Disturbing Trends in the CBMS Data

*David M.
Bressoud June, 2008*

The *CBMS Statistical Abstract of Undergraduate Programs *[1]
is a source of information that I have mined for many of these columns. For
this month, I would like to draw attention to a trend that I find very disturbing:
While college calculus enrollments and the total number of mathematics majors
have been roughly constant over the period 1990–2005, there has been
a steady decline in enrollments at both small colleges and comprehensive universities.
All of the growth has occurred at the major research universities. This shift
in the site where mathematics is studied has implications that I shall address
in four sections:

In the graphs that follow, the three types of institutions are labeled as "research universities," "comprehensive universities," or "undergraduate colleges." The actual determination of institution type in the CBMS data is by the highest degree in mathematics that is offered at the institution: PhD, MA, or BA. The graph shown below gives the total number of bachelor's degrees in Mathematics, including dual degrees of Mathematics with another specialty, by type of institution. It does not include degrees in Mathematics Education, Statistics, or Operations Research.

While some universities have added graduate programs over the past fifteen years, the overall numbers are stable enough to be able to draw conclusions, as the graph below of "BA/BS in Math per Institution" illustrates.

Among the striking features of this graph is that the three types of institutions exhibit little similarity in their patterns of growth and decline. The NSF VIGRE grants have been one factor affecting the growth in majors at research universities over the period 2000–05. I suspect that they have had a measurable impact, but the pattern of math majors at PhD-granting universities is also highly correlated with that of engineering majors (engineering data from [2]). We only have four data points: 1990 through 2005, but the correlation coefficient is a substantial 0.909. In particular, the pattern of decline over the decade 1990–2000 followed by a sharp increase from 2000 to 2005 is common to both.

The correlation is only with Engineering and not more broadly with STEM majors. The Biological Sciences grew by almost 50% from 1990 to 1995, stagnated for five years, and then grew by another 16% from 2000 to 2005. The Physical Sciences grew by a more modest but still substantial 20% from 1990 to 1995, lost about half of that growth from 1995 to 2000, and have since returned to just above the 1995 number. Computer Science and Information Technology was stagnant from 1990 to 1995, almost doubled from 1995 to 2000, and has seen very modest growth since then [2].

Small colleges have seen a small net growth over the 15 years 1990–2005, but what is most noticeable is the sharp drop from 2000 to 2005. Comprehensive universities have experienced a marked decrease in majors, dropping by over a third since 1990. The recent decline in majors at small colleges and the erosion of majors at comprehensive universities is disturbing because it raises questions about the long-term viability of these programs.

## Women in Mathematics

The shift of majors from small colleges and comprehensive universities to research universities is also disturbing for another reason. Research universities have traditionally done worse than small colleges and comprehensive universities at attracting women to the mathematics major. In 2005, women made up 43% of the math majors at colleges where the highest available degree in mathematics was either a BA or an MA. The figure was below 36% at PhD granting universities. After reaching a high of 44% of all math majors in 1995, the percentage of women has been declining, and is now just under 40%.

The decline in the percentage of women among math majors has been masked by the fact that women make up 60% of majors in mathematics education and 48% of those majoring in statistics. Combining mathematics, mathematics education, and statistics, women constitute almost 44% of these majors. Nevertheless, the decline in math majors as such should be of concern because it will impact both the recruitment of women into graduate programs and the presence of women in the mathematical workforce.

As the graph below illustrates, the problems are not unique to research universities. The percentage of women among math majors has been generally decreasing across all types of institutions. In fact, research universities are the only types of institutions that today are ahead of where they were in 1990. But as a whole, they have trailed well below small colleges and comprehensive universities in their ability to attract women to mathematics, and their increasing dominance as the source of math majors only promises to accelerate the decline.

## The Danger for Small Colleges

The implications of the decline over the past five years in the number of majors coming from BA institutions is clearer when we look at the average number of majors per college.

When small colleges lose mathematics enrollments and majors, it is easy to tip into a situation where standard upper division courses can no longer be offered. This may be behind the CBMS data revealing a substantial number of 4-year colleges that no longer offer modern algebra and/or real analysis on a regular basis (at least once every two years). See my column from February, 2007,

What has happened to Modern Algebra and Real Analysis?. With an average of only 5.6 majors per year, a college does not have to be very far below average before it becomes difficult to offer advanced courses on a regular basis.The peak of 6.8 in 2000 is too large to be attributable to random fluctuation. My best guess is that this was driven by the explosion of growth in computer science during the period 1995–2000. At many small colleges, the computer science program sits within the mathematics department or is closely allied with it so that computer science majors find it easy to add or switch to a math major. And while, nationally, computer science majors have grown since 2000, it appears that this growth has been entirely at the large universities. Computer science enrollments at Macalester dropped sharply after 2000, and my evidence from colleagues at other small colleges is that we have all suffered a sharp decrease in computer science enrollments.

## Calculus Enrollments

While it is good news that majors are up substantially at the research universities, I also have some concern here because calculus classes at large universities are large and getting larger, and increasingly they are taught by adjunct faculty. (See my column from October, 2007,

Who Teaches Our Calculus Classes?) As the CBMS data make clear, the only reason that enrollments in Calculus II and III are holding steady is because they are increasing in our large universities. Everywhere else, these enrollments are in decline. These graphs include enrollments in two-year colleges.The pattern of calculus enrollments at PhD-granting universities over the period 1990–2000 mirrors the number of graduates in mathematics (as well as the number of graduates in engineering), but occurs three to four years earlier as one would expect. The increase in calculus enrollments from 1995 to 2005 is actually very close to the increase in total college enrollments over that period (22.6% increase [2]), and the growth trails the national increase in enrollment (25.6%) if we look at the period 1990–2005.

The steady decline in calculus enrollments at comprehensive universities, small colleges, and two-year colleges occurs in the face of a substantial increase in total enrollment and is thus all the more remarkable and discouraging.

## Conclusion

At our large research universities, engineering is the main driver for both calculus enrollments and the creation of a pool of potential math majors. Away from these universities, both enrollments in Calculus II and higher and the number of math majors are in a slow but steady decline. This is particularly surprising and discouraging because the number of first-year students who arrive with college credit for a calculus course taken while in high school has grown from about 60,000 in 1990 to almost 200,000 in 2005. Calculus II fall enrollments should not be dropping anywhere.

Even where we see growth, it is below the rate of growth in total enrollment.

It should not be this way. Mathematics is a core discipline that should be building cooperative programs with many different disciplines. It should be capable of capitalizing on growth in any of the sciences, most especially the biological sciences. The data show that there is still much to do.

[1] CBMS data is taken from

• Albers, Donald J., Don O. Loftsgaarden, Donald C. Rung, Ann E. Watkins,Statistical Abstract of Undergraduate Programs in the Mathematical Sciences and Computer Science in the United States, 1990–91 CBMS Survey,MAA NotesNumber 23, www.ams.org/cbms/cbms1990.html

• Loftsgaarden, Don O., Donald C. Rung, Ann E. Watkins,Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, Fall 1995 CBMS Survey,MAA ReportsNumber 2, www.ams.org/cbms/cbms1995.html

• Lutzer, David J., James W. Maxwell, and Stephen B. Rodi,Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, Fall 2000 CBMS Survey, American Mathematical Society, www.ams.org/cbms/cbms2000.html

• Lutzer, David J., Stephen B. Rodi, Ellen E. Kirkman, and James W. Maxwell,Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, Fall 2005 CBMS Survey, American Mathematical Society, www.ams.org/cbms/cbms2005.html

[2] National Center for Education Statistics,Digest of Education Statistics: 2007, US Department of Education nces.ed.gov/programs/digest/d07/

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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and president-elect of the MAA. You can reach him at bressoud@macalester.edu. This column does not reflect an official position of the MAA.

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