Attrition

By David Bressoud @dbressoud

As of 2024, Launchings columns appear on the third Tuesday of the month.

This month I’d like to share some data gathered by Andrew Ekstrom, a lecturer at Macomb Community College and the Flint campus of the University of Michigan. He was able to obtain anonymized data on student enrollment and performance over roughly a ten-year period in mathematics classes along the trajectory from pre-college mathematics through Calculus III at four nearby institutions, two of which are regional public universities and two are public community colleges. All four have enrollments between ten and twenty thousand students, a very large proportion of which require pre-college mathematics. Because I believe that what he found is not unique to these particular institutions, I have chosen to designate the regional public universities as RPU1 and RPU2 and the community colleges as CC1 and CC2. It is not surprising that all four experience high attrition along the trajectory from pre-college mathematics through Calculus I. After all, most of these students probably had no intention of making it to and through the first semester of Calculus. They could satisfy the mathematics or quantitative reasoning requirement with a variety of courses. What is arresting is how high the attrition actual is.

It was Danny Kaplan who brought Ekstrom’s work to my attention. Using Ekstrom’s raw data for RPU1, Kaplan learned that less than 1 out of every 300 students who began in pre-college mathematics made it to and successfully through Calculus I.

Ekstrom’s data show that persistence to the next class is usually at least as great a source of loss as failure to pass the next course. At RPU1, Intermediate Algebra is not pre-college mathematics, but neither is it one of the mathematics courses that satisfies their Quantitative Reasoning requirement, something that is satisfied by College Algebra and Calculus I. The following tables show the number of students who passed a given course: Pre-college Mathematics, Intermediate Algebra, or College Algebra with a grade of A, B, or C; the number of each who then enrolled in the next course (and as % of those passed with that grade), and the number who passed the next course (and as % of those who enrolled).

Table 1. Transition from Pre-college Mathematics to Intermediate Algebra

 Table 2. Transition from Intermediate Algebra to College Algebra

Table 3. Transition from College Algebra to Calculus I

This confirms what has been observed elsewhere, that choosing to persist into the next course is at least as great a barrier as passing the next course in the sequence. In 2015, as part of the MAA’s Progress through Calculus initiative, we surveyed all departments of mathematics in the United States that offer a graduate program (Master’s or PhD) in Mathematics. We found that 41% said that they regularly track persistence rates. This is good, but given the importance of persistence, but it could be much better.

There is some alarming data that Ekstrom discovered. That is the tremendous discrepancy in pass rates among faculty who regularly teach these classes (have taught at least 100 students in that course). Each of the following percentages is for a specific instructor. The range of pass rates is particularly large at the two community colleges.

For Pre-college Mathematics

RPU1: 89% to 74%

RPU2: 80% to 45%

CC1:    80% to 20%

CC2:    75% to 28%

For Intermediate Algebra

RPU1: 94% to 46%

RPU2: 84% to 55%

CC1:    83% to 33%

CC2:    91% to 27%

For College Algebra

RPU1: 94% to 52%

RPU2: 81% to 40%

CC1:    84% to 26%

CC2:    95% to 36%

For Calculus I

RPU1: 89% to 47%

RPU2: 85% to 44%

CC1:    91% to 25%

CC2:    94% to 59%

What would be interesting is an analysis that reveals how pass rates are correlated with persistence and with success in the next course. Does a high pass rate for a given instructor encourage persistence? Does it suggest that those who pass are less well prepared for the next course?

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