(Re)Inventing mathematical logic : a case study of set-based meanings for conditional truth

Advisors: Paul C. Dawkins.Committee members: Helen Khoury; Mary Shafer.Includes bibliographical references.Includes illustrations.The way students interpret mathematical sentences involving logical connectives sometimes differs from the way mathematicians interpret such sentences. This research study identifies and analyzes some understandings that one student constructed while interpreting conditional statements relating to numerical relationships and geometric shape categories. Through a modified teaching experiment, a pair of students were guided to reinvent normative understandings of truth-functional logic, namely that of material conditionals (conditional statements) and their contrapositive's equivalence. Through the case study of Hugo, the researcher identifies shifts in his reasoning about conditional statements that gave rise to set-based meanings for conditional truth, as well as the challenges that he faced in systematizing them. The researcher further proposes a framework to characterize mathematical logic learning within mathematical content, and distinguishes three sequential levels of logic learning. These three levels operationalize logic learning analytically and pedagogically by providing concise criteria for collecting and measuring mathematical logic learning data. This study contributes to the body of related research by providing elements of a Local Instructional Theory for the guided reinvention of truth-functional logic.M.S. (Master of Science