Beyond Plug and Chug: an Analysis of Calculus I Homework

Abstract

We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan's (ZDMThe International Journal on Mathematics Education, 44(5), 601-612, 2012) adaptation of the instructional triangle and Brousseau's (1997) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.Keywords Post-secondary . Calculus . Homework . Student reports . Didactical contract . Mixed methodsHomework is an important part of how students develop fluency with the ideas and techniques in mathematics in general, and in calculus in particular. This is especially true at the undergraduate level, where the expectation is that students spend considerable time outside of class working on homework and studying course material. For example, Int. J. Res. Undergrad. Math. Ed. (2015) Rasmussen and Ellis (2013) found that post-secondary science, technology, engineering, and mathematics (STEM) intending students in the United States (US) reported spending approximately six h a week preparing (studying, reading, and doing homework or lab work) for Calculus I, a course with typically four contact hours per week. The time undergraduate students spend outside of class is an important venue to grapple with the material and interact with the content. In this study, we investigate the relationship between the nature of Calculus I homework at five PhD-granting universities identified as having a more successful Calculus I program than comparable universities. The Calculus I programs at the five universities were selected as part of a large, US national study at over 500 institutions, including Associates-granting 2-year colleges, Bachelors-granting 4-year colleges, Masters-granting universities, and PhD-granting universities (as determined by the highest degree offered in mathematics). These five sites were selected because students at these universities were more successful in Calculus I when compared to students at comparable universities when controlling for student background and other factors. Student success variables included increased confidence, interest, and enjoyment of mathematics, grade in Calculus I, and persistence to Calculus II. This project enabled us to ask the following questions that shed light on how homework is...

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