The Role of Calculus in the Transition from High School to College Mathematics

This past March I ran a small workshop in Washington, DC to look at “The Role of Calculus in the Transition from High School to College Mathematics,” funded by the National Science Foundation (#1550484). As the introduction to the workshop, cited below, makes clear, this is a critically important issue. Regular readers of my column will recognize that I return to it often. Part of the problem is that we don’t even know what we know and what we need to know (echoes of the “unknown unknowns”). The stated purpose was to bring together stakeholders to

1. Clarify the current state of knowledge of the effects on college performance and retention in STEM disciplines of acceleration into calculus at or before 12 th grade, as well as the effects of lack of access to calculus while in high school.
2. Identify the most pressing research questions.
3. Suggest strategies for answering these questions and identify the appropriate researchers or organizations to tackle them.

As it turned out, my hopes for the workshop were too ambitious. We were not able to leave with a research agenda, but we did make progress toward identifying what we know about the problems surrounding this transition and in clarifying the complex issues surrounding the movement of calculus into the high school curriculum.

The two days of the workshop provided an opportunity for a rich exchange. Participants included post-secondary mathematics faculty, high school calculus teachers, state and district supervisors of mathematics, researchers in both K-12 and post-secondary mathematics education, as well as representatives of The College Board, the National Council of Teachers of Mathematics, the National Research Council’s Board on Science Education, the National Math and Science Initiative, and Achieve. What is most gratifying is that all of these players recognize that there are serious problems around issues of preparation for post-secondary mathematics as well as equity and access that are being exasperated by the tremendous pressures to bring students into calculus ever earlier in their high school careers. My intention is that over the coming months it will be possible to build on the foundation laid by this workshop.

Before concluding with the preamble that I wrote for this workshop, I would like to send out an appeal for all readers who would like to contribute to this conversation to send me their thoughts at bressoud@macalester.edu, subject line: Role of Calculus.

Last year, at least three quarters of a million U.S. high school students were enrolled in a calculus class.[1] This was three times the number of U.S. students who took their first calculus class in college. High school calculus enrollments are still growing at roughly 6% per year,[2] with increasing pressure on the most advantaged students to take calculus ever earlier. In 2015, over 120,000 students took the AP Calculus exam by the end of grade 11, and these numbers are growing by 9% per year. [3]

If we make the assumption that most of the students who enroll in calculus in high school will go on to matriculate as full-time students in a four-year undergraduate program—of whom there are 1.5 million each year[4]—then roughly half of these full-time, first-year students enter having already studied calculus. Calculus in high school is now commonly perceived as a prerequisite for college admission, with the result that high schools must start students with Algebra I in 8th grade high school if they are to be on track for calculus by grade 12, and calculus teachers find themselves under increasing pressure from parents and administrators to admit into their classes students they know are not adequately prepared. How do we provide support and alternatives for those students who cannot handle this accelerated progression?

We have learned from our study of Characteristics of Successful Programs in College Calculus (NSF DRL 0910240) that a quarter million of the students who study calculus in high school will retake mainstream Calculus I at the post-secondary level, and 40% of these quarter million will fail to get the A or B that signals they are prepared to continue in mathematics.[5] College faculty are very much aware that many of the students who enter with calculus on their high school transcript are, in fact, not ready for college-level mathematics. Of particular concern is that we know almost nothing about what happens to the remaining half million students who have studied calculus in high school: How many take advantage of advanced placement, and how well prepared are they? What are the mathematical trajectories of those who do not take calculus in college? How has the experience of calculus in high school shaped the aspirations and attitudes of these students and their ability to continue on toward mathematically demanding careers? 

At the same time, half of all U.S. high schools do not even offer calculus. [6] Students from underrepresented groups, even when they are in a high school that offers calculus, are often discouraged from enrolling in this course. Those who have not taken calculus in high school find themselves in competition against students with a much richer preparation. What does this do to their chances for admission to college or the pursuit of a STEM major? 

The questions are manifold. The goal of this workshop is to better understand these questions and to begin to develop strategies for answering them. Specifically, we seek to

1. Clarify the current state of knowledge of the effects on college performance and retention in STEM disciplines of acceleration into calculus at or before 12th grade, as well as the effects of lack of access to calculus while in high school.

1. Identify the most pressing research questions.

1. Suggest strategies for answering these questions and identify the appropriate researchers or organizations to tackle them.

Footnotes

[1] Based on the NCES longitudinal study (HSLS:09) reporting that 19% of the four million students who were in 9th grade in 2009 had taken a calculus course in high school by the time they graduated.

[2] From the College Board’s AP Program Summary Reports from 2002 to 2015.

[3] Ibid.

[4] Higher Education Research Institute.The American Freshman: National Norms Fall 2015.

 [5] Data from Characteristics of Successful Programs in College Calculus project’s maalongdatafile. See David Bressoud. 2015. Insights from the MAA national study of college calculus. The Mathematics Teacher. 109 3:179–185.

[6] U.S. Department of Education Office of Civil rights. Issue Brief No. 3 (March, 2014).
http://ocrdata.ed.gov/Downloads/CRDC-College- and-Career- Readiness-Snapshot.pdf