David M. Bressoud May, 2006
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C.1: Develop mathematical thinking and communication skills
Courses designed for mathematical sciences majors should ensure that students
This month, I have chosen to address the second bullet of CUPM’s elaboration of what it means to develop mathematical thinking and communication skills. It is a point that will reappear in recommendation C.3 where the assertion is made that students need to be aware of mathematics as stochastic as well as mathematics as deterministic. In this recommendation, the phrase “analysis of data” was chosen intentionally over “statistics” to make it very clear that a course in probability would not be an acceptable substitute.
There are two strands to what it means to “gain experience in careful analysis of data.” The first is that majors in the mathematical sciences should be particularly adept at quantitative reasoning (QR). It may appear that this comes automatically with a mathematics major, but that is not necessarily the case. Over five years of refining our program in QR, Macalester College has identified six skill sets that mark what we mean by basic QR. Students should be able to
At many institutions, a major in mathematics by itself provides no guarantee that a student can do any of these. A good course in statistics should address these goals. A description of what constitutes a good course in introductory statistics is available in the American Statistical Association’s GAISE Report .
The second strand is more directly related to what our majors need as future mathematicians. Information technology is shaping the direction of mathematics for the 21st century, the development of Google’s search engine being one of many illustrations of this. Understanding stochastic processes and how to deal with large amounts of data are an essential part of mathematics, whether this is for the student going directly to work as an “analyst” for a large corporation, for the student who will hone mathematical skills in order to bring them to bear on financial, health-related, or environmental problems, or for the student pursuing a doctorate who might one day tackle the complex mathematical problems now being generated by Biology, Chemistry, Economics, and Physics.
For mathematicians to sideline statistics would be as serious a mistake as that made by philosophers when they decided to exclude psychology, a field that was growing within their own discipline. Philosophy would not have been subsumed by its child. Rather, it could have been reinvigorated. Philosophy is poorer today for the chasm that often lies between these disciplines.
Statistical thinking is part of mathematical thinking. Its importance is real and growing. It needs to be addressed intentionally and specifically.
Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?
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We would appreciate more examples that document experiences with the use of technology as well as examples of interdisciplinary cooperation.
|David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at email@example.com.|