FOCUS: The Newsletter of the Mathematical Association of America, Vol. 18, No. 5, May/June 1998, pp. 1 and 4.
REALITY CHECK: AT BALTIMORE STANDARDS FORUM, ALL QUIET ALONG "MATH WARS" FRONT
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 arenÃÂ¹t 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) E-mail: JBECKER@SIU.EDU