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
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
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.
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Last Update: 12/19/95