David M. Bressoud July, 2006
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C.2: Develop skill with a variety of technological tools
All majors should have experiences with a variety of technological tools, such as computer algebra systems, visualization software, statistical packages, and computer programming languages.
There is no technology we can teach our students today that will serve them,
unchanged, for the rest of their careers. Not even paper and pencil. Our challenge
is to prepare them so that they can learn and use new technologies that are
helpful for what they will be doing. This is best done by giving them experience
with a variety of tools. Our courses should not be about the technology, but
neither should they shy away from it. Students learn by watching and imitating
what we do. If we approach problem-solving by drawing on a variety of tools,
using what is appropriate for the task at hand, they will learn to do the same.
The greatest challenge for us as instructors is to find what is most useful
and insightful in various contexts. A few well-chosen illustrations over the
course of a semester can be far more useful than an attempt to cram in as many
demonstrations as possible. The tools you ask students to use should be ones
they can master easily and that really will help them experiment and so see
for themselves the points you wish to make. One of the best examples of this
that I have used is DETools from Differential Equations by
Blanchard, Devaney, and Hall [1].
At the same time, we should expect a certain level of competence of all mathematics majors in one or two tools that have great flexibility. I think especially of computer algebra systems such as Maple or Mathematica. At Macalester, we happen to favor Mathematica. What is important is that all students get a basic introduction to this computer algebra system before they finish single variable calculus. Few are experts at this point, but they all have a basic familiarity that means that instructors in subsequent courses can expect students to be able to open and work through a Mathematica notebook and to use simple commands and graphing capabilities to generate and explore patterns. This is empowering to the students, and it greatly simplifies the use of this tool in subsequent courses where we know we do not have to introduce this tool from scratch. The students who skip single variable calculus and so miss our introduction to Mathematica are—by and large—pretty quick learners who pick up the basics when and as they need them.
The CUPM Illustrative Resources has links to Maple, Mathematica, and MatLab resources as well as many web-based tools. The MAA, under the direction of Lang Moore, is doing an excellent job of collecting technological tools and demonstrations in the Journal of Online Mathematics and its Applications [2] and Digital Classroom Resources [3]. There are also other sites that catalog electronic resources, including the Electronic Proceedings of the International Conference on Technology in Collegiate Mathematic (EPICTCM) [4] and The Math Forum Internet Mathematics Library [5].
Incorporating technology into our teaching should not be an onerous task. It is really a question of finding one or two new good examples each semester and building a personal repertoire of exploratory projects that work for us and our students.
[1] Blanchard, Devaney, Hall, Differential Equations, 3rd
edition, Thomson Brooks/Cole, 2006, math.bu.edu/odes/
[2] Journal of Online Mathematics and its Applications, mathdl.maa.org/mathDL/4/
[3] Digital Classroom Resources, mathdl.maa.org/mathDL/3/
[4] Proceedings of the International Conference on Technology in Collegiate Mathematic (EPICTCM), archives.math.utk.edu/ICTCM/
[5] The Math Forum Internet Mathematics Library mathforum.org/library/
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. |