By Dave Kung
When I was department chair at St. Mary’s College of Maryland, we carefully tracked data about how we were serving students. Regularly updated spreadsheets showed how many students were in each course we offered and we used them to look for enrollment patterns and adjust our offerings as needed.
We were particularly proud of the number of math majors we graduated each year. For about a decade, over 5% of each graduating class earned a degree in math. Of the ~160 Calc I students and ~100 Calc II students who went through our student-centered system, about 20-30 ended up as math majors. We had a sense we were above the national average – but we weren’t entirely sure. Keeping tabs on that number was vital for monitoring the health of our department. If it dropped too low, we wouldn’t be able to offer some of the upper-level courses we loved teaching. More importantly, we wouldn’t have been fulfilling our goal of getting students excited about math.
What we never had was a detailed sense of how our program compared to others. What was the national picture like? What types of institutions were attracting the most majors? I would love to have been able to brag to the administration about the ways in which we were above average – and we could have learned from the schools that were doing even better.
Our second largest enrollment course was Survey of Math (a quantitative literacy course that fulfilled a graduation requirement). For the non-STEM majors at St. Mary’s, were we meeting their needs? Were the numbers of students in our Calculus classes about right given the majors students would finish? Should more of those students have been in Statistics or Survey? Our data set didn’t help us there.
TPSE Math now has data that can answer important questions both about the state of math and statistics majors and about the need for calculus - at your institution and nearly 2000 others.
Every college and university submits data to the Department of Education, all of which is available (at least for now) in the Integrated Postsecondary Education Data System (IPEDS) database. We analyzed data from 2020-2023 to answer two big questions:
- How are institutions doing in terms of graduating students in the mathematical sciences? What proportion of bachelor’s degrees are earned in math or statistics majors? (Short answer: overall about 2% – but institutions range all the way up to 29%.)
- How big is the demand for calculus in each institution? What proportion of bachelor’s degree recipients are likely to have needed at least one semester of calculus to graduate? (Short answer: overall about 34% of graduates had a major that required calc - with large variations by type of institution, and many engineering schools well over 60%.)
There are over 1300 institutions that awarded bachelor's degrees in the mathematical sciences and over 1900 that graduated students who probably required calculus. To see so many data points, the institutions are shown grouped in two different ways: by state and by Carnegie classification. These visualizations are now available on the TPSE website – but I’m going to make you read a few more paragraphs before giving you the link.
Math & Math/Stat Majors
Overall, the 1.9% of bachelor’s degrees that are awarded in the mathematical sciences are not distributed evenly. The top schools by percentage are both tech-heavy and relatively small (the size of the dot represents the overall graduation numbers): Harvey Mudd (29%), Amherst (21%), Carnegie Mellon (17%) and MIT (15%). Research institutions also produce more than their fair share of majors; R1 schools average 2.7% math/stat majors. Notable among the larger publics are Stony Brook (11%) and three California schools: UC Santa Barbara (10%), UC SD (8.5%), and UCLA (8.1%). All of these schools are outliers; since the vast majority of schools were grouped between 0.5% and 2.0%, the visualizations use a log-scale to spread them out.
As for St. Mary’s, it turns out our impression was correct: we had a much higher proportion of math majors compared to all schools – and to schools in Maryland. Here’s how the visualization looks after typing in the college’s name and hovering over the small circle that lights up.
Slicing the data by Carnegie group shows that we were only slightly higher than average for liberal arts colleges (4%):
If those were numbers for math and statistics, how many of them were just in mathematics? There things get somewhat complicated: different institutions report the sub-majors differently. For completeness, two additional visualizations show the data for Mathematics by itself (CIP code 27.01).
Seeing these data raised all sorts of questions for me. Why are some schools producing significantly more math majors? What differences in curriculum, pedagogy, culture matter? How could we set up a system where the successes of some institutions spread to others – making for a healthier mathematical sciences ecosystem?
The Need for Calculus
How many students actually need calculus? While it would be cumbersome to get the exact figure for each institution, looking at the majors that typically require calculus (all STEM fields, economics, and some business degrees) is a good first approximation. That analysis shows that about 34% of bachelor’s degree recipients had a major that (probably) required calculus - with 24% needing STEM Calc and the other 10% needing Business Calc.
It gets more interesting if you dig into differences between types of institutions. As expected, tech-heavy schools were at 100%. The comprehensive R1s average over 50% of students needing calc, with some far higher, like Notre Dame (82%) and my own alma mater, the University of Wisconsin (76%). The average at liberal arts colleges is slightly lower (47%), just ahead of R2 schools (42%).
In most states the flagship school has one of the higher percentages – frequently 60-70%. At less prestigious schools, just 1 in 5, or even 1 in 10 students needs calculus. The average for master’s colleges and universities is just 16% at the large ones and 18% at the medium ones.
At St. Mary’s, about 43% of students end up with a major requiring calculus. For the rest a statistics or quantitative literacy course would undoubtedly suit their mathematical needs better. Even a decade ago, we knew that we should have been teaching more statistics – but the embarrassing truth is we didn’t make that change because none of us wanted to teach it. (So much for “student-centered.”)
Collectively, we in the mathematical sciences have inherited a system that pushes most high school students and far too many college students toward a course that only one in three college graduates will need. Changing that system brings all sorts of challenges. If we reduce the numbers of students taking calculus, will we still be able to recruit enough math majors to keep our departments healthy? Could other courses serve as gateways to a major in the mathematical sciences, like Linear Algebra without a calculus requirement? How can we ensure that all students have access to calculus (and high-value STEM fields), no matter what their race, gender, zip code, or economic status?
These are just some of the questions a deep dive into IPEDS data prompted for me. What questions do the data raise for you? Explore the data (and read up on the methods) on the TPSE website - and head over to MAA Connect to compare notes.
Addendum: Since the inception of this column, I have benefited greatly from the support of Kira Hamman, who has ably served as editor of MathValues. She has moved on to other endeavors and will be sorely missed. Kira, thanks for your dedication, your keen insights, and your friendship.
Footnotes:
The analysis of the demand for calculus grew from work by Aidan Sheeran-Hahnel during his summer internship at the Charles A. Dana Center.
This analysis was supported by a contract from Educational Strategy Group (ESG).
The data visualizations were completed in collaboration with ESG and Data Science 4 Everyone.
Dr. Dave Kung [LinkedIn] has worked in the intersection of mathematics and equity for three decades. He served as the Director of Policy at the Charles A. Dana Center at The University of Texas at Austin, and as Director of MAA Project NExT. He also works closely with K-12 and higher ed organizations, especially concentrating on equity issues in mathematics. Kung was awarded the Deborah and Franklin Tepper Haimo Award, the MAA’s highest award in college math teaching, for his work at St. Mary’s College of Maryland. He resides there, working as a consultant for a variety of organizations, as well as playing violin and running–never simultaneously, but sometimes alongside his partner and daughter. The views expressed in this column are Dave’s alone and do not represent those of any organizations he works with or for.