Justification and Proof-Writing in Calculus I through Group Homework Assignments

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or four, beginning in class and finishing outside of class. In this paper, we explore examples of homework questions that promote abstract thought and the details necessary to implement this system in a calculus class. We discuss the ways in which group assignments invalidate solutions found online and ease the grading burden for the instructor. We mention possible pitfalls of this approach as well as ways in which to avoid them. Finally, we discuss student attitudes and feedback on this particular method of homework.