Title: Beyond the Surface: Exploring the Content Underlying Instructional Tasks in Calculus 

 

Abstract: Although lecture still dominates calculus instruction, incorporating more inquiry has been advocated to make the course more accessible. Despite this shift, existing research in undergraduate mathematics education has primarily focused on pedagogical variables, often overlooking the critical role of content. This oversight has not consistently yielded positive student outcomes. Alternatively, I shift my focus to the content instructors and students engage with in these classrooms. In this talk, I will share what I have learned about the teaching of calculus with inquiry through eight instructors’ instructional tasks for teaching derivatives. A pivotal finding emerges as the analysis reveals that, although instructional tasks may exhibit surface-level similarities and common patterns across instructors, there exists a high variability in work that is expected of students. This finding highlights the importance of understanding the nuanced ways in which instructors structure tasks to effectively implement inquiry-based teaching strategies in calculus education.