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Topic: The Standards and the California Frameworks
Replies: 2   Last Post: Jul 12, 1995 1:49 AM

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Ted Alper

Posts: 51
Registered: 12/6/04
The Standards and the California Frameworks
Posted: Jul 10, 1995 5:32 PM
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(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 9-12 is
to the one for grades 5-8 -- and what a wide variety of specific
syllabi could meet those standards) and instead promotes more
attention to the emphasis on problem-solving 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






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