David M. Bressoud July, 2005
Recommendation 5: Use computer technology to support problem solving and to promote understanding
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At every level of the curriculum, some courses should incorporate activities that will help all students progress in learning to use technology
I am not going to argue for the use of technology in the classroom. Those who use it know how effective it can be. Those who do not are a dying breed. It is time to move on and consider how this technology should shape what and how we teach. In particular, I want to focus on the role of computational science in the mathematics curriculum.
Computational science is the orphan of the sciences. Viewed as a collection of tools rather than as a discipline, it falls somewhere between Mathematics and Computer Science, usually fitting the self-image of neither discipline and therefore neglected. But it is of critical importance to many disciplines, among them Biology.
In November of 2000, fifteen biologists and bio-mathematicians [1] gathered at Macalester College as part of CRAFTY’s Curriculum Foundations Project to respond to the MAA’s request for a description of what Biology majors need and will need from Math departments. I had the pleasure of being one of the flies on the wall observing their three days of deliberations.
Biologists are not united in their view of the subject. This is reflected in the fact that there is no national association for all of Biology but rather a myriad of associations based on specialty. The Macalester discussions were far-ranging and often heated. In the end, the participants agreed that six themes had emerged. These are worth quoting:
I find it striking that the only mention of a traditional mathematics course, calculus, is to emphasize its lower priority. Instead, terms such as data, statistics, graphical representation, computer simulation and technology appear across the themes. Biology is becoming much more mathematical, but this is not the mathematics that I was taught as an undergraduate. It is the mathematics of data analysis and modeling made possible by the computing power that is now available. It is rooted in computational science.
This is true not only of biology. Most of these themes hold for all of the sciences as well as many of the social sciences. The MAA through the CUPM has affirmed its belief that “departments of mathematical sciences can and should play a central role in their institutions’ undergraduate programs” [3]. Such a role requires that our departments support computational science and find ways of engaging it in our curricula.
Macalester College is fortunate to have among its mathematics faculty a bio-medical physicist, Daniel Kaplan. He has developed a sequence of courses in computational science and has written a textbook [4] to support the introductory course. The goals and issues of computational science are laid out in his article “Teaching Computation to Undergraduate Scientists” [5]. This course is closer to computer science than it is to mathematics, but it is not traditional computer science. Computational science builds, like applied computer science, on an ability to program: understanding data structures and operators on them, construction of functions and their application to arguments, indexing, file operators, conditionals, and loops, etc. But fully half of the introductory course is devoted to building mathematical models and exploring applications such as sound and image processing. The course includes ways to represent mathematical entities such as relationships and operate on them. This complements and reinforces the traditional, pre-computer mathematical approach.
We are a joint department of Mathematics and Computer Science, and so the proper home for computational science is not at issue. Our first course in computational science, Introduction to Scientific Programming, is listed as Computer Science but is required of Mathematics majors. The mathematics curriculum has begun to draw on computational science to enrich and motivate its material, especially in calculus and statistics. It is not yet clear how far we will go in incorporating computational science into mathematics. It is not clear how far we should go. But we do recognize that if we are to live up to the vision of a Mathematics department that plays a central role in the undergraduate programs of our institution, then the role of computational science is something that we need to consider very seriously.
[2] Dilts, Judy and Anita Salem, Biology report, pages 15–17 in The Curriculum Foundations Project, William Barker and Susan Ganter, editors, Mathematical Association of America, Washington, DC, 2004. www.maa.org/cupm/crafty/cf_project.html
[3] page 3 of Undergraduate Programs and Courses in the Mathematical Sciences: CUPM Curriculum Guide 2004, Mathematical Association of America, Washington, DC, 2004. www.maa.org/cupm/curr_guide.html
[4] Kaplan, D.T., An Introduction to Scientific Programming and Computation, Brooks/Cole, 2004. www.macalester.edu/~kaplan/ScientificProgramming/index.html
[5] Kaplan, D.T., Teaching Computation to Undergraduate Scientists, SIGCSE ‘04, March 3–7, 2004, Norfolk, VA, Association for Computing Machinery. www.macalester.edu/~kaplan/ScientificProgramming/SIGCSE-paper.pdf
Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?
Submit resources at www.maa.org/cupm/cupm_ir_submit.cfm.
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 bressoud@macalester.edu. |