A procedural route toward understanding aspects of proof: Case studies from real analysis

In this paper, I describe how some students can successfully develop their understanding of proof techniques by viewing the act of proving as a procedure. This learning route is discussed within the context of a study in which 1 investigated the learning of six undergraduates in a first course in real analysis. These undergraduates first understood proof as an algorithm—or a step‐by‐step mechanical prescription for proving certain types of statements. They then condensed this algorithm into a process—or a shorter list of global, qualitative steps. By reflecting on the process, the successful students in this study viewed proving as forming an argument, or as an act that establishes the veracity of a mathematical statement. I illustrate this learning route by presenting a detailed analysis of two of the students from this study. Finally, I note that many of the students in this study who viewed proof as a process failed to view proof as an argument by the end of the course and I discuss the consequences of these students’ narrow view of proof.