Another quotation from the same issue of the TLS comes in fittingly here to wind up this random collection of disquieting thoughts--this time from a review of Sir Richard Livingstone's "Some Tasks for Education": "More than once the reader is reminded of the value of an intensive study of at least one subject, so as to learn 'the meaning of knowledge' and what precision and persistence is needed to attain it. Yet there is elsewhere full recognition of the distressing fact that a man may be master in one field and show no better judgement than his neighbor anywhere else; he remembers what he has learnt, but forgets altogether how he learned it."
I would draw your attention particularly to that last sentence, which offers an explanation of what the writer rightly calls the "distressing fact" that the intellectual skills bestowed upon us by our education are not readily transferable to subjects other than those in which we acquired them: "he remembers what he has learnt, but forgets altogether how he learned it."
There exist many people, including some math professors, who DO love such curricula, though. They say things like, "I was taught what to do and not why to do it. Isn't it wonderful that [Everyday Math, etc.] challenges a child to understand why a math principle is true instead of settles for 'rote learning'?" Maybe my traditional math education was different from theirs, but I was typically taught how and why to do an algorithm and then given so much practice that it became automatic. Since I had no need to remember afterward why something worked, I often didn't bother to remember the "why". Getting the right answer was my goal. That changed temporarily in my university math theory and proof classes, where the math professors were trying to make a mathematician out of me. They didn't succeed; I got my B.S. in Mathematics and then went into computer programming and finally law school. I'm still content to be an excellent calculator.
Taking humanity as a whole, very few people are going to be actual mathematicians. Yes, everyone should be able to calculate and have enough experience with math through pre-calculus that they can understand general statistics terms and do their own taxes and home improvement project purchases (e.g., vinyl flooring, paint, etc.) without relying on a calculator. However, this low-level math isn't intriguing like fractals and vigesimal Mayan math, and it certainly isn't what university math professors spend their time on.
Why do we listen to these professor-mathematicians when they speak in glowing terms of elementary math programs, especially constructivist curricula that cover lots of "cool" topics in "creative" ways? Basic math is a limited, rather boring thing--although one which the non-mathematician will use throughout life--and the university professors rarely teach that subject matter. In fact, the professors often were the kind of child that learned most basic math seemingly by osmosis and never had to do timed drills to remember the multiplication table. They are experts at posing problems in and teaching certain areas of mathematics that the average person has no need or interest in: set theory, number theory, topography, cryptology, game theory, etc. They are rarely experts in teaching calculation and very basic geometry. I don't think they are in a position to opine on the fitness of elementary math curricula. I would rather read curriculum evaluations from high school math teachers who have to teach students after they have been subjected to a given curricula for several years. They seem to me better positioned to be experts on the effectiveness of elementary math curricula.
