my life as a math dog
We are creating thousands of math refugees, kids who don't fit in anywhere. They are told they are bright throughout elementary school. In sixth grade, to prove to itself that these kids go to a great school or are part of a great school district, the kids' school tells the kids they are qualified to take algebra I in seventh grade. Never mind that there are only a handful of kids city- or county-wide who are so qualified. The kids and their parents believe it. And perhaps algebra goes OK, and they have a teacher who is not going to really demand all the rigors of a full-fledged algebra I class. After all, the teachers are part of the same school/district who believe in this system. The same thing occurs in eighth grade. The kids take a watered down geometry class and are given a B. Then one of two things usually happens:
1. They change schools, and their new school tests them for algebra and geometry proficiency. There isn't much there. They should get placed down in algebra I, but they bitch and moan (or their parents do) and end up in algebra II and struggle. They hire a tutor. They lose their self-esteem in math.
2. They stay in the same school that started them down this treacherous road in the first place, and they get B's but they don't learn very much. Eventually, they get to pre-calc or calculus and the feces hits the fan. They can't do anything, and they either hire a tutor or take AP statistics. They lose their self-esteem in math.
When I started teaching 30 years ago, we used to complain about too many eighth graders taking algebra. Now it is truly insane.
posted by paul @ 5:31 PM
1 Comments
1 Comments:
There is so much wrong with math ed in America that one hardly knows where to begin. Algebra I for 7th graders isn't even the worst of it. I agree with 90-95% of what Paul Lockhart wrote on this subject in his subversive, dead-on commentary entitled "A Mathematician's Lament."
I part company with him when he launches his anti-geometry diatribe, especially since I think any good teacher would explain that the 2-column proof format is like training wheels, something you can safely remove after you have your logical thinking firing on all cylinders. But the rest of the article is frighteningly accurate in its detail and systematic dissection of the failure of math pedagogy.
As far as I am concerned (and I had this thought long before I came across Lockhart's essay), there are 3 main questions:
1. What is math?
2. Can you "do" math? (as measured by standardized tests)
3. Can you think like a mathematician?
The "traditionalists" focus on question #2, the "reform math" (a.k.a. fuzzy math) folks on question #3. They are both right, and they are both wrong. Without a concerted effort to combine both #2 and #3 toward an approach that respects question #1, the students have wasted their time.
If the students don't know fractions, decimals, and their times tables (for crying out loud), doing math is as frustrating as writing with one's non-dominant hand.
But if they don't know (conceptually) the purpose of factoring, the quadratic formula, etc., then all the "technique" in the world is pointless. A good symbolic manipulation calculator will have as much technique--and about as much understanding. (Actually more, if you count zero as being better than faulty understanding.)
Math is something students have been interested in since they were very young, namely the study of patterns (abstraction).
I think the only lessons many students retain from their 10-12 years of so-called mathematics instruction are (a) that math equals computation, (b) that they are not especially good at math, and (c) that they don't particularly like math. All students, even those who end up learning (b) and (c), should at least learn something different from (a).
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