David M. Bressoud May, 2007
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Our inability to get students to major in the mathematical sciences
is symptomatic of problems throughout undergraduate mathematics. That we do
have a problem in attracting and retaining majors is illustrated by the graph
shown below, based on data collected for the Conference Board of the Mathematical
Sciences [1] since 1975.
(Act/OR = actuarial science, operations research)
The precipitous drop with which this graph begins is the tail end of a dramatic
drop in majors that began in the early 1970s. The fifteen years to 1995 saw
a substantial recovery, but one due almost entirely to a dramatic growth in
the number of mathematics education, actuarial, and operations research majors.
The record of the past 25 years is even less impressive when we note that
the total number of bachelor degrees conferred has increased by 55% since
1975.
year |
% majoring in math |
1975 |
2.03% |
1980 |
1.23% |
1985 |
1.33% |
1990 |
1.22% |
1995 |
1.07% |
2000 |
0.87% |
2005 |
0.86% |
We are capturing a very small fraction of the students who are capable of studying mathematics. While it is certainly not a prerequisite for a major in mathematics to arrive at college with credit for calculus, these students do present us with a large—between 150,000 and 200,000 per year—pool of potential math students. Almost a third of these—48,000 of them—arrive with a score of at least 3 on the Advanced Placement BC Calculus exam. And this number is growing fast as shown in the next graph. [2].
The number of BC Calculus tests taken is growing at 8% per year,
with no sign that this exponential rate of growth is diminishing. These are
good students. They do not choose to take BC Calculus unless they are ready
for challenging mathematics. Over 80% of them score at least a 3, over 60%
score at least a 4, over 40% earn the highest score of 5.
A recent study by The College Board [3] conducted at twenty-one
top tier undergraduate programs [4] shows that students
with a 3 or higher on the BC exam who use this credit to move directly into
the third semester of calculus—usually this means several variable calculus—perform
better in this class than students who had studied single variable calculus
at that college. Students with a 5 on the BC exam average more than half a
grade higher than their peers who studied single variable calculus at that
college or university.
There is a lot that we do not know. How many of the students who do well on the BC exam choose not to take any mathematics when they get to college? For those who do continue with calculus or other mathematics, what is their college experience? Do they continue to study mathematics? I worry that many of these students have been learning from some of our very best high school teachers in highly supportive environments, and they enter a system that does not give them the kind of individual challenge and attention to which they are accustomed. While they do well in mainstream several variable calculus, it is not clear that this is the right place to start them on the rigors of college-level mathematics.
And I have another worry. With all of the pressure to put together a high school transcript that will stand out, more and more students now take BC Calculus before their senior year. This number has grown from 8818 in 2002 to 13,809 in spring, 2006, an increase of 57% in just four years [2]. There is evidence [5] that many of these students choose not to take or are unable to take any mathematics in their senior year of high school. We need more information about this phenomenon and what it means for the future of the mathematical sciences.
Not everyone with mathematical talent should major in one of the mathematical sciences, but the argument that we do not have a sufficiently well trained cadre of high school students from which to draw does not stand up. There is much for us to do if we are to understand the new dynamics of the transition from high school to college mathematics, but understanding will not be enough. Once we know what is happening, we need to be prepared to modify what and how we teach.
[1] College enrollments from
• Albers, Donald J., Richard D. Anderson, Don O. Loftsgaarden, Undergraduate
Programs in the Mathematical and Computer Sciences, the 1985–1986 Survey,
MAA Notes Number 7.
• Albers, Donald J., Don O. Loftsgaarden, Donald C. Rung, Ann E. Watkins,
Statistical Abstract of Undergraduate Programs in the Mathematical Sciences
and Computer Science in the United States, 1990–91 CBMS Survey, MAA
Notes Number 23.
• Loftsgaarden, Don O., Donald C. Rung, Ann E. Watkins, Statistical
Abstract of Undergraduate Programs in the Mathematical Sciences in the United
States, Fall 1995 CBMS Survey, MAA Reports Number 2
• Lutzer, David J., James W. Maxwell, and Stephen B. Rodi, Statistical
Abstract of Undergraduate Programs in the Mathematical Sciences in the United
States, Fall 2000 CBMS Survey, American Mathematical Society
• CBMS Survey, Fall 2005, preliminary tables www.math.wm.edu/~lutzer/cbms2005/.
[2] College enrollments from [1]. AP enrollments from AP Program Summary Report, latest at apcentral.collegeboard.com/apc/public/repository/ap06_prog_summary_rpt.pdf
[3] Morgan, Rick and Len Ramist, Advance Placement Students in College: An Investigation of Course Grades at 21 Colleges, ETS Report No. SR-98-13, 2002. Available at apcentral.collegeboard.com/apc/public/repository/ap01.pdf.in_7926.pdf
[4] Boston College, Brigham Young University, Carnegie Mellon University, Clemson University, College of William and Mary, Cornell College (IA), Cornell University, Duke University, Michigan State University, Pennsylvania State University, Stanford University, Tulane University, University of California-Davis, University of California-Irvine, University of Georgia, University of Illinois, University of Texas-Austin, University of North Carolina-Chapel Hill, University of Utah, University of Virginia, Yale University
[5] A survey was conducted of the 4000 high schools that participated in the 2007 American Math Competition, asking about students who complete their school’s highest level of calculus before their senior year. This data is now being analyzed. Results should be released some time this summer.
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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at bressoud@macalester.edu. |