Investigating a potential format effect with two-column proofs

Abstract

Abstract The current study aims to explore the impact of the two-column format in writing simple mathematical arguments. That is to say, a structured method of presenting a mathematical proof or argument by using a tabular layout with two columns. The underlying goal of the research reported in this paper is to inform understanding of how to effectively assess students’ proof construction, particularly online. In this paper, we report the results of an experiment designed to test the hypothesis that students provide more justifications when using the two-column format in writing mathematical proofs. The participants were 80 first year undergraduate mathematics students at the University of Edinburgh who were enrolled in a calculus course. The findings supported this hypothesis: overall frequency of justification were higher in the two-column condition compared with the traditional condition. This is due to the format structure where students are expected to justify each line in the statements’ column with a corresponding explanation in the justification column. However, as a side effect of increasing the amount of justifications, students in the two-column group generated more non-explanation statements which we classed as paraphrasing. A secondary outcome was our use and further development of the coding scheme.