PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
A Framework for Characterizing Students’ Thinking about Logical Statements and Truth Tables
Page: 105
While a significant amount of research has been devoted to exploring why university students struggle applying logic, limited work can be found on how students actually make sense of the notational and structural components used in association with logic. This project borrows the theoretical framework of unitizing and reification, which have been effectively used to explain the types of integrated understanding required to make sense of symbols involved in numerical computation and algebraic manipulation, to investigate students’ conceptualizations of truth tables and implication statements. We use a continuum as a framework to analyze the degree to which students’ thinking of each is compartmentalized versus unified. Results indicate that students tend to treat the constituent pieces that make up these mechanisms independently without an understanding of each as a whole or an integrated view of the two together. Consequently, students manipulate symbols without an appreciation of the overarching meaning.