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I'd like to address the MCAS test and math education together. If what I suggest is happening (inflated evaluations in our schools) is true, we do need to have some measuring instrument which will accurately assess the comprehension of material beyond what the schools are reporting. In 1970, 6 percent of college freshmen reported having an "A" average in high school. In 2005, this figure was over 22 percent. In 1970, most of my 11-year-old sixth graders could pass a test on fractions, decimals and percents. In 2004, many of my above-average freshmen struggled if I included those concepts on an algebra test. Recently, a college-age clerk at a food store asked if 99 cents a pound was "close enough" to "a little over a half a pound." A junior college student thought that there were 12 yards in a mile. Understanding of this degree, or should I say misunderstanding, is just not acceptable.
That does seem to comport with today's math reality, rather than the rosy rhetoric. Math is supposedly now being taught with understanding, yet what we see is that many students have little real understanding of math and little facility solving simple math problems.
The traditional curriculum was far from perfect--too few kids learned higher math skills. But. today's math instruction seems to have gone from mediocre to worse.
I, for one, blame NCTM who are largely responsible for this current state of affairs. They claim to know how to teach math to kids. In reality, they don't. Their bromides have been failures. Sure, you can go through their standards and twist the words to come up with some sound math principles, but, overall, the framework they've laid down has resulted in actual instruction that is worse than what we had before.
It's time to give them the boot.
1 comment:
I would add that NCTM's focal points are a reprise of the Who's song about "meet the new boss; same as the old boss". First NCTM disavows any fault to the original 1989 and revised 2000 standards and says the Focal Points are just a "clarification" of those. Second, the focal points don't require long division to be mastered, nor does it say anywhere that students have to "memorize" the number facts. Rather it says "Children use their understanding of addition to develop quick recall of basic addition facts and related subtraction facts.” Similar wording for multiplication.
I'm all for understanding what addition and multiplication are, but really, folks, once you teach the principle that 2 x 3 is either 2 + 2 + 2 or 3 + 3, kids get it. You don't have to go to first principles to "prove" each multiplication fact. And while there are "strategies" to help learn the facts,ultimately they are to be memorized. Period.
But now NCTM is saying that the standards were "misunderstood". "Oh, gee, we never meant for geometry texts to do away with proofs for gosh sakes; are people really doing that? Goodness me!" Then they claim that states' misinterpretation of the standards resulted in the mile wide inch deep curricula, so no one mastered anything. Now they are saying, it's only a quarter mile wide. But it's still an inch deep and if you read the focal points you'll see they can be interpreted to ensure that mastery of anything worth while will be off the agenda for quite some time.
Has anyone noticed how much Skip Fennell looks like The Skipper on Gilligan's Island? Beware folks. We're on another three hour tour. Well meaning Gilligan/math teachers who are trying to get kids off the island are thwarted at every turn. Well, at least on the island they didn't have calculators. "But we do have a professor," says Gilligan. "Except he only listens to the Skipper."
GILLIGANNNN
Ooops.
Sorry Skip.
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