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The Standards and the California Frameworks
Posted:
Jul 10, 1995 5:32 PM


(in response to the question: have you read them?)
I own the 1989 curriculum and evaluation standards and the (1992) "Mathematics Framework for California Public Schools" and look at both occasionally. Once I got past the introduction to the 1989 book, I found a lot to agree with. Clearly by intent, the book tries to minimize a commitment to specific TOPICS (it's startling, for example, how similar the description of the algebra standard for grades 912 is to the one for grades 58  and what a wide variety of specific syllabi could meet those standards) and instead promotes more attention to the emphasis on problemsolving and communication as opposed to drill on routine tasks. Even this is worded softly: "increased attention" to this and "decreased attention" to that  what the specific amount of attention should be is left to the individual.
The California Framework is similar, but one addtional topic in it that troubles me somewhat is the desire to abandon tracking in favor of heterogeneous classrooms with a "multidimensional" curriculum. This alternative is never completely defined, but a few pages of arguments against tracking and putting advanced eight graders into the high school curriculum follow. Some of the arguments are valid (IMHO), some are debatable, and some are completely silly (again, IMHO).
I could quibble here and there with things. Often, the goal of mathematical communication and understanding, when reduced to a specific question, seems to be just replacing the old stock answer with a new one. So, say, on page 219 of the 1989 book, a student is asked:
If 35  20 = 15, what is 35  19? WHY?
the first answer is 16, and the second answer must not be "because 35  19 *is* 16" but instead "because when you take away one less than before, you end up with one more than before" as the former is simply recalling a fact and the latter demonstrates deductive reasoning. Phooey. If you know 35  19 = 16, then giving the second answer is less about deductive reasoning than about learning to recognize the hoops your teacher wants you to jump through. (Come to think of it, I suppose that's deductive reasoning, too  and quite applicable outside of math class.)
Then, too, while I appreciate the desire to allow the standards to apply to a wide arrange of specific curricula, it's mildly troubling to see how little specific math is actually IN the standards.
The five general goals of the standards (stated on page 5) don't include gainin a knowledge of any particular topic in mathematics. Students must "value" math, become "confident in their ability" at math, "become mathematical problem solvers", "learn to communicate" and "reason" mathematically. I agree with all of them, but isn't something missing?
I hate to focus on the parts that trouble me, because there is a lot that I like in them. Carefully implemented, they could help a lot of students and probably won't hurt too many too much. Poorly implemented... well, how much worse will they be than the status quo? (that's a serious question.)
Incidentally, I wonder about the AMS endorsement of the Standards. Most mathematicians I know have never read them and have only a hazy idea of what is in them. While the AMS is certainly capable of issuing judgements without polling its members, there *is* a sense that their endorsement reflects the opinion of its members and I don't know that it's true.
Ted Alper alper@ockham.stanford.edu



