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Who Owns School Mathematics?

Different Visions, Different Expectations

No one ever seems satisfied with school mathematics. Test scores are always too low, students are often bored, and adults feel students don't learn what they need to know.

"Schools need to provide students with the tools of productivity," says Linda McIsaac, CEO of EXPCT, Inc. in Middleton, Wisconsin. "For mathematics, that means spreadsheets, computer graphics, and other software that is of vital importance in today's workplace. These things can be taught, and should be taught."

"But mathematics is a language," says Tom Kurtz, Professor of Mathematics at the University of Wisconsin, "and without mastery of skills in basic algebra and geometry students will never understand how mathematics is used. Students without skills are students without language."

On October 19, 1995, twenty individuals from the Madison area gathered at the University of Wisconsin to discuss the issue of "Who Owns School Mathematics?" The session was sponsored by the National Institute for Science Education (NISE) and chaired by Denice Denton, Professor of Engineering and Co-Director of the Institute. The discussion ranged fluidly over a diverse set of issues, mostly centered on the different expectations of business and higher education, and on the dichotomy of skills and understanding. Individuals who participated in this discussion--business leaders, educators, mathematicians, and policy leaders--expressed sharply different visions of what mathematics students should know and be able to do when they finish high school. Through this Web report, we open the dialogue to others, and invite submissions of commentary and electronic letters for subsequent posting in this space. Just send e-mail to extend@stolaf.edu or click here.

Different Visions, Different Expectations

Professional Standards and Public Expectations

The National Council of Teachers of Mathematics ([NCTM]) offers one vision of school mathematics in their 1989 report Curriculum and Evaluation Standards for School Mathematics. This vision is rooted in the lessons of educational research (that students learn better when they construct their own insights) and in the implications of the global shift from an industrial to an information economy (which suggests the need for greater emphasis on data, on computers, and on communication skills).

More recently, the American Mathematical Association of Two-Year Colleges ([AMATYC]) issued its own standards called Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus. This report calls for a broad foundation in core mathematics as preparation for technical mathematics, liberal arts mathematics, or transfer programs.

Both the NCTM and AMATYC standards are "constructivist" documents, emphasizing the need for students to actively participate in mathematical discourse by working in groups, using technology, and communicating mathematically. Yet polls consistently show that parents believe that mastery of basic skills--not calculators and computers--are the foundation of excellence in mathematics education. Parents want the primary emphasis in mathematics class to be on developing mathematics skills, not on other goals such as communication or teamwork. Especially in a supposedly absolute subject like mathematics, parents expect teachers to teach and children to learn. Many parents are uneasy at the thought of children discovering or constructing mathematics for themselves. Most parents want their children to be grouped according to their mathematical abilities and interests. They want their children to learn mathematics for practical reasons--primarily to earn a good wage. Thus parents' goals often appear to be very different from the published standards of the mathematics profession.

Mathematics for Work and for University

"In today's world, the application of knowledge is as essential as the attainment of it." This observation, cited in the recent [MSEB] report [Mathematical Preparation of the Technical Work Force], signals a significant reorientation in the nature and purpose of school mathematics. Even as leaders of NCTM and AMATYC have expressed educators' goals for mathematics education, so also technical industries are now developing sets of [occupational skills standards] to provide transportable, national expectations for well-prepared workers. These skills are often quite specific (e.g., calculate percentages and ratios, solve algebraic equations) and frequently include topics (e.g., control charts) that are rarely taught in school. Business leaders often stress specific skills important for the world of work.

Although both government and employers frequently express the need for graduates who are better prepared for the world of work, the dominant influence on school mathematics remains the siren call of universities. "Our curriculum is driven by the university," reports John Janty, Mathematics Coordinator of Waunakee High School in Waunakee, Wisconsin. "Despite the obvious benefits of graphing calculators, we had to wait for the blessing of the University before we were able to fully utilize them in our classrooms."

University faculty, especially mathematicians, often decry the open-ended problems that dominate emerging curricula, believing that this approach undermines the technical fluency crucial to success in later courses. Mathematicians worry that by stressing exploration and multiple approaches to solving problems, the new curricula undermine important characteristics that give mathematics its distinctive power: accurate answers and definitive proof. Indeed, many colleges and universities continue to expect proficiency in traditional skills that are no longer emphasized in some school curricula.

Conflicting Expectations

Divergent views about the nature of mathematics put teachers in the awkward position of choosing among differing expectations-- of NCTM, of parents, of higher education, and of the technical work force. Who really should determine what is taught in school mathematics? Teachers or parents? Employers or universities? Scientists or mathematicians?

Conflicting expectations are themselves an impediment to change. "We have teachers who are afraid to change," says Mazie Jenkins of Abraham Lincoln Elementary School in Madison "because they have to face parents who come in and say 'Why aren't you teaching this and that...That's the way I learned it.' We have others who say that we need to teach kids to be thinkers and problems solvers, to be motivated about mathematics. We can't expect teachers to sort all this out. Until we bring our different communities together, classroom teachers will not be able to meet the needs of kids in the classroom. If we don't all start speaking the same language, we're not going to get teachers to change-- because teachers have to face the parents."

Questions for Discussion

To begin the process of "speaking the same language," we invite commentary on key questions concerning expectations of school mathematics: In short, is school mathematics really one subject? Is mathematics for work the same as mathematics for education? Or are there perhaps "multiple mathematics," as some argue that there are "multiple literacies?" Questions such as these are at the heart of many of the public debates about standards in mathematics education.

Excerpts from the Roundtable

Voices at the Madison Roundtable reflect views of many citizens about mathematics education--conflicted, concerned, and anxious. Samples of these views are on key issues can be found by clicking on the following:

What Society Expects of School Mathematics
Postsecondary Perspectives
Teaching for Skills vs.Understanding
Views on Effective Pedagogy

To add you voice to this discussion, e-mail comments, letters, and op-ed articles to: extend@stolaf.edu or click here if your Web browser is set up for e-mail.


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Last Update: 12/21/95