This chapter explores the potential of using scripted student responses,
embedded in a task titled Who is right?, as a tool to diagnose argumentation and proof-related conceptions of high-school students and pre-service mathematics teachers (PSTs). The data, collected in two separate studies, were examined for evidence of participants’ conceptions of the role of examples in proving and refuting universal statements. Additional analysis explored what types of criteria are
used by the high-school students and the PSTs when evaluating scripted arguments, as well as whether participants were consistent in their evaluations across the collection of arguments. The data revealed that, when evaluating scripted arguments, high-school students used mainly mathematical criteria and strived to maintain consistency in their evaluations across the collection of arguments. On the contrary,
PSTs applied both mathematical and pedagogical considerations in their evaluations, thus judging multiple, and even contradictory arguments as correct.
