Undergraduate and Instructor Perspectives on Learning in First-Year Mathematics Courses in the United States: A Case Study in Calculus

Abstract

This paper reports on post-secondary student and instructor perceptions of teaching practices they see as supporting student success in calculus. The study used a mixed-methods design, combining survey, classroom observation, and interviews. Analysis identified two central clusters of survey response, each aligned with one of two well-specified aspects of self-regulation: coping intention or learning intention. In the coping intention factor, students sought supports to reduce uncertainty, such as having precise instructions and predictable question types on tests. Interview analysis offered insight into ways of coping in situations that students experienced as high-stakes—where the goal of self-regulation was to survive. The learning intention factor included student reports on knowledge of the prerequisite mathematics for the course and assertions that they had responsibility for their learning (rather than assigning it to the instructor). Interviews shed light on how students managed responsibility and motivation in the context of being challenged in mathematics learning. Implications for future research and for instruction attend to the complex dynamics of cognition, affect, motivation, and regulation in the teaching and learning of calculus.