Friday, May 1, 2015

Calculus at Crisis I: The Pressures

By David Bressoud

Crisis: A decisive moment. The choice of preposition in the title of this new series is intentional. To be “in crisis” indicates a desperate situation that is not sustainable. I have chosen “at crisis” to indicate a degenerating situation that calls for decisive change. I will begin this series with an account of some of the pressures that have brought us to this pass.

In February of 2012, the President’s Council of Advisors on Science and Technology (PCAST) produced a report, Engage to Excel [1], that called for an additional one million majors in Science, Technology, Engineering and Mathematics (STEM) over the next ten years (see also my column On Engaging to Excel, March 2012). By coincidence, that spring there was a 7.5% increase over the previous year in the number of Bachelor’s degrees awarded in five primary STEM disciplines: Engineering as well as the Biological, Physical, Computer, and Mathematical Sciences. Obviously, this had little to do with PCAST’s wishes.

As I pointed out many years ago [2], economic considerations drive much of how students choose their field of study. Many if not most of those 2012 graduates had arrived in college in the economically momentous fall of 2008. In fact, beginning with the class that entered in fall 2008, there has been a sharp and continuing increase in the number of students who come to college with the intention of pursuing a STEM degree (Figure 1).

Figure 1. Number of full-time first-year students in four-year undergraduate programs
who intend to major in the designated field. Dashed line at 2007.
Source: HERI [3].

From 2007 to 2008, the number of entering students intending to major in Engineering rose by 32.5%. From 2007 until this past fall, the number of freshmen heading into any of these STEM fields rose by 92%, from 276,000 to 531,000.

There is, of course, a four to six year lag between matriculation and graduation. It is still early to assess the full impact of the increased interest in STEM that began in 2008. Figure 2 compares the number of entering freshmen in a given year who intend to major in one of the five primary STEM fields with the number who received a Bachelor’s degree in one of those disciplines in that year.

Figure 2. Number of entering freshmen intending to major in one of the given primary STEM disciplines versus the number of Bachelor’s degrees awarded in these disciplines.
Source: HERI [3] and NCES [4].

It is interesting to observe that, starting in 2009 to 2010, annual growth in the number of STEM degrees switched from 1 to 2% per year up to 5 to 7% per year. This growth started before the class that entered in 2008 could have graduated and may reflect recognition of the value of staying in a STEM major. The large jump in intended majors from 2007 to 2008 is not reflected in a comparably large jump in the number of degrees from 2012 to 2013. Part of this is probably due to the fact that an engineering degree is often a five-year degree. But it also almost surely reflects the fact that a large increase in the number of students seeking such a degree will include a significant number of students who are only marginally qualified to successfully complete this degree.

Implications. Enrollment in introductory STEM courses is driven by incoming students. This is especially true for Precalculus and Calculus I. Unfortunately, the same economic pressures that are pushing more students into STEM fields are forcing staff reductions in our universities. At the same time that more of the marginally prepared students are seeking STEM degrees, more of the best prepared students are using Advanced Placement® and other credits to skip over these introductory courses. And financially strapped states are requiring greater accountability for the dollars given to their universities, mandating higher success rates.

It is a perfect storm: University mathematics departments are required to teach greater numbers of students who are less well-prepared, using fewer resources and with increased expectations for student success. These alone would be sufficient to warrant the designation “at crisis.” In fact, much more is now forcing us toward change, including the rush to calculus in high school and changing demands of the client disciplines as illustrated in PCAST’s Engage to Excel. Over the next several months I will describe these challenges and what it will take to meet them.


[1] President’s Council of Advisors on Science and Technology (PCAST). 2012. Engage to Excel: Producing one million additional college graduates with degrees in science, technology, engineering, and mathematics.

[2] David Bressoud. 2010. A Benefit of High Unemployment, MAA Launchings,

[3] Higher Education Research Institute (HERI). 2007 through 2014. The American Freshman: Forty Year Trends and The American Freshman. Los Angeles, CA: HERI, UCLA.

[4] National Center for Education Statistics (NCES). 2002 through 2014. Digest of Education Statistics. Washington, DC: U.S. Department of Education.

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