I'm a victim of friendly fire in the math wars...wait, scratch that... I'm a victim of used-to-be friends fire.... you apparently have to be on one side or the other, and recently I am catching hell from both sides.
I guess it is my own fault. For the last ten-plus years I simply refused to enter into any dialog involving the "New Math/intuitive math/discovery math" camp on the one side and the "gimme that old time religion/long division or die/calculators are evil" camp on the other. The problem, at least as I see it, is that each group is assuming that it has to be all one or all the other. As one blogger put it, it is a choice between "why" vs. "how".(No one apparently envisions that a teacher might actually try to teach both how AND why.) California has fallen aside as the chief battleground after a victory, more or less, by a coalition of anti-reform elements (many of whom would not be caught dead championing the excess of the most conservative among them), and now Washington state seems to be the new battleground..(see A University View)
I can understand parents getting upset... as one observer of the process wrote, "Parents .... don’t understand what the specific tasks are, or how to perform them, or even why their kids are being taught this way instead of the older one. And again the proponents of this style (rehashing the why vs. how discussion) come off as arrogant. Their concerns aren’t for the parents’ ability to follow along with what their children are learning — and something tells me these are the same educators who insist that parental involvement is key — but just that the parents aren’t screwing up all their hard work." I admit I was shocked to read the following from the teachers resource packet for a program called "Everyday Learning"...
"The authors of Everyday Mathematics do not believe it is worth students’ time and effort to fully develop highly efficient paper-and-pencil algorithms for all possible whole-number, fraction, and decimal division problems. Mastery of the intricacies of such algorithms is a huge endeavor, one that experience tells us is doomed to failure for many students. It is simply counter-productive to invest many hours of precious class time on such algorithms. The mathematical payoff is not worth the cost, particularly because quotients can be found quickly and accurately with a calculator." I am reminded of a quote from my wall at school,” For every problem there is a solution which is quick, easy, and wrong! "
For me the intuitive learning and process learning support each other; the kids learns the multiplication algorithm, then he sees in algebra that two digit multiplication is the same as the "foil" method he is learning, and the rigor and intuition feed each other. One guy calls it the Mr. Miyagi method (from the Karate Kid movies). OK, that means teach the algorithm, but don't expect every kid to achieve 100% accuracy on the most difficult problems in the fourth grade, and then show them the intuitive approach that helps them understand WHY the algorithm works
Strangely, most of the good HS math teachers I know support a mixture approach; learn the long division algorithm, learn to multiply fractions, then use the mastry to understand concepts and big ideas..(see"Easier Than You Thought")Education Professors keep pushing the idea of concept based learning without foundation training (I think that is wrong) and Ultra conservatives keep pushing the abstract calculation as if mentioning a use of math was a sin (I think that's wrong too, most of us learn math to use it, only a very few use pure math untainted by application, and then when the least expect it, we find an application for what they did.)
So now I have two ex-correspondents who have , me off, each because I endorse their view too weakly, or more likely, because I am too tolerant of the opposition viewpoint. But I will go on teaching long division and multiplication, factoring and all the other taboo subjects and trying my best to balance them with an intuitive understanding of why these ideas work, why the are actually esthetically beautiful ..at least until some administrative zealot of one or the other side of the math wars tells me to pack my bags and leave. But even them, look for me in your public park standing on a soap box selling my "evil" to anyone who will listen. But if you get caught in the Math wars, my best advice is from those old Uncle Remus stories by Joel Chandler Harris..."Ol’ Brer' Fox, he don't say nothing. He just lay low."