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Article
Beyond the binary: dexterous teaching and knowing in mathematics education
Mathematics Teacher Education and Development
  • Raoul Adam, James Cook University
  • Philemon Chigeza, James Cook University
Document Type
Article
Publication Date
1-1-2014
Peer Reviewed
Peer-Reviewed
Abstract

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive, student-centred/teacher-centred, discovery/transmission, constructivist/behaviourist) and epistemically relevant binaries (e.g., concrete/abstract, pure/applied, interpretivist/positivist, subjective/objective) that operate in mathematics classrooms. The premise of this paper is that ways of knowing mathematics (i.e., epistemologies) are actualised in ways of teaching mathematics (i.e., pedagogies), and vice-versa. The binary-epistemic model describes oppositional, equipositional and parapositional ways of knowing and teaching in relation to these binaries. We argue for a more a relational-contextual or parapositional approach to binary polarities that have otherwise proven divisive in mathematical discourse. In the context of the new Australian Curriculum, we illustrate epistemically differentiated ways of teaching measurement in a Year 5 mathematics classroom.

Disciplines
Citation Information

Adam, R & Chigeza, P 2014, 'Beyond the binary: dexterous teaching and knowing in mathematics education', Mathematics Teacher Education and Development, vol. 16, no. 2, pp. 108-125.