There is a sense that universities have lost sight of their primary goal of educating students, as exemplified in Rep. Schroeder's comments above. Philip Griffiths, director of the Institute for Advanced Study, writes,
...I suggest universities should fundamentally rethink their missions. Another unintended effect of The Endless Frontier has been a redirection of mission of our research universities. Although usually stated as having the dual missions of teaching and research, the reality is that in the so-called research-intensive universities the education mission has taken a second seat to research. The research grant is the badge of honor, and the professor who devotes primary energy and creativity to teaching is de facto penalized and often looked down upon by peers. [Griffiths, 1994]
Dartmouth's strong emphasis on teaching has prevented many of these problems from occurring here. However, a broader reading of the university's mandate to educate is that our department has a responsibility to educate all students and not just the future specialists in our field. In this respect, we have room for improvement. The 1993 Report of the Mathematics and Computer Science Review Committee [Review, 1993] notes the ``serious and innovative effort'' spent on the undergraduate curriculum, but raises serious concerns about the drop in enrollments over the past 15 years. The number of annual math credits taken has fallen by 31% between 1981-82 and 1993-94, and the greatest decline has been in introductory courses for non-majors.
In part, the decline in course credits taken is a reflection of a national trend. Indeed, Harvard labor economist Richard Freeman makes a convincing case that the number of graduating physics majors in any given year is strongly influenced by the economic conditions for physicists two years before [Freeman, 1989], which bodes especially ill for future enrollments should the same be true of mathematics majors.
While there is little the department can do to affect national interest in mathematics, our enrollment figures suggest that departmental actions have a significant effect on course enrollments, especially on the enrollments of the non-majors who make up the bulk of our clientele. For example, the streamlining of the calculus sequence in 1985-1988 coincides with a sudden, dramatic decrease in calculus enrollments. Similarly, the switch of calculus texts to Greenspan, Benney, and Turner in 1990-91 corresponds to a sharp downturn in calculus enrollments, mostly from Math 8, the second term calculus course. Although the relationships between these departmental actions and calculus enrollments are not necessarily causal, they are certainly suggestive of the magnitude of the effect that changes in the curriculum might have. On the positive side, the introduction of the CHANCE course in 1990 has led to a substantial increase in survey course enrollments.
If we are careful to address the needs and interests of our students, we can attract larger audiences. The national decline in interest in mathematics means that the burden of proof of the importance of our courses is upon us. It is essential that we work to ensure the relevance of our teachings and that we communicate the importance of our discipline.
In addition to declining student interest, part of the decrease in enrollments has resulted from other departments' perceptions that our courses are inappropriate for their needs. The departmental review cites a consistent concern on the part of other departments that ``their students were being taught theory at the expense of practical skills.'' For example, the material in Fourier Series and PDE's (the old Math 33), once a class of 140-170 students per year, is now being taught at Thayer. Although enrollments in ODE's (Math 23) have roughly compensated for the loss, the fact remains that the Engineering School has found it necessary to take responsibility for teaching this material. Statistics for Design of Experiments (the old Math 30), a class averaging 16 students per year, now averages 6 students per year as an Introduction to Linear Models.
There are several things we can do to stop the downward trend in enrollments. In the long term, we can redesign our offerings in order to fit more closely with the needs and interests of a broader group of students. The Mathematics Across the Curriculum initiative seeks to accomplish just such a redesign, and it is a laudable step towards increasing the number of beneficiaries of the mathematics department. It is important that we implement the central ideas in the initiative regardless of the availability of NSF funding for the initiative.
An immediate step we can take to adapt our courses more closely to majors in other departments is to offer specialized versions of the basic calculus/linear algebra/ODE sequence. Students could be offered a choice between more applied courses and more theoretical, depending on their interest. Multivariable calculus could be taught with an emphasis on the vector calculus necessary for the study of electromagnetic fields. Alternatively, elements of continuous probability could be introduced in order to motivate multivariable calculus problems. Linear algebra could be given as a proof-oriented course for math majors, and as an applied, problem-solving-oriented course for non-majors or applied math majors.
A second short-term step we can take to extend the benefits of mathematics education to others is to merchandise our wares more effectively. By designing and marketing custom mathematics minors for students in other majors, we can give these students an idea of what mathematics courses are important for their fields. A particularly effective means of conveying the utility of various course offerings would be to ask our recent graduates to list their most valuable math courses and to describe how they have used their mathematics education in their careers. The packaging of the courses into different minors provides a certification of basic mathematical competence which can be valuable in a job search or in graduate school applications. By refining the existing math minors, we can make them more accessible and relevant, and by explaining and advertising these minors to freshmen we can ensure that these minors become a valuable educational experience for students outside our department. For course credit purposes, the fundamental relationship
is an important one to remember.