Tuesday, February 19, 2008
Truth, Lies, and Math
Mathematics education in the U.S. is a problem because in elementary school our teachers lied to us repeatedly. Two related lies: you cannot subtract a larger number from a smaller number, and there is nothing smaller than zero. When we are later told abut negative numbers, many of us shut ourselves off from math. Why believe these math teachers, who are telling us we were lied to earlier, by our other math teachers? We believe in the value of something we learned was founded in lies? Of course, it was the teachers who were the liars -- but the young mind does not differentiate between the two. Many thus reject math's value and close themselves off to it. Others reject it, having become confused at the contradictory information. It is less confusing to the student if the truth is always told.
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It's also a problem because students are taught twenty different ways to guess-timate, flail, and dance around the answer instead of simply learning how to accurately calculate it. Working backwards, "guessing and checking," drawing squares etc. would be just fine if students were actually learning how to do math, which they aren't. Textbooks have 20 page full color inserts on how to use a calculator, and supplementary sections on planning trips around the world and how birthdays are celebrated in other cultures, but somewhere in there something is getting left out. We have the biggest, shiniest, most expensive math books in the entire world, and our math scores are abysmal.
Japanese math books have no pictures, and the Japanese have the highest math scores in the world. Hmm.
Typo.
Singapore, too. Their books are lean, mean, and cumulative, and schools that adopt the Singapore content usually see almost immediate improvement.
It's ironic that the "spiral curriculum" touted by the constructivists operates by covering the same ground over and over--I've read that in many state math curricula the behavioural learning objectives (not like they're worth much anyway) are word for word the same each year for a number of years--while a cumulative sequential curriculum that applies mastery of one subject to the next subjects in the sequence actually creates the kind of feedback loop graphically represented by the fibonacci spiral.
You'd think people who are paid for their mathematical expertise would be able to figure this out.
Nobody who does math curriculae are mathematicians. Also, they don't believe in nonlinear models.
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