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

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Scripting Approaches in Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

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.

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Notes

  1. 1.

    A version of the task which used a true existential statement with a set of accompanying arguments was also developed and field tested, but will not be discussed in this chapter.

  2. 2.

    This feature was introduced into the task design after gender bias was detected in a pilot study, when both male and female characters were used.

  3. 3.

    Text in square brackets is added to clarify the meaning, or describe student actions.

  4. 4.

    All emphases and comments in parentheses appeared in the originals. PSTs’ names are replaced with pseudonyms.

  5. 5.

    For this analysis, the four rating options (incorrect, more incorrect than incorrect, more correct than incorrect, and correct) were collapsed into two, roughly, incorrect/correct options.

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Author information

Authors and Affiliations

  1. University of New Hampshire, Durham, NH, USA

    Orly Buchbinder

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  1. Orly Buchbinder
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Correspondence to Orly Buchbinder .

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Editors and Affiliations

  1. Simon Fraser University, Burnaby, British Columbia, Canada

    Rina Zazkis

  2. University of Michigan, Ann Arbor, Michigan, USA

    Patricio Herbst

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Buchbinder, O. (2018). Who is Right? – What Students’ and Prospective Teachers’ Responses to Scripted Dialog Reveal About Their Conceptions of Proof. In: Zazkis, R., Herbst, P. (eds) Scripting Approaches in Mathematics Education . Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-62692-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-62692-5_5

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