David M. Bressoud January, 2007
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D.2: Majors preparing for the nonacademic workforce
In addition to the general recommendations for majors, programs for students preparing to enter the nonacademic workforce should include
At most colleges and universities, most mathematics majors are heading neither into teaching nor toward a graduate degree in mathematics. After graduation, they will be looking for a job. While mathematician is not a common job title in the nonacademic workforce, there are a lot of jobs for mathematics majors. The mathematical societies have put together resources to show students what can be done with a Bachelor’s degree in Mathematics. Links to the various sites can be found at www.maa.org/students/undergrad/career.html and www.ams.org/employment/undergrad.html#careers. The Mathematical Science Career Information website, a joint project of AMS, MAA, and SIAM with support from the Alfred P. Sloan Foundation, is a particularly rich source of information. The Illustrative Resources provides links to programs at several colleges and universities that inform students about both the opportunities and requirements for employment in government and industry.
One of our greatest difficulties in communicating the usefulness of a degree in mathematics comes from the fact that there is a sharp disconnect between the skills we appear to assess in our courses and the skills our students will need in their future careers. Few of our students will have any occasion to differentiate or integrate a function, to find an exact solution to a differential equation, to invert a matrix or find its eigenvalues, or to prove a theorem. Our students know this, and they often wonder what they are equipped to do with the skills they think they are learning in our classes.
What employers value in mathematics majors are problem-solving and communication skills. In spite of ourselves, we often do a good job of nurturing these abilities. We could be much more effective if we were conscious of these goals as we think about what and how we teach, and if we communicated these goals to our students.
Problem-solving is not easy to teach. It rests on a bed of competency with many different types of mathematics and is more likely to draw on discrete mathematics than continuous, areas such as combinatorics, linear algebra, statistics, and number theory. It relies on knowing when and how to draw on available tools, especially computers, and so requires familiarity with a variety of computing tools and the ability to come quickly up to speed with new software. And it requires practice.
Students learn techniques of problem-solving by solving problems. Every course needs to include challenging problems for which the methods and techniques are not prescribed. A problem that occurs in the section on the product rule probably has a solution that employs the product rule. That is the kind of big hint that is not available outside the classroom. Students need to tackle problems for which it is not immediately clear what knowledge is applicable. Students need to progress through increasingly challenging and open-ended problems during their four years, culminating in a project or internship that requires them to experience the complexity and ambiguity of true problem-solving.
Communication skills provide the other requirement for successful employment. While aspects of these skills are taught in other departments, mathematics faculty have a particular responsibility to help students learn the effective communication of technical information, especially mathematical information with its requirements of logical reasoning and precision. Again, this takes time and is something that should be woven into every mathematics course. It is not enough to be able to find a solution to a difficult problem. Students need practice explaining how they came to their solution, how they justify it, what it means, and how it can be applied. Proof plays a particularly important role here. To dissect a proof is to explore and come to understand how someone else solved a problem. To construct a proof is to communicate one’s own understanding of how a particular result relates to the rest of mathematical knowledge. Our students need to develop confidence in giving these explanations both in writing and orally, both formally and informally.
At Macalester College, all senior mathematics majors are required to write a senior thesis and then explain it to an audience of undergraduates ranging across the full four years. We have found that employers focus in on this experience. Students who can give a clear and succinct account of how they solved a particular problem and why this solution is both interesting and useful find themselves at a great advantage as they compete for employment. Even those who are not heading into the nonacademic workplace benefit from these skills.
It is also important to help our students build the networks that will enable them to meet and learn from mathematicians who are out in the general workforce. Internships, if well designed and supervised, can do this. The Harvey Mudd Mathematics Clinic is a model for combining both problem-solving and networking.
The nonacademic workforce is often so far from what we do as mathematicians that it can be hard for us to connect to its particular requirements. But we do our students a great disservice if we do not make the effort.
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. |