The following recently appeared on a blog of one of those fiercely opposed to reform mathematics instruction in Ridgewood, NJ. "GK" stands for "Gifted Kid"
GK prefers fractions and division to simple multiplication
A mom of a Gifted Kid gave him some multiplication drill. She keeps it to a minimum, but once in a while it's a good idea. However, it turns out she didn't give him a hard enough problem.
Here's the problem she gave her 9 year old and the expected partial products and final product:
But that's not how GK worked the problem. Instead, he did all this in his head:
21/5 X 6/25 = 126/125 = 1 1/125 = 1.008
Just like with reform math, Mom asked him to explain his reasoning, but not because of any ideology about language and math, but rather, because she had no idea what he had done until he spelled it out for her. S-L-O-W-L-Y.
Then she asked him why he didn't use the standard way, and he said because he liked his own strategy better.
Given harder problems, he does do them the standard way, which has now been dubbed "mom's way." Mom scratches her head a lot these days.
To which I replied: "Your son has made an excellent argument for so many of the things you argue against so bitterly, and he's done so articulately and with no ideology. Too bad you don't hear it."
Would not this child's teacher and classmates benefit from hearing about his strategy and discussing it? Are the other alternatives that this child would benefit from hearing that might emerge if the teacher were able to conduct a good class discussion about this problem, about his strategy, about how other kids think about this problem?
There is no "ideology about language and math" involved in asking children to explain their thinking. The ideology is in believing that it's a "waste of precious instructional time" that "should" be spent listening to a lecture by a teacher (who might well, like the "Clueless Mom," never think of this approach or might not understand it, either, on first blush) or doing drill and practice. As I already suggested, this post unwittingly cries out for precisely the things that this blogger and her allies have worked so hard to stamp out in their schools. The irony is beyond belief.