"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.

- Professional Standards and Public Expectations
- Mathematics for Work and for University
- Conflicting Expectations
- Questions for Discussion
- Excerpts from the Roundtable

More recently, the American Mathematical Association of Two-Year Colleges ([AMATYC]) issued its own standards called

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.

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 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."

- What are the real mathematical skills needed for today's workplace? How are they likely to change in coming years?
- What mathematical skills are especially suited to supporting students' learning in science and technology?
- Are the mathematical skills required for work significantly different from those required for post-secondary education?
- How should college expectations change in response to changes in the K-12 mathematical preparation of students or expectations of employers?
- Can a curriculum built on needs of the workplace successfully address the broad expectations for school mathematics?

What Society Expects of School Mathematics

Postsecondary Perspectives

Teaching for Skills vs.Understanding

Views on Effective Pedagogy