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Topic: NCTM C&E Stds II (Feb 27)
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Ronald A Ward

Posts: 298
Registered: 12/4/04
NCTM C&E Stds II (Feb 27)
Posted: Feb 29, 1996 4:13 PM
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This is the second in a series of posts concerning questions, concerns,
issues related to the 1989 NCTM publication "Curriculum and Evaluation
Standards for School Mathematics." All questions are numbered
consecutively for later reference purposes. If you have missed any and
want them, just e-mail me direct and I'll send them your way.

Ron Ward/Western Washington U/Bellingham, WA 98225

4. It is clear from the Introduction that creating a vision of what it
means to be "mathematically literate" is CENTRAL to this document.
Literacy items permeate the "new societal goals" on pages 3 & 4, and, in
the discussion of "new goals for students," the writers declare:
"Educational goals for students must reflect the importance of
mathematical literacy." It is interesting to COMPARE what this document
says about literacy with the message of Everybody Counts [I've included
an excerpt later on in this post *]. It is also interesting to note that
relatively little is said about literacy in the Professional Standards
["Being mathematically literate includes having an appreciation of the
value and beauty of mathematics as well as being able and inclined to
appraise and use quantitative information.], and literacy is not really
discussed per se in the Assessment Standards.

A related concept is "mathematical power," defined in the C&E document on
page 5. It is worth comparing that definition with a brief one from
Everybody Counts ["A capacity of mind of increasing value in a
technological age that enables one to read critically, to identify
fallacies, to detect bias, to assess risk, and to suggest
alternatives"]. Later in this post I also include some statements about
mathematical power from both the Professional Standards and the
Assessment Standards.**

I am interested in the CONNECTION between math literacy and mathematical
power. The C&E Standards gives a very brief comment about this on page
6. How do YOU see them as related? Does your awareness of the meaning
of either one affect the way you prepare your students? Can you think of
any way in which the discussions about literacy need to be updated? [both
the C&E Standards and Everybody Counts came out about seven years ago.]

*Here is the LITERACY discussion from Everybody Counts that I
referred to earlier. The writer is Lynn Arthur Steen, the sponsor is the
National Research Council, and the publisher is National Academy Press.

"To function in today's society, mathematical literacy--what the
British call 'numeracy'--is as essential as verbal literacy. These two
kinds of literacy, although different, are not unrelated. Without the
ability to read and understand, no one can become mathematically
literate. Increasingly, the reverse is also true: without the ability to
understand basic mathematical ideas, one cannot fully comprehend modern
writing such as that which appears in the daily newspapers.
Numeracy requires more than just familiarity with numbers. To
cope confidently with the demands of today's society, one must be able to
grasp the implications of many mathematical concepts--for example,
chance, logic, and graphs--that permeate daily news and routine decisions.
Literacy is a moving target, increasing in level with the rising
technological demands of society. Indeed, there is some evidence that
the decline in reading comprehension scores over the last several decades
is due in part to the growing mathematical content of what one is
required to read. It is not just computer manuals or financial reports
that require an understanding of mathematical ideas; so do reports of
political polls, debates about AIDS testing, and arguments over the
federal deficit. Even Supreme Court decisions resemble mathematical
arguments whose subject matter is law rather than numbers; often, legal
cases rest as much on probabilistic inferences (for example, DNA
fingerprinting, fiber analysis) as on direct evidence.
Functional literacy in all its manifestations--verbal,
mathematical, scientific, and cultural--provides a common fabric of
communication indispensable for modern civilized society. Mathematical
literacy is especially crucial because mathematics is the language of
science and technology. Discussion of important health and environmental
issues (acid rain, waste management, greenhouse effect) is impossible
without using the language of mathematics; solutions to these problems
will require a public consensus built on the social fabric of literacy.
The study of mathematics can help develop critical habits of
mind--to distinguish evidence from anecdote, to recognize nonsense, to
understand chance, and to value proof. Citizens in a democracy must
recognize that change is a process with expected regularities; that order
can beget disorder (as in turbulence) and vice versa (as in statistical
experiments); that similar mathematical models can represent different
phenomena (for example, patterns of growth in biology, economics, and
chemistry); and that simple models can clarify complex systems (as in
linear models of economnic systems), even though simplistic analysis can
result in misleading interpretations. Citizens who are bombarded daily
with conflicting quantitative information need to be aware of both the
power and limitations of mathematics.
The great majority of American children spend most of their
school mathematics time learning only practical arithmetic. Few retain
much of what they learn about geometry; fewer still learn anything about
chance. Secondary education is particularly devoid of exposure to modes
of mathematical thought required for intelligent citizenship. Even
colleges and universities seem unable to infuse appropriate mathematical
ideas into liberal education. There is no consensus whatsoever on a
collegiate mathematics curriculum for students outside the
preprofessional programs where mathematics serves a well-defined yet
strictly utilitarian purpose. Rarely does mathematics contribute as it
should to liberal education, to the honing of values, and to effective
citizenship." [pages 7-9]

** Some additional comments about MATHEMATICAL POWER from the
Professional Standards:

"Mathematical power includes the abilit y to explore, conjecture,
reason logically; to solve nonroutine problems; to communicate about and
thru mathematics; and to connect ideas within mathematics and between
mathematics and other intellectual activity. Mathematical power also
involves the development of personal self-confidence and a disposition to
seek, evaluate, and use quantitative and spatial information in solving
problems and in making decisions. Students' flexibility, perseverance,
interest, curiosity, and inventiveness also affect the realization of
mathematical power."

and from the Assessment Standards:

"... the phrase "mathematical power" has been used to capture the
shift in expectations for all students. The shift is toward
understanding concepts and skills;drawing on mathematical concepts and
skills when confronted with both routine and nonroutine
problems;communicating effectively about the strategies, reasoning, and
results of mathematical investigations; and becoming confident in using
mathematics to make sense of real-life situations. It is away from
mastering a large collection of concepts and skills in a particular
order. In this document, the terms 'know,' 'know how,' 'be able to do,' and
'disposition toward' are used as indicators for the complexity of
'mathematical power.'"

Thus, in a sense, the Assessment Standards make assessment the process of
gathering evidence about a student's mathematical power. Therefore, it
seems to me that there has been a major shift in emphasis from

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