January 31, 2007
Modern Math "Education"
There is a good video on YouTube which shows how math is "taught" in some modern schools: the anti-conceptual way.
Watch the video, then just imagine the fun and cognitive clarity which must ensue when students get to algebra, and work on quadratics or cubics. (OK, it's really "pain and cognitive dissonance.")
Imagine trying to solve the equation x^2 + 14x + 40 = 0 by the methods shown in the video.
"OK, I have to add some numbers to get 0. Let's see...um...since I didn't learn that x^2 is always positive -- necessity is such an old-fashioned, oppressive idea!! it causes global warming!! -- anway...since I can't use an oppressive concept like "always," I can't reason that 14x must be negative, to cancel out the 40 and the x^2. So I have to guess and check, like I was taught. Let's see...10^2 is (pause to use calculator) 100. Um...now what?...oh, yeah, put 10 in for x in 14x. That gives me (pause to "construct" the answer or to use a calculator) 140.
So let me tabulate:
100
140
That adds to 240. Then, uh, 240 + 40 = 280. No, that didn't work... So let me try 11."
Ick. I used to actually have kids -- back when I tried teaching in public schools -- who would do something like try 11 after 10. They never learned the "number sense" to try a lower number!! (But that was not in solving quadratics as illustrated above; the lack of "number sense" would show up in everything.)
Here's how I (and probably you) learned to solve this. Factor it out:
(x + _)(x + _) = 0. What factors of 40 add to 14? It's obvious at this point, but kids could list them:
1, 40
2, 20
4, 10
5, 8
It's 4 and 10. So our factorization is:
(x + 4)(x + 10) = 0. Solving this gives x = -4 and x = -10.
But of course, this method depends on TELLING the kids about the "zero product property," instead of letting them "discover" it, as some educators want the students to do.
Or, worse, try x^2 + 7x + 11 = 0. This quadratic is not factorable!! The solution has the square root of 5 in it!!
There are other anti-conceptual methods used specially for "teaching" algebra and geometry.
I have heard so many horror stories about math curricula, Cyrano, that I truly expected to be horrified. I read about a test question "if math were a color, what color would it be?"
The terc (sp?) method codifies how I would solve any of those problems. If I have to grab paper, I'll grab a calculator. That method lends itself to solving 133/6 in your head.
I'll agree that teaching traditional long division and multiplication is valuable. What separates people who "do math" from those that don't is the more abstract relationship with numbers. I don't know that this would teach it, but I can't say I'm horrified. (The lattice was pretty cool.)
I think it's much worse that they leave this Math class and go to a science class where they're taught recycling, then onto social studies where they learn how cruel white settlers were to the indigenous peoples.
Posted by: jk at January 31, 2007 10:25 AM | What do you think? [1]