Undergraduate course variations in precalculus through Calculus 2

Abstract

Precalculus and single-variable calculus courses are a critical early juncture for the success of science, technology, engineering, and mathematics (STEM) students in the United States (US). The default course structure is often a required three-term sequence of precalculus, differential calculus, and integral calculus. In this paper we analyse variations to this structure, the nature of such variations, their frequency across US universities, and how instructional approach and performance rates in those variations compare to those in the standard course offerings. We found that course variations are relatively common, and are primarily targeting students with more math preparation, less math preparation, or those majoring in a specific discipline. We found that for less prepared students, who are typically at the highest risk of failing, course variations resulted in similar passing rates, essentially levelling the playing field for these students. Although we had conjectured that disruptions to the standard offering would allow for greater use of active learning strategies, no such difference was observed. Ways in which these course variations can redress systemic educational inequalities, opportunities for design improvement, and future research are discussed.

KEYWORDS:

• Calculus
• precalculus
• curriculum
• course variations
• undergraduate

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The conventional sequences institutions on the quarter system may be slightly different (e.g. three quarters to cover Calculus 1 and 2), but similar in spirit. For ease of description we only spelled out the conventional sequence in terms of semesters.

2 Calculus AB is a first course in differential calculus offered through the advanced placement system, which is a programme in the US and Canada that offers college level curricula and examinations to high school students.

3 The SAT is a standardized test widely used for college admissions in the US with scores for the math portion of the examination ranging between 200 and 800.

Additional information

Funding

Support for this work was funded by the National Science Foundation (NSF) under Grant number 1430540. The opinions expressed do not necessarily reflect the views of NSF.