When the Problem Seems Answerable yet the Solution is Unavailable: Affective Reactions Around an Impasse in Mathematical Discourse

Einat Heyd-Metzuyanim, Jason Cooper

Research output: Contribution to journalArticlepeer-review

Abstract

Situations where students encounter mathematical "impasses" – instances where their current discourse is incommensurable with the discourse demanded to solve a task – have the potential to stir emotional responses of different types. They can engender feelings of confusion and bafflement, or even embarrassment, or alternatively open students' curiosity to the ways by which more advanced mathematics can solve a problem. In this study, we closely examine the subjectifications (affective communication) of a group of graduate students encountering such an impasse in the form of a request to account for the area and perimeter of the Sierpiński triangle. We analyze these subjectifications in relation to an a priori mathematical analysis of the impasse inherent in the task. We show two major types of subjectifications, found to be communicated by distinct members of the classroom: "I'm baffled", and "this is not a problem". We show how the students subjectifying "this is not a problem" were those who avoided engagement with the impasse by attending only to the infinite process that defines the fractal, while those students who subjectified "I'm baffled" were those who engaged with the process as well as its outcome. Moreover, despite the lack of substantial contribution to the exploration of the impasse by those students who subjectified "this is not a problem", they were positioned as the "explainers", in a position of power relative to those students who expressed bafflement. We conclude by discussing the dialectical relationship between identity and engagement with mathematical impasses.

Original languageEnglish
Pages (from-to)605-631
Number of pages27
JournalInternational Journal of Research in Undergraduate Mathematics Education
Volume9
Issue number3
DOIs
StatePublished - 13 May 2022

Keywords

  • Affect
  • Commognition
  • Discourse
  • Discussion
  • Identity
  • Impasse
  • Inquiry
  • Positioning
  • mathematical explorations

All Science Journal Classification (ASJC) codes

  • Education
  • Mathematics (miscellaneous)

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