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Postsecondary Perspectives

Many comments at the October 1995 Roundtable at the University of Wisconsin, Madison, focused on the mathematical expectations of higher education. Excerpts that follow are by Richard Askey and Tom Kurtz, Department of Mathematics, University of Wisconsin; Gary Britton, University of Wisconsin [two-year] Centers; and John Janty, Mathematics Coordinator, Waunakee High School, Waunakee, Wisconsin.

Richard Askey: While there are a number of things in the NCTM Standards that are worthwhile, many of the programs that are being developed to implement these Standards are at too low a level. For instance, the University of Wisconsin Mathematics Department was asked to examine the Tech-Prep program from the [Center for Occupational Research and Development] (CORD) to see if it could count towards admission to the University. It is far too low a level for this. We talked to a teacher who was using it for the bottom quarter of students and were told it works well for these students. However, it was developed for the middle fifty percent. This illustrates one of the things that frequently happens in educational programs: they get watered down.

Everyone now recognizes that "general math" is a disaster. But if you go back to the 1920's when general math was introduced, the original outline was not so bad. Yet it rapidly degenerated into nothing. So you have to be very specific when writing things down, because whatever you say is going to be watered down.

Gary Britton: A while ago I gave my students a problem based on some real data from airplane flights. Several students came up with totally unrealistic answers. When I talked with them about this, I discovered that they were not bothered by it at all, since in all their years of prior schooling they never had any reason to expect their answers to be realistic. It didn't bother them at all, but it bothers me.

Tom Kurtz: I have come to believe that we know how to teach well locally, but not very well globally. That is, we can identify the mathematical skills necessary to succeed in certain courses, and teach those courses so that most students do well on final exams. But later on, in a different context--a different time and place-- nothing happens the way we expect. Students appear to have never learned what they knew so well six months before, or what they studied last week in a different course.

Mathematics courses are not the only place where students learn mathematics. Yet there remain inexplicable barriers in minds of students separating what they learn in one course from what they need to use in another. This separation may help explain why students don't expect their answers to make sense and rarely exercise judgment about their results. Part of the problem undoubtedly lies in the low expectations we place on students. I confess that I design problems requiring methods that I think my students are capable of doing, rather than expecting them to use the full repertoire of what I know they have studied.

John Janty: Let's face it: university systems dictate many of the skills that are taught in the high schools. When my students use graphing calculators, they understand so much more. These calculators bring to life things that in the past a lot of students have been denied. In fact, it was only recently that I got the blessing of the University of Wisconsin so that we could use graphing calculators at all. Yet even today former students report that there are still pockets at the University that do not allow graphing calculators.

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: 12/19/95