PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Partitioning a Proof: An Exploratory Study on Undergraduates’ Comprehension of Proofs
Page: 581
In this paper, we explore eleven undergraduate students’ comprehension of two proofs taken from an undergraduate abstract algebra course. Our interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). This study in particular examines the extent to which undergraduate students are able to modularize a proof using the proof’s key ideas. Additionally, eleven doctoral students in mathematics, referred in this paper as experts, were asked to provide modular structures for the same proofs that the undergraduate students received. We employed experts’ modular structures of the proofs to analyze that of undergraduates’. The main finding of the study is that, contrary to experts’ proof modularization, undergraduates partitioned the proofs in a way that failed to highlight how key components of the proofs are logically linked, suggesting an inadequate proof comprehension.