headache

This is immature, but I just looked up "malkin" in the dictionary, and, well, see for yourself. A ton of Hawaii schools use Everyday Math (woe betide them if everything Michelle Malkin says is true - ha) and while I'm glad I was on a curriculum committee that chose Math Trailblazers (rejecting Everyday Math), she is, as usual, half-baked on the issue on which she chose to spout off.

Matthew Clavel (suffering in 2003 from Everyday Mathitis, aka "Hey Mister! What the hell is this crap!?" till he threw down his book and decided to teach math his way) equates Constructivism with fuzz. Fuzzy Math, Constructivist Math, it's all the same to Matthew Clavel, Michelle Malkin, and scores of teachers and parents whose exposure to Everyday Math is unfortunately their only exposure to so-called constructivist teaching.

What's the root of Constructivism? Construction. The building of understanding. Of course we're pissed off when kids come to us with nary an idea of times tables beyond the sixes. My argument is that truly Constructivist teaching can work alongside traditional methods of mathematics instruction. Let's take the infamous operation in question: multiplication. Let's say you're teaching a kid to multiply fractions:

Traditional: Write the fractions so numerator and denominator are aligned. Multiply straight across. Reduce the product to lowest terms. Great. The problem? Doing this proficiently does not guarantee any true understanding of the operation of multiplication. It certainly doesn't show kids what it means to multiply fractions.

Constructivist: To multiply one-third by one-half, have students take an 8-by-11 sheet of paper and fold it in thirds. Shade in one of the thirds, using a light color. <-- Visual representation of the multiplicand. Cut off the shaded portion but keep it near the remainder to illustrate that it is still a fraction of the whole. Fold the third in half, and shade in half of the third in a darker color. In relation to the whole, you have isolated a sixth. You have shown that to multiply something by one-half is, essentially, to cut it in half - e.g., to reduce the size. Therefore, multiplication by a fraction (non-improper fraction) does not increase a quantity. BAM. Concrete, visual demonstration of an abstract concept that would boggle the grade-school mind otherwise - or never enter the mind if all we relied on were algorithms and instructions of the "because I said so" variety. Decrying the use of manipulatives in math instruction is stupid. No, the checker should not need sticks and beans to ring up your purchase at Wal*Mart but I can bet that there are bunches of adults who never had fancy manipulatives (such as a piece of paper to fold up) who cannot explain what it means to multiply a whole number by a fraction, let alone a fraction by a fraction. When kids have concrete understanding of an operation, introducing formulas and algorithms makes sense. So do timed drills to increase fluency with basic facts. Not before. I don't know how badly Everyday Math sucks. Probably a lot. I believe in integrated curricula - especially integrating the Language Arts into seemingly incongruous content areas - but I draw the line at asking kids what color math would be when they should be learning - really learning - multiplication.