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Topic: 'Math Wars' Session at MAA
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Jerry P. Becker

Posts: 16,576
Registered: 12/3/04
'Math Wars' Session at MAA
Posted: May 25, 1998 8:34 PM
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FOCUS: The Newsletter of the Mathematical Association of America, Vol. 18,
No. 5, May/June 1998, pp. 1 and 4.


By Ken Ross

The problem that no one cares what is going on in mathematics education is
gone! Major newspapers from New York to California have published columns
about the problems in school mathematics, and the California "math wars"
have been a national concern. As usual, the newsworthy stories report on
the extreme positions taken. Frequently the culprit is identified as the
NCTM Standards. Meanwhile, the invisible majority of concerned
mathematicians is not heard from.

At the Baltimore meeting, it was heartening to see the invisible majority
speaking up. The tone was set by the excellent keynote address given by
Education Secretary Riley. In reference to the so-called "math wars" in
California and elsewhere, he said, "Let me say right now that this is a
very disturbing trend, and it is very wrong for anyone addressing education
to be attacking another in ways that are neither constructive nor
productive. It is perfectly appropriate to disagree on teaching
methodologies and curriculum content. But what we need is a civil and
constructive discourse."

Though there were still some heated discussions at the meeting, in general
the cease-fire held. In particular, there was a very constructive and
well-attended panel discussion on the NCTM Standards. This was
co-sponsored by the AMS Committee on Education and the MAA President's Task
Force on the NCTM Standards, which are chaired by Roger Howe of Yale
University and me. In the fall of 1996, several mathematics organizations
were asked by NCTM to have a group assist with the revision process of the
NCTM Standards. The assisting groups have come to be known as ARGs, which
stands for Association Review Groups. The panelists represented six of the
ARGs. They were Roger Howe and me, Terry Herdman from the Society for
Industrial and Applied Mathematics, Deborah Hughes-Hallett from the
Association for Women in Mathematics, Jean Larson from the Association for
Symbolic Logic, and Tom Moore from the American Statistical Association.

Roger Howe gave an overview of some of the issues involved in mathematics
education reform. He observed that one of the driving forces has been the
international comparisons, in which the U.S. has consistently done poorly.
He mentioned some of the key issues such as equity and the increasing need
for mathematically talented people. New technology and the changing needs
of users of mathematics make curriculum development more difficult than
ever. More topics need to be added, but people are reluctant to let go of
items now in the curriculum. Roger also discussed the issues of teacher
preparation and certification and the issue of assessment.

I began my remarks by giving credit to the NCTM for having the courage to
get out there and tackle these issues and for addressing the needs of all
students. I also credited NCTM with getting people inside and outside of
mathematics interested in these issues. I mentioned our concerns that the
NCTM Standards need to be less vague and much less subject to
misinterpretation, since a huge variety of things have been done in the
name of the Standards. There also has to be recognition that mathematics
is not always fun, that it's not always easy, and that it's a myth that
only some people can do mathematics. We dealt with the questions from NCTM
with an emphasis on a balanced approach.

The other panelists built on the remarks made by Roger Howe and me. Terry
Herdman stressed that most students do not see the beauty of mathematics,
so that we must respond to the reasonable question, "What's it good for?"
The SIAM people talked a lot about estimation and approximation, the
ability to realize when answers are reasonable, and about modeling. They
felt that modeling should be taught at an early age. Deborah
Hughes-Hallett emphasized that the Standards need to be shorter, crisper,
and more specific. She amplified my comment about balance and added that
balance means that none of us is going to get exactly our vision of the
Standards. She mentioned that many of the ARGs would like to see greater
attention devoted to logic and reasoning in mathematics. We need to
recognize that many of the key words, like "proof" and "verification," have
different meanings to different communities. Deborah also warned us that,
as difficult as writing and rewriting the Standards has been,
implementation will be a greater challenge.

Jean Larson pointed out that the term "algorithms" also has different
meaning to different communities. She focused on the creation and use of
algorithms by elementary students and gave some interesting specific
examples involving areas of simple geometric figures. Tom Moore began by
pointing out that statisticians are a little like doctors and car
mechanics; they live on the problems of other people. He stressed that his
ARG is very pro-Standards and especially applauded their over-arching theme
of problem solving. The approaches to learning encouraged by the Standards
are just right for learning statistics and data analysis at an early age.
Moreover, the Standards consistently emphasize the statistical paradigm of
collecting, analyzing and interpreting data, which is at the heart of all
good statistical data analysis. Tom encouraged the use of technology when
appropriate, but cautioned against introducing it too early.

The remainder of the session was devoted to questions and comments from the
audience. There were many hard-hitting remarks, but most were in the
spirit of cooperation, and the atmosphere was amiable. Manuel Berriozabal
explained that when he first read the Standards he thought our students
would be world class if the kids learned mathematics the way Standards
wanted it taught. He has since been dismayed at how the Standards have
been interpreted, especially with the deemphasis on proofs.

William McCallum, following up on Terry Herdman's comment that his ARG
agreed on the need for basics, said that "basics" is another word that
means different things to different people. He's concerned that he has
many students with algebraic skills who have no graphing skills. Kenneth
Millett cautioned that it is very difficult to identify mathematically
talented students early on, and that the attempt to do so often results in
identification that has a strong correlation with family income or status
rather than the ability and capacity of the students.

Malcolm Sherman was critical of the idea that statistics and data analysis
should be done at the elementary level. Regression, for example, should
not be introduced before students have done analytic geometry. Dan Fendel
strongly disagreed and pointed out that students can get a feel for these
concepts at an early age. Then later they'll have the intuition and
experience in order to be able to appreciate the mathematical rigor. Tom
Moore agreed.

Ed Dubinsky raised the issue that college students aren¹t learning the
mathematics required by the Standards, and that this is our responsibility.
He, Ed Barbeau and Marjorie Enneking pointed out that math majors who do
well in standard mathematics courses often flounder in courses designed for
pre-college teachers. I indicated that these issues will be addressed by
the CBMS Partnership in Education.

Jean Larson stated that we need to go out and observe teachers in the K-12
setting and see the kinds of problems they are facing. Nancy Dennin
introduced herself as a high school teacher and received a big round of
applause. She agreed that we need to see for ourselves, and she pointed
out that: "Nothing you can do will prepare a person for teaching in the
classroom. We have wonderful children, but it is a different world down in
the public schools, and I welcome you to join our world anytime."

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618)453-4244
Phone: (618)453-4241 (office)

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