Student Understanding of Reasoning and Proof and Its Connections to Curriculum

Welcome to In Search of Research. In this column I will review research in mathematics education and discuss the implications of that research for teaching. I would like to begin with the topic of reasoning and proof since mathematicians consider it to be a key ingredient in the practice of engaging in mathematics (Ross, 1998; Schoenfeld, 2009), yet it is an area in which students consistently struggle (Chazan, 1993; Harel & Sowder, 2007; Healy & Hoyles, 2000; Senk, 1985). In this column I will describe the areas in which students struggle in learning proof, discuss a tool to help think about students' reasoning and proof understandings, describe research involving the prevalence of reasoning and proof within written curricula, examine the connections between students' reasoning and proof capabilities and classroom lessons, and suggest how considering the roles that reasoning and proof can serve can help place importance on reasoning and proof in the classroom.