Math Education: An Inconvenient Truth

What a b....

The cluster method was what I taught FM after school - it made so much more sense to him than any other way he had learned this stuff before, as I said in my mental math post. Obviously, as the woman says, the textbooks seem a little absurd, but really they are no more absurd than the insistence that all students use the standard algorithm (which she continues to call the most efficient, least error-prone, based on what evidence I wonder?) to the exclusion of all others. Certainly, it is often the best algorithm for multiplying five or six numbers by hand, but when will such a skill be neccessary or even useful? As far as division goes, until I started teaching I had used long division maybe once or twice in eight years. Clustering in division problems makes so much more sense.

Furthermore, the fact that this is being debated as the part of standard 4th and 5th grade math curriculum is almost as ridiculous as the fact that I am teaching in to high school freshmen. Whole number multiplication and division should be mastered by the end of third grade. Students should be able to compute fluently in decimals and fractions by the end of fifth grade, and in sixth grade should begin a two year course in algebra I. In 8th grade they should take geometry, algebra II in ninth grade, Precalc and Trig as sophomores, calc as juniors (basic single variable derivitive and integral calculus) and some elective their senior year, whether it be a serious statistics course, linear algebra, or multivariable calculus. Maybe I'm wrong - I don't know that much about how the brain develops at a young age and I am basing this mostly on my own experiences, which apparently are not the norm. Besides, to have anything like this actually work, we'd have to have middle school teachers who understand algebra and geometry and high school teachers who can explain eigenvalues and integrals in spherical coordinates. Not to mention students who want to learn.