[QUOTE=DSYoungEsq]
Now, while the concept was rightly abandoned, it sprang from a correct thought, in my opinion (and I’m in the process of being educated to teach math, so it’s a subject near and dear to my heart, having had to suffer through “New Math” as a child). In short, the idea behind New Math was that students shouldn’t simply be taught rote approaches to arithmetic, followed by rote approaches to more complicated arithmetic problems, until they reach high school and suddenly get introduced to algebra, geometry, trigonometry, etc. In short, students at an early age should be learning mathematical processes. It’s equally important to know why 4 + 3 = 7, or 5(6 + 4) = 50. And they need to be able to articulate this to others, and make connections between these concepts and other concepts, both mathematical and non-mathematical. Theory is important.
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Although I missed New Math by a few years, I was fortunate to be introduced to some of the more abstruse concepts of algebra and analytical geometry relatively early in life by virtue of being gifted a few old college-level texts on the subject, and found them relatively easy to understand in concept (though it was a few more years before I found access to applications of said theories). I think the real problem with New Math was two-fold: it was so focused on theory that relationship to real-world applications of set theory and combinatorics was underdeveloped, and both the teachers and texts failed to really understand the concepts and therefore presented them in a manner that was unclear and unintuitive; this combined with the fact that most parents were not familiar with the material made the whole effort futile and counterproductive. Richard Feynman has an anecdote in “Surely You’re Joking, Mr. Feynman” about serving on a board to review math and science texts for the state of California in the 'Sixties, and finding a math text that had a problem involving adding up the temperatures of various colors (classes) of stars (some of which don’t exist) to get the “total temperature”, which is a complete nonsense concept. He also reported a science text which repeatedly invoked the phrase, “Energy makes it go!” without ever explaining conceptually what energy is or where it comes from.
Set theory really isn’t that complicated, and the concepts behind it should be accessible to any eight year old of average intelligence. Then again, the basic concepts of geometry and calculus are not beyond the grasp of a reasonably sophisticated child, nor is fundmental symbolic logic. And despite the mistaken belief that there are no real world applications of this outside of computer science and esoteric sciences, there are plenty of ways in which we apply set theory, logic, statistics, et cetera implicitly on a daily basis; only, we’re not conscious that this is what we’re doing any more than most people realize that in catching a baseball they’re solving a complex nonlinear problem in differential equations.
People get freaked out by math and the physical sciences because they see numbers and get intimidated, but a conceptual understanding of the basics is no more complicated than grammar or music, and certainly more simple and consistant than phonics and spelling. Like those topics, the appropriate way to teach math and science is to introduce a concept, develop it sufficiently to make use of it, show applications of it (and go through the rote exercise of applying it to increasingly more abstract situations), and then move onto the next concept; repeat ad nausum.
There is great merit in training students to think in terms of logic and quanta, rather than the murky, thick-headed way most people cope with the world. Certainly, an adult that is to be trusted with an automobile, household cleaning solvents, and the vote should have a basic understanding of statistics so that they know when to cry, “Bullshit!” to obtuse claims and misdirections by pundits and politicians. The real problem, in my estimation, that educators themselves are, by and large, not trained in such thinking, and especially not the pedagogy of teaching the same to students.
And so, if you come up with a clever way of doing long division from left to right, you get penalized and humiliated because the teacher can’t cope with something she doesn’t understand and has no willingness to absorb. But hey, I’m not bitter and resentful, and I learned a lot by spending hours facing the corner.
Stranger
