Assessment model for proof comprehension in undergraduate mathematics
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. We addressed these issues by developing a multidimensional model for assessing proof comprehension in undergraduate mathematics. The model describes ways in which teachers and researchers can generate tests to evaluate students' understanding of seven different aspects of a proof in advanced mathematics.
Why and how mathematicians read proofs
An important goal in undergraduate mathematics education is to lead math majors to think and behave more like mathematicians with respect to proof. In order to address this goal we first need to have an accurate understanding of the different proof-related activities that mathematicians engage in, the ways in which they perform them, and what their beliefs about proof actually are. Recently, we have conducted studies on the ways in which, and reasons why, mathematicians read proofs.
Comprehending alternative methods of proof presentation
In order to address students’ difficulties understanding proof in undergraduate mathematics, some researchers have proposed methods for presenting proofs that differ from the linear, abstract format in which they are traditionally presented. In a series of both qualitative and quantitative studies, we have started to address the assessment of novel proof presentation formats, focusing on the effect of structured proofs and generic proofs on student comprehension.
Preparations for proofs as instructional explanations
Another way of addressing students’ difficulties understanding proof is to design activities that would better prepare them for the reading of specific proofs. We are currently designing studies to test the effectiveness of some of these activities in student proof comprehension.