RUME 26
2024
Omaha, Nebraska
Factors Influencing Undergraduate Students’ Logical (in)Consistency (LinC) in Mathematical Contexts
Page: 378
This study delves into undergraduate students’ ability to self-monitor and organize their claims coherently to ensure logical consistency when evaluating mathematical statements and validating accompanying arguments. To assess the capacity of undergraduate students to maintain logical consistency in mathematical contexts, we designed an online instrument comprising twenty statement-argument pairs, each rooted in mathematical content. We administered this online instrument to 205 undergraduate students, encompassing various levels of proof experience, across three diverse U.S. higher education institutions, including two large public universities and one small liberal arts college. Our analysis reveals a substantial number of undergraduate students displayed logical inconsistencies. It also appears that students may exhibit different levels of logical inconsistencies when the accompanying argument is framed using proof by contradiction, as opposed to direct proof. This prevalence underscores a critical concern in mathematics education, particularly proof-oriented mathematics.