The Calculus I Student

David M. Bressoud, May 2011 (corrected December, 2011)

The data from the MAA survey [1] of mainstream Calculus I classes are in, and we are in the process of preparing it for analysis. The survey was a great success. We had responses from almost 700 instructors and over 14,000 students at all types of post-secondary institutions. While it is too early to report on any associations that appear, I do have some basic summative data that should be of interest.

The following are the characteristics of students who were enrolled in mainstream Calculus I after the second week of classes in Fall term, 2010. (Numbers in parentheses are for all full-time first-year students in four-year undergraduate programs [2].) After showing what we have learned about these students, I will end this column with my own thoughts and reactions.

Demographics and Aspirations

The low ratios for the Physical Sciences (6:3) and Mathematics (1:1) probably reflect the large numbers of these students who place directly into Calculus II or higher.



The actual distribution of final grades for all of these students was A: 22%, B: 28%, C: 23%, D, F, or withdrew: 27%. [5]

Thoughts and Reactions

What strikes me very forcefully in this description of Calculus I students is how accurately it portrays those who have been successful in high school mathematics:

I am distressed by how poorly these students do in Calculus I: Over a quarter essentially fail, and only half earn the A or B that is the signal that they are likely to succeed in further mathematics. I know the frustration of high school teachers who see what they consider to be the best and brightest of their students run into mathematical roadblocks in college. I recognize that much of the fault lies on the high school side of the transition. Many students who consider themselves well prepared for college mathematics in fact are not. We need to do a better job of communicating what these students really need and working with their teachers so that they can provide it. I also know that we in the colleges and universities can do a better job of supporting these students after they have arrived on our campuses, moving them forward with challenging and engaging mathematics while bringing them up to the level they need to be at to succeed.

Over the next several months, we will be analyzing our data to identify eight departments across a variety of types of colleges and universities that have particularly effective programs. This does not necessarily mean high pass rates, but rather evidence that they are doing significantly better than their peers in preparing their students for further mathematics. We will then send teams into these institutions to prepare detailed case studies that we hope will promote best practices throughout the country.

[1] Characteristics of Successful Programs in College Calculus, NSF DRL REESE grant no. 0910240.

[2] Cooperative Institutional Research Program at the Higher Education Research Institute at UCLA. 2010. The American Freshman: National Norms 2010. University of California Press. Berkeley, CA.

[3] When instructors were asked at the start of the semester: Given the choice between “When studying Calculus I in a textbook or in course materials, students tend to memorize it the way it is presented” and “When studying Calculus I in a textbook or in course materials, students tend to make sense of the material, so that they understand it”, 64% chose the former. There is a significant disconnect between what students plan on doing and what instructors believe they will do.

[4] When instructors were asked at the start of the semester: Given the choice between “My primary role as a Calculus instructor is to work problems so students know how to do them” and “My primary role as a Calculus instructor is to help students learn to reason through problems on their own”, 90% chose the latter. On the role of the instructor, there is greater, though not perfect, alignment.

[5] At the start of the term, instructors were asked to estimate what percentage of the students would receive D, F or withdraw. The average estimate was 26%.

Access pdf files of the CUPM Curriculum Guide 2004 and the Curriculum Foundations Project: Voices of the Partner Disciplines.

Find links to course-specific software resources in the CUPM Illustrative Resources.

Find other Launchings columns.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and Past-President of the MAA. You can reach him at [email protected]. This column does not reflect an official position of the MAA.