MIDDLE GRADES STUDENTS' EMERGING BELIEFS ABOUT ARGUMENTATION

Students learn norms of proving mathematically by observing teachers generate proofs, engaging in proving, and generalizing features of proofs deemed convincing by their mathematics instructor or textbook. This study investigated aspects of proofs and non-proofs that were convincing to middle grades students. Fourteen students completed proof evaluation items in number theory and geometry. In each item, both an empirical and a general argument were provided. Students tended to prefer the empirical argument for the number theory statement but valued the explanatory power of an argument when evaluating a proof for a true geometry statement that provided a diagram. Data analysis yielded a descriptive model to illustrate the factors that middle grades students' value when evaluating arguments.