Who is Right? – What Students’ and Prospective Teachers’ Responses to Scripted Dialog Reveal About Their Conceptions of Proof



  • 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.
  • Status

    Publication Date

  • 2018
  • Keywords

  • Conceptions of proof
  • Examples and proving
  • High-school students
  • Prospective teachers
  • Scripted arguments
  • Digital Object Identifier (doi)

    International Standard Book Number (isbn) 13

  • 9783319626918
  • Start Page

  • 89
  • End Page

  • 113