PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Cognitive Consistency and Its Relationships to Knowledge of Logical Equivalence and Mathematical Validity
Page: 257
The purpose of this study is to explore how cognitive consistency in logical thinking is related to knowledge of logic and knowledge of mathematical validity. We developed a logic instrument and administered it to forty-seven (47) undergraduate students who enrolled in various sections of a transition-to-proof course. The analysis of the students’ scores on the logic instrument indicated that students’ knowledge of logical equivalence and their knowledge of mathematical validity were somewhat related to one another. On the other hand, cognitive consistency was not closely related to either student knowledge of logic or knowledge of mathematical validity. Based on these findings, we address the importance of cognitive consistency in logical thinking and discuss implications for the teaching and learning of logic in mathematical contexts.