College Calculus: What We Don't Know

*David
M. Bressoud** September, 2008*

I have postponed until a later column the further discussion of *Making
the Connection* because I need your help. Working with SIGMAA on RUME
(Research on Undergraduate Mathematics Education), MAA is putting together
a proposal to NSF to fund a large-scale study of first-semester college calculus
that would be conducted during the 2010–11 academic year. The purpose
of the study is to determine what factors within the context of calculus contribute
to attracting students to mathematics, encourage their persistence through
calculus, and ensure that they have the mathematical preparation needed for
their intended major. We are seeking to involve as many two- and four-year
colleges and universities in this study as we can. In determining whether
or not such a study will be feasible, we need a sense of how many individuals
and departments might be interested in participating. Please take a moment
to log onto www.maa.org/Surveys/TakeSurvey.aspx?SurveyID=mlLK8m3
to let us know how important such a study would be to you and to indicate
your level of willingness to participate in this study.

The transition from high school to college mathematics is one of the most critical junctures in the preparation of individuals to meet the mathematical demands of the 21st century in engineering, in business, and in the natural, mathematical, biological, and social sciences. I’ve written in many of these columns about the discouraging number of students who pursue mathematics in college at the level of calculus and above, despite the tremendous growth in the number of students who study calculus in high school. It appears that we are losing many students who would like to pursue a mathematically intensive career and are capable of learning the mathematics they would need.

As Elaine Seymour and Nancy Hewitt have documented [1], it is not just the under-prepared students we are losing. Poor teaching, an overwhelmingly fast paced curriculum, and poor advising and support are leading reasons given by students who abandon the STEM (Science, Technology, Engineering, and Mathematical sciences) disciplines. But these characteristics were also described by students who stayed. Of those who completed a major in a STEM discipline, 74% identified poor teaching as a concern they experienced, 41% described the curriculum as overwhelming, and 52% felt that advising and help with academic problems was inadequate (page 33).

The message of Seymour and Hewitt is that the real problems in attracting
and retaining students lie in the culture of the science and mathematics classroom.
This is not to say that we need warm and fuzzy mathematics. But it does mean
that learning mathematics should not be seen as the rapid absorption of a
large and confusing body of knowledge in a highly competitive environment.
We need to think about how to encourage team-building and support networks
and to generate enthusiasm for tackling challenging problems and ideas. Simply
to list these desiderata brings to mind Uri Triesman’s *Emerging
Scholars Program* (ESP) which has been so successful precisely because
of its emphasis on these aspects of the learning experience (for a description
of ESP, see [2]).

This is also echoed in the conclusion reached by Stigler and Hiebert [3] regarding their recent international study of teaching patterns across the world:

A focus on teaching must avoid the temptation to consider only the superficial aspects of teaching: the organization, tools, curriculum, content, and textbooks. The cultural activity of teaching – the ways in which the teacher and students interact about the subject – can be more powerful than the curriculum materials that teachers use. (p. 16)

But how do we improve this culture in the context of a large public university
where tight budgets and inadequate staffing levels force us to teach calculus
in large, impersonal classes with faculty who lack the incentives and cannot
afford the time needed to make substantive changes?

The answer is two-fold. First, we must identify the adjustments that have
the greatest impact for the least investment in time and resources. There
is tremendous variety in how colleges and universities approach the teaching
of calculus. There is a great deal of trial and experimentation by thoughtful
teachers. The purpose of a broad study is to tap into this expertise, systematically
investigate how this expertise manifests itself in classrooms and programs,
and to share what works in what contexts.

The second half of the answer lies in the fact that the leaders of most large public universities, especially those with an engineering program, recognize the importance of calculus and the need to make it work. A strong case for a means by which a reasonable investment can pay large dividends will be listened to attentively, especially if it means improved retention and success in science and engineering. Clear evidence of the impact these efforts will have in recruiting and nurturing the minds of future mathematicians and mathematics teachers can help to mobilize a department. We must undertake the large-scale studies that can discover and document the changes that will have the greatest effect at the least cost.

The task is large and daunting. To get the broad participation that will be needed, basic participation in the study needs to be very simple: a questionnaire for the instructor to gather information about how she or he sees the course, short surveys for students to take at the start and end of the course, follow-up on grades and subsequent courses taken. We also need to select a few classes for more in-depth study of what is happening in the course and how that affects student learning.

We needed this information yesterday. Optimistically, it will take four to five years to plan, execute, and report out the results of the study I have described here. But if we do not start the process now, when will we? If my presidency of the MAA accomplishes nothing more than getting us well into this process, it will have been a great success.

[1] Elaine Seymour and Nancy M. Hewitt,

Talking About Leaving: Why Undergraduates Leave the Science, Westview Press, Boulder, CO, 1997.[2] Eric Hsu, Teri J. Murphy, and Uri Triesman. Supporting High Achievment in Introductory Mathematics Courses: What We Have Learned from 30 Years of the Emerging Scholars Program, pages 205–220 i

n Making the Connection:Research and Teaching in Undergraduate Mathematics Education, Marilyn Carlson and Chris Rasmussen, editors, MAA Notes #73, Mathematical Association of America, Washington, DC, 2008.[3] Stigler, J. and Hiebert, J. Improving mathematics teaching.

Educational Leadership, Feb., 2004, 12-19.

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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.