David M. Bressoud, November, 2010
Correlation is not causation, but when one has a reasonable expectation that a causal link might exist between two phenomena and a linear regression finds a high correlation coefficient, then there is good reason to suspect that a causal link really does exist. This article will string together a sequence of arguments that strongly suggest that high national unemployment leads to higher numbers of mathematics majors at research universities, but that the link is only strong at universities with engineering programs.
I begin with a graph that appeared in my June 2008 column, Disturbing Trends in the CBMS Data, showing the number of mathematics majors by type of institution. What is particularly striking is that the patterns of growth and decline in these numbers have been so different at different types of institutions. I focused on the mathematics majors at research universities (defined as universities that offer a Ph.D. in Mathematics) and sought to see whether I could explain why these numbers declined during the 1990s, then came back so strongly.
Graph 1: Number of BA/BS degrees in Mathematics by type of institution. Source: CBMS .
If we look at Fall term calculus enrollments (all levels of mainstream calculus) by type of institution, we see a general trend of slow decline at undergraduate colleges and comprehensive universities,but at research universities there is a very distinctive pattern of sharp decline in the early '90s followed by strong growth since then, consistent with a turn-around in the number of majors around the year 2000.
Graph 2: Total mainstream calculus enrollments, Calculus I through IV, Fall term, by type of institution. Source: CBMS .
If we do a simple linear regression of total mainstream calculus enrollments across all four-year undergraduate institutions with the number of graduates majoring in mathematics four years later, we only have four data points to work with , but nevertheless there is a very strong correlation with an R-squared value of 0.98.
year Fall Calculus enrollment Math majors 4 years later 1985 402,000 15,218 1990 373,000 14,369 1995 337,000 12,539 2000 352,000 13,327
This is not greatly surprising. With more students taking more calculus, one would expect to get more math majors.
The question is why the mid-90’s turn-around was so dramatic at research universities. While not all research univesities are large state flagship universities, they carry the overwhelming majority of students who are in research universities. Most state flagship universities have large engineering programs, and when there is an engineering program, it is the dominant provider of clientele for mainstream calculus. We have annual data both on the number of incoming students intending to major in engineering and the number who graduate in engineering, but the former seem to be the natural driver for calculus enrollments.The next graph shows the number of incoming students intending to major in engineering from 1985 through 2009. From 98,000 in 1990, the number dropped to 83,000 in 1995, then recovered to 96,000 in 2000 and 109,000 in 2005.
Graph 3: Number of incoming full-time freshmen who declare engineering as first choice for major. Source: HERI .
The linear regression of prospective engineers against mainstream fall calculus enrollment at research universities again produces an R-squared value of 0.98. While future engineers dominate calculus classes at our large universities, they generally do not constitute 98% of the calculus enrollment. This suggests that whatever drives the number of engineering students also factors into the decisions of other students whether to take calculus, at least at large state universities.
Graph 4: Number of freshman who intend to major in engineering against total mainstream Fall term calulus enrollments at research universities. Sources: HERI  and CBMS .
One of the interesting features of Graph 3 is the high variability, suggesting that the calculus enrollments and number of majors at research universities saw much greater variability during the 1990s than the few data points of Graphs 1 and 2 would suggest. The variability in prospective engineers is even more apparent if instead of absolute numbers we look at the fraction of the incoming class that intended to major in engineering.
Graph 5: Fraction of incoming freshmen intending to major in one of the STEM disciplines. Source: HERI .
I was struck by the fact that engineering has a much higher degree of year-to-year variation than the sciences (ignoring the boom or bust cycles in computer science). A reasonable hypothesis is that the economy affects the decision whether or not to pursue a degree in engineering. Indeed, looking at employment rates over this same period, we see that it shows very similar peaks and troughs.
Graph 6: July unemployment rate (seasonally adjusted). Source: BLS .
Even accounting for the variation due to the unemployment rate, there also seems to be a general downward trend in the percentage of incoming students who intend to major in engineering. I did a multiple regression on both unemployment rate and elapsed time since 1980. It produced an R-squared value of 0.71, with an underlying decline of just under one-tenth of one percentage point per year. Subtracting the unemployment effect—assuming that the unemployment rate was at its historical average of the past thirty years: 6.2%—one would expect that 7.9% of incoming freshmen in 2009 would have entered with the intention of majoring in engineering. That translates nationally into 25,000 fewer prospective engineers than actually showed up.
Caveats and Conclusions: Only the CBMS data break down the numbers by type of institution. CBMS did this for research universities in 1985 and separated into the three tiers only in 1990. They only collect their data every five years. The result is a very sparse set of data points. It will be interesting to see how well the 2010 data, which should be available a little over a year from now, fit these trends.
Unemployment rates only seem to have an effect on mathematics programs at research universities, presumably because of the prevalence of schools of engineering at these institutions. Looking at the total number of mathematics majors who graduate each year, the unemployment rate from four years previous only explains 14% of the variability.
It is probably not the unemployment rate as such that influences the choice of whether or not to major in engineering. Students entering college are less concerned with the current job market that what they foresee for four years down the road. In fact, the July unemployment rate for the summer after they enter college is a very slightly better predictor (the multiple regression explains 72% as opposed to 71% of the variability) than the rate that pertained the summer before they entered college. Collectively, entering freshmen appear to have a pretty good sense of what the unemployment rate will be the following year. Note, for example, that the number of prospective engineers spiked in 2008 while unemployment was still under 6%, but at a time when everyone knew that we were heading into a recession.
Also while the trend is down on the percentage of incoming students who intend to major in engineering, the total number of matriculating full-time students has increased by 40% over the past thirty years. The result is a slight increase, less than 5% over thirty years, in the total number of prospective engineers after adjusting for the unemployment rate.
The conclusion is that these should be fat times, in terms of number of students taking math courses at the level of calculus and above, at those universities with schools of engineering. Unfortunately, as the job market recovers, these universities may see fewer engineering majors, fewer calculus students, and fewer math majors. Math departments need to think about not just the attractiveness of their own math programs, but how they can generally encourage students to pursue the mathematically intensive majors from which we draw. What is good for engineering is good for mathematics.
 CBMS data are 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 Notes Number 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 Reports Number 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
 The number of math majors is taken from National Center for Education Statistics, Digest of Education Statistics: 2009, US Department of Education nces.ed.gov/programs/digest/d09/. The number of mathematics majors for 2009 has not yet been reported. The mainstream calculus enrollments are from the CBMS data . Total mainstream calculus enrollment for Fall, 2005 was 360,000
 Higher Education Research Institute. The American Freshman. www.heri.ucla.edu/index.php
 Bureau of Labor Statistics. US Department of Labor. www.bls.gov/cps/
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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and President of the MAA. You can reach him at email@example.com. This column does not reflect an official position of the MAA.