Monday, October 1, 2012

MAA Calculus Study: Intended Careers

This is the first of what I intend to be a series of reports that delve into the data on Calculus I instruction that were collected in fall 2010 as part of MAA’s study Characteristics of Successful Programs in College Calculus (NSF #0910240). Some of the raw summative data was reported in earlier Launchings columns [1,2], but we have now separated the data by type of institution, characterized by highest degree offered in mathematics. Combined with knowledge of the number of students who took Calculus I in fall 2010 at each of the types of institutions—thanks to the Conference Board of the Mathematical Sciences (CBMS) 2010 survey—it is now possible to appropriately weight the data that has been collected.  A preprint of an article that summarizes the methods and instruments used for the surveys with selected results [3] has been posted on the website

For this month, I want to focus on the intended careers of students as they begin mainstream Calculus I. This is a course that took on its modern form after the Second World War, and in most places it still follows the curriculum as laid out in George Thomas’s Calculus and Analytic Geometry of 1951 [4].  The course was designed to meet the needs of engineers and those in the physical sciences. However, as illustrated in Figure 1, just under 35% of those taking Calculus I today are on one of these tracks. Today’s Calculus I student is more likely to be pursuing a career in the biological or life sciences than in engineering.

These percentages were calculated by determining the percentages for each of the four types of postsecondary institutions as classified by CBMS. We refer to universities that offer a doctorate in mathematics as research universities, those for which the highest degree in mathematics is the master’s as masters universities. If bachelor’s is the highest degree we call it an undergraduate college, and if associate’s is the highest degree we call it a two-year college. The distributions were then weighted according to the number of students who were enrolled in Calculus I that fall: 110,000 at research universities, 41,000 at masters universities, 82,000 at undergraduate colleges, and 65,000 at two-year colleges.

It is interesting to look at the data by type of institution. Only at research universities and two-year colleges do those heading into engineering outnumber those with an intended major in the biological or life sciences. Even there, the majors that normally require a full year of single variable calculus account for less than half of the Calculus I students. See Figures 2 and 3.

These are also the only types of institution where students going into science, technology, engineering, or mathematics (STEM) fields constitute over 75% of all Calculus I students. The biological sciences are much more dominant, and students are significantly less likely to be intending a STEM major, at masters universities and undergraduate colleges. See Figures 4 and 5.

The following graphs show the distribution of intended careers for women, Asian-American students, Black students, and Hispanic students. See Figures 6–9.

The variation in distributions is most dramatic for women. A women in Calculus I is three times as likely to be headed into the biological sciences as into engineering. It may come as a surprise to some that Asian-American students in Calculus I are almost twice as likely to be majoring in the biological or life sciences as engineering, but this follows a general trend of Asian-American students out of engineering and into biology. While Asian-Americans are still very well represented in engineering, making up over 12% of the bachelor’s degrees in engineering while they are only 7% of all bachelor’s degrees earned in the United States, Asian-Americans constitute almost 18% of the bachelor’s degrees in the biological sciences. See Figure 10.

Of course, these data are skewed by the fact that many students, especially many of those going into engineering or the physical or the mathematical sciences, never take Calculus I in college. They begin their college mathematics at the level of Calculus II or higher. Unfortunately, there are no good estimates for the size of this population. But that still leaves the question that we have addressed at Macalester: Why teach Calculus I as if it is the first half of a year-long course when—for most of the students who take it—the next calculus course is not required or even expected?

[1] Bressoud, D.M. 2011. The Calculus I Student. Launchings.

[2] Bressoud, D.M. 2011. The Calculus I Instructor. Launchings.

[3] D. Bressoud, M. Carlson, V. Mesa, C. Rasmussen. 2012. Description of and Selected Results from the MAA National Study of Calculus (pdf). Submitted to International Journal of Mathematical Education in Science and Technology.

[4] G.B. Thomas. 1951. Calculus and Analytic Geometry. Addison-Wesley. Reading, MA.

[5] National Center for Education Statistics (NCES). 2011. Digest of Education Statistics. US Department of Education. Washington, DC.

The MAA national study of calculus, Characteristics of Successful Programs in College Calculus, is funded by NSF grant no. 0910240. The opinions expressed in this column do not necessarily reflect those of the National Science Foundation.