In my Launchings column of this past April, I wrote of “The Crisis of Calculus,” pointing out that while the number of students taking calculus in college has held steady over the past quarter century, the number of students taking calculus in high school has been growing exponentially. We have reached the point where high school calculus enrollments are overtaking those of college calculus. At the same time, there have been significant shifts in who teaches calculus in our colleges and universities, shifts that I believe should raise concern.
Beginning in 1990, the Conference Board of the Mathematical Sciences (CBMS) began tracking the number of students taking Calculus I and Calculus II by the type of institution: 2-year college (TY), BA/BS as highest degree offered in mathematics (BA), MA/MS as highest degree offered in mathematics (MA), or university offering the PhD in mathematics (PhD). Five years later, they also began tracking who teaches these courses: tenured or tenure eligible faculty (T/TE), other full-time faculty, part-time faculty, or graduate TAs. Though we only have a few data points and it is dangerous to extrapolate from so few points, there are clear trends.
All enrollment numbers are in thousands, and enrollment is for fall term only.[1]
Calc I
| year | PhD | MA | BA | 2-year |
| 1990 | 101 | 39 | 62 | 53 |
| 1995 | 84 | 42 | 66 | 58 |
| 2000 | 89 | 42 | 59 | 53 |
| 2005 | 105 | 30 | 65 | 51 |
Calc II
| year | PhD | MA | BA | 2-year |
| 1990 | 47 | 17 | 23 | 23 |
| 1995 | 42 | 16 | 25 | 23 |
| 2000 | 48 | 18 | 22 | 20 |
| 2005 | 54 | 12 | 19 | 19 |
PhD-granting universities are now teaching a larger share of the students taking Calculus than they have in the past, handling 42% of the students who take Calculus I in college and 52% of those who take Calculus II in college.
In itself, this is not an issue for concern, but when it is combined with the fact that calculus sections at PhD-granting universities are taught in larger sections, are more likely to be taught by graduate TAs, and generally have a lower passing rate than calculus sections at other types of colleges, it does raise concerns.
The other trend that worries me is that combined with a shift of our calculus students to PhD-granting universities, at these institutions there is a shift away from sections taught by tenured and tenure-eligible faculty and, at least for Calculus I, a considerable increase in the reliance on graduate TAs. The CBMS data presented in the appendix to this article documents these trends. It is worth noting that while a much smaller number of tenured and tenure-eligible faculty are teaching these courses at doctoral institutions, other types of colleges and universities have not seen a comparable decrease.
There are no easy answers. I am very aware of the pressures that make it difficult to get tenured and tenure-eligible faculty into these classes at research universities. The challenge before us is to find ways of improving undergraduate education in mathematics, especially what happens to students in their first year of college, despite such pressures.
The teaching of undergraduate mathematics has always been a central priority at MAA. Through the work of CUPM, CRAFTY, and other education committees, through its journals, books, and other publications, through sessions at meetings as well as minicourses and workshops, MAA has collected and disseminated information on what works and how we can improve our teaching. I am encouraged by the fact that AMS is aware that here is an issue that it also needs to address, and that Jim Glimm, President of the AMS, has set up a special Task Force on the First-Year College Experience that is looking for ways large universities can give students the support needed to succeed in calculus. Today, there is tremendous potential to make a real difference as the two societies work together to determine what we can and should do to support first-year mathematics instruction at all undergraduate institutions.
We also should not simply yield to the pressures that divert faculty from paying attention to first-year courses. What happens in the first year of college mathematics, whether it be in calculus, pre-calculus, or another introductory course, should be the concern of all faculty in every mathematics department. Even when it is not possible to get tenured and tenure-eligible faculty to teach these classes, that does not remove their obligation to be aware of what is happening and to get involved in promoting and facilitating effective instruction.
Appendix
The percentages are percentage of total sections taught in the fall term.[1]
Calc I PhD
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 62.0% | 16.0% | 7.0% | 15.0% |
| 2000 | 51.6% | 21.6% | 12.4% | 14.4% |
| 2005 | 39.6% | 27.5% | 8.8% | 24.2% |
Calc II PhD
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 59.6% | 13.1% | 7.1% | 20.2% |
| 2000 | 58.3% | 17.7% | 10.4% | 13.5% |
| 2005 | 45.7% | 27.2% | 8.7% | 18.5% |
Calc I MA
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 77.0% | 12.0% | 9.0% | 2.0% |
| 2000 | 65.3% | 17.3% | 14.3% | 3.1% |
| 2005 | 79.3% | 13.0% | 6.5% | 1.1% |
Calc II MA
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 84.0% | 11.0% | 5.0% | 0.0% |
| 2000 | 73.2% | 10.3% | 16.5% | 0.0% |
| 2005 | 80.2% | 8.8% | 11.0% | 0.0% |
Calc I BA
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 84.0% | 6.0% | 10.0% | 0.0% |
| 2000 | 78.5% | 14.0% | 7.5% | 0.0% |
| 2005 | 80.6% | 12.2% | 7.1% | 0.0% |
Calc II BA
| year | T/TE | other full-time | part-time | graduate TA |
| 1995 | 88.0% | 10.0% | 2.0% | 0.0% |
| 2000 | 86.2% | 7.4% | 6.4% | 0.0% |
| 2005 | 94.0% | 6.0% | 0.0% | 0.0% |
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.