[QUOTE=Tully Mars]
My memory is fuzzy (pun intended), but I seem to remember that part of the resistance to Set Theory and New Math in general was that it wasn’t being presented as being related to basic arithmetic or as an addendum, it was being taught instead of basic arithmetic.
[/QUOTE]
That is doing it a disservice. Like I said, I was working under New Math texts, but I most certainly had to fill all the squares in first grade with stars to show I knew my add by 1, add by 2, add by 3, etc. facts. Same in third grade with multiplication. So it wasn’t that basic arithmetic was ignored, so much as it was that time previously devoted to basic math concepts was devoted instead to more abstruse basic math concepts. And, because many who were teaching math at the elementary and Jr. High levels were not mathematicians, they weren’t easily able to make the connections between the set theory stuff and the arithmetic stuff. It just kinda sat out there on its own.
Brahier talks about this in the textbook *Teaching Secondary and Middle School Mathematics * (Allyn & Bacon) 2005 2d ed. He notes the basis for the movement (a sense that we needed to be able to compete and a recognition that the teaching of math hadn’t changed in 300 years), and the basis for the opposition that grew to the movement (see, e.g.: Why Johnny Can’t Add (1973) by Morris Kline). In the end, the New Math movement catered to the top students with better mathematical skills, was applied by teachers who didn’t know what they were doing or why, and was underappreciated by a public that didn’t understand it. Thus, it died a relatively swift death.
Contrast to the approach of the New Math the approach advocated by the National Council of Teachers of Mathematics in 1980, which said we needed to focus on problem solving skills, regardless of how basic math facts are taught. This is eminently sensible, and yet, 27 years after they said this, in your average classroom, the only nod made to this concept is to include “story problems” in tests, as if that is what is meant by “problem solving.” The TIMSS reports from 1995 and 1999 showed that the United States was significantly behind several countries in diverse areas of the world when it came to solving math problems. A look at the typical classroom in the US, when compared to a classroom in, say Singapore, or Japan, shows why. In the former (and the one I’m observing now for my “methods” classes is no different), the focus is on providing the students with a mathematical fact, then having them drill the use of that fact with a series of problems that vary only in the numbers used. By comparison, the Asian classroom involves the students in discovering the “fact” in question (say, for example, the relationship of the two shorter sides of a right triangle to the hypotenuse), and does not bother to drill them on it much at all. Students who feel the need for drill obtain those drills outside of the classroom (Japan, for example, has supplementary programs done privately which offer what we in the US would consider normal seatwork/homework). End result: when a US student is provided a problem (that is, not an equation to solve, but a fact set that requires deciding on a method of resolution and successfully carrying that method out to an accurate conclusion), the US student has no classroom experience in doing that.
In the face of that, the fact that Susie can’t add 4 and 5 without punching buttons on her calculator seems almost immaterial… :eek: