned out of context and apart from actual real world experience that is repeated over and over are not retained. . . .
[K]ids don't like math much and it is clear why. They find it boring and irrelevant to anything they care about doing. If you think math is so important, then why not teach it within a meaningful context, like business, or running a school doing the kind of math you had to do to do that which certainly wasn't algebra II. There is plenty of evidence that shows that teaching math within a real and meaningful context works a whole lot better than shoving it down their throats and following that with a multiple choice test. . . .
[T]here is no evidence whosoever that says that a nation that is trailing in math test scores will somehow trail in GDP or whatever it is you really care about. This is just plain silly, but we keep repeating the mantra that we are behind Korea in math as if it has been proven that this matters in some way. . . .
[N]early every grown adult has forgotten whatever algebra he or she ever learned to pass those silly tests, so it is clear that algebra is meaningless for adult life. I ask every important person in public life that I meet to tell me The Quadratic Formula. No one has ever been able to do so.
Recent pronouncements from Washington regarding math education have suggested that pedagogical points of view don't matter in the teaching of mathematics. For example: "There is no basis in research for favoring teacher-based or student-centered instruction," Dr. Larry R. Faulkner, the chairman of the panel, said at a briefing last Wednesday. "People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other."
Well, actually, Larry, if you read the "Rising Above the Gathering Storm" document (National Academies Press, 2007) you will likely be shocked to learn that, in fact, there are two methodologies proven to improve math proficiency: Statewide specialty high schools (e.g., IMSA) and inquiry-driven project-based learning (e.g., constructionism.) Now it may well be that Dr. Faulkner has more reliable sources than those at the National Academy of Science and other groups that contributed to this 591 page report on the challenge faced by the US in the areas of science and math education. However, let's assume for the moment that the National Academies tend to use fairly reliable folks to generate their reports. In this case, then Faulkner is simply flat out wrong. There IS research showing that one methodology is better than another, and I just cited it. The fact that this research was reported by the same government that claims it does not exist is a puzzlement at best, and an example of the "big lie" at worst. Faulkner's strategy seems to be that, if you lie to the American public loudly enough, it will believe you.
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