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

•Students’ learning about tangents, a topic met in different mathematical domains.•Discursive footprint of tangents is manifested to students’ consequent learning.•Learning across domains requires subsuming of discourses and new narratives.•Geometry-local hybrid discourse between what is known and w...

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Bibliographic Details
Published inThe Journal of mathematical behavior Vol. 62; p. 100870
Main Author Biza, Irene
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2021
Subjects
Commognition
Discursive footprint
Mathematical discourse
Precedents
Subsuming discourses
Tangent line
Discursive footprint
Subsuming discourses
Mathematical discourse
Precedents
Tangent line
Commognition
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Summary:•Students’ learning about tangents, a topic met in different mathematical domains.•Discursive footprint of tangents is manifested to students’ consequent learning.•Learning across domains requires subsuming of discourses and new narratives.•Geometry-local hybrid discourse between what is known and what to be known.•Potency of the discursive footprint in research and teaching. 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.
ISSN:0732-3123
1873-8028
DOI:10.1016/j.jmathb.2021.100870