On the Persuasiveness of Visual Arguments in Mathematics

Abstract

Abstract. Two experiments are reported which investigate the factors that influence how persuaded mathematicians are by visual arguments. We demonstrate that if a visual argument is accompanied by a passage of text which describes the image, both research-active mathematicians and successful undergraduate mathematics students perceive it to be significantly more persuasive than if no text is given. We suggest that mathematicians' epistemological concerns about supporting a claim using visual images are less prominent when the image is described in words. Finally we suggest that empirical studies can make a useful contribution to our understanding of mathematical practice.

Are You Convinced? Middle‐Grade Students' Evaluations of Mathematical Arguments

“…What is clear is that even as seventh graders, these students are reading arguments beyond surface features they might have generalized from classroom work, such as that writing complete sentences is good or providing examples is bad, and they are looking for whether the arguments provide enough information to help the reader understand why the statement is true. Similarly, mathematicians expect visual arguments to be accompanied by verbal explanations (Inglis & Mejia‐Ramos, ), and these results suggest that students begin, at the middle‐school level, to adopt conceptions aligned with the discipline that arguments must be clear and illustrate why a statement to be mathematically convincing. Table provides a summary of the reasons students provided for their choice in question 1.…”

Challenges in mathematical cognition: A collaboratively-derived research agenda

“…Recent eyemovement studies, for instance, have confirmed that undergraduate students pay less attention than mathematicians to words (as compared with symbols) in purported proofs, and that they are less likely to shift their attention around in a manner consistent with seeking deductive justifications (Inglis & Alcock, 2012). Other recent studies have revealed that mathematicians disagree on the validity of even fairly simple mathematical arguments (Inglis, Mejía-Ramos, Weber, & Alcock, 2013), that they respond in more nuanced ways than is traditionally believed to arguments based on diagrams (Inglis & Mejía-Ramos, 2009a) or presented as from an authoritative source (Inglis & Mejía-Ramos, 2009b), and that their sense of beauty in a mathematical proof is not systematically related to that proof's perceived simplicity (Inglis & Aberdein, 2015). Several of these findings challenge conventional claims about the nature of mathematical expertise by revealing more than expected heterogeneity in the experiences and judgments of mathematicians.…”

The Argument of Mathematics

“…At the same time, there is a more mature but still advancing literature on the use of diagrams in mathematical reasoning (e.g. There have been efforts to bring the two together (see in particular Inglis and Mejía-Ramos, 2009). There have been efforts to bring the two together (see in particular Inglis and Mejía-Ramos, 2009).…”