The discursive footprint of learning across mathematical domains: The case of the tangent line

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Abstract

This paper employs the commognitive frame (Sfard, 2008) to investigate how experiences with tangents across mathematical domains leave their marks on students’ subsequent work with tangents. To this aim, I introduce the notion of the discursive footprint of tangents and its characteristics by reviewing how tangents are used across mathematical domains in school textbooks. Manifestations of this footprint were sought in 182 undergraduate mathematics students’ responses to a questionnaire about tangents by labelling their responses and by identifying patterns in the endorsed narratives. Manifestations include the identification of characteristics of sole (and combination of) discourses (geometry, algebra, calculus, mathematical analysis) in student responses. Five themes emerged from the analysis: apparent replication of word use in different narratives; geometry-local hybrid discourse; endorsement of conflicting narratives; enrichment of familiar narratives with new words; and, mathematical analysis as a subsuming discourse. Finally, I discuss the potency of the discursive footprint in research and teaching.
Original languageEnglish
Article number100870
JournalThe Journal of Mathematical Behavior
Volume62
Early online date15 Apr 2021
DOIs
Publication statusPublished - Jun 2021

Keywords

  • Commognition
  • Discursive footprint
  • Mathematical discourse
  • Precedents
  • Subsuming discourses
  • Tangent line

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