Are indirect proofs less convincing? A study of students’ comparative assessments

Abstract

It has been argued that students not only dislike but also experience a lack of conviction in relation to indirect proofs (Harel & Sowder, 1998) due to the proof’s non-constructive nature (Leron, 1985; Harel & Sowder, 1998) and students’ difficulties accepting the logi- cal theorems employed (Antonini & Mariotti, 2008). Yet, researchers have not examined these claims using comparative selection tasks involving a direct and an indirect proof, even though studies of the forms of proof students find “most convincing” often employ such tasks. To address the need for an empirical basis, three studies were conducted that employed comparative selection tasks to explore the question, “Do undergraduate mathe- matics students find indirect proofs less convincing?” Findings indicate that students’ views of the “most convincing” proof may be more nuanced and subjective that than indicated by prior research on indirect proofs and that the various forms of indirect proof (contraposition and contradiction) may not be equally compelling in the eyes of students. Dispositions towards, as opposed to against, indirect proof are also discussed.