Fuzzy Math Must Cause Fuzzy Logic

Constructivist educators say the kookiest things sometimes. Here's a good example in today's NYT.

Many parents and teachers remain committed to the goals of reform math, having children understand what they are doing rather than simply memorizing and parroting answers. Traditional math instruction did not work for most students, say reform math proponents like Virginia Warfield, a professor at the University of Washington.

Have you ever read an article on education that didn't contain enough false dilemmas to fill an undergraduate logic text?

There's reform math on one hand that has "children understand what they are doing" though no one has ever been able to prove that this is in fact the case since students taught using typical constructivist math programs tend to score just as poorly as the more traditional math programs which simply require "memorizing and parroting answers." Oddly enough, if constructivist taught students were better at "parroting answers" we might not have a math war going on now would we. But, the sad fact is that they are not any better than the traditionally taught kids in this regard which tends to give one pause when constructivists parrot the "children understand what they are doing" meme. No doubt such sentiments were learned by rote.

There is some truth in the "[t]raditional math instruction did not work for most students" meme that traditional math proponents should take to heart. Same holds for proponents of traditional phonics instruction. Most traditional math and phonics programs weren't and aren't any good, though constructivist heavy math and balanced literacy programs offer no improvements other than rosy rhetoric.

One area where reform math programs do fall down is in computation skills. All those hide-the -ball problem solving lessons that chews up mucho class time come at the expense of the all important practice that all but the looniest constructivists recognize is still needed to learn math. Understanding math (whatever that means) may be beneficial, but if that understanding doesn't translate into computational fluency, then the hapless students are not going to have a fun time in algebra or anything else that comes later.

Moving right along.

"It produces people who hate math, who can't connect the math they are doing with anything in their lives," Dr. Warfield said. "That's why we have so many parents who see their children having trouble with math and say 'Honey, don't worry. I never could do math either.'"

Any program that does not result in students learning math is going to cause those students to hate math. Those who can't do math (and by do, I mean compute) won't be able "connect the math they are doing with anything in their lives."

If constructivist taught students hate math any less than traditionally taught students it is not because they understand or are any better in math. Such has never been shown in any legitimate study. Only possible explanation is the "ignorance is bliss" theory that might be causing all this unexplained happiness. Kids who are never asked to do long division or manipulate fractions aren't going to be too upset that they can't do those things.

In part, the math wars have grown out of a struggle between professional mathematicians, who say too many American students never master basic math skills, and math educators, who say children who construct their own problem-solving strategies retain their math skills better than those who just memorize the algorithm that produces the correct answer.

Talk is cheap. Educators can say whatever they want. But, no one has ever proven that "children who construct their own problem-solving strategies retain their math skills better."

Remember, these kids who've constructed their own problem-solving strategies aren't scoring any better in test of simple math skills. They might be retaining something better, like maybe all the bad strategies they discovered along the way, but it's not math skills.

Memorizing the algorithm isn't going to do squat either. Practicing the algorithm until it can be performed with automaticity is what's needed. And, if it can be taught in an efficient way so that it is learned with understanding, all the better. It is a conceit of constructivists that they believe they are the only ones teaching with understanding. That and the inability to distinguish between memorization and practice leads one to the conclusion that they really have no idea what they are talking about.