Proof, proving, and teacher-student interaction: theories and contexts
Jones, Keith and Herbst, Patricio (2012) Proof, proving, and teacher-student interaction: theories and contexts. In, Gila Hanna and Michael de Villiers (eds.) Proof and Proving in Mathematics Education: the 19th ICMI Study. New York, US, Springer, 261-277. (New ICMI Study Series, 15). (doi:10.1007/978-94-007-2129-6_11).
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This chapter focuses on the role of the teacher in teaching proof and proving in the mathematics classroom. Within an over-arching theme of diversity (of countries, curricula, student age-levels, teachers' knowledge, and so forth), we review three carefully-selected relevant theories: socio-mathematical norms, teaching with variation, and instructional exchanges. Each of these theories starts from the abstraction of observations in existing school mathematics classrooms and uses those observations to probe into the rationality of teachers in order to understand what sustains those classroom contexts and also how such contexts might be changed. We argue that each theory offers insight into the role of the teacher in the teaching and learning of proof and proving. In informing future research, this chapter provides support for meeting the challenge of theorising about the role of the teacher in the teaching and learning of proof and proving in mathematics classrooms across the diverse contexts worldwide.
|Item Type:||Book Section|
|Digital Object Identifier (DOI):||doi:10.1007/978-94-007-2129-6_11|
|Additional Information:||The pagination of this author's version is almost identical to the published version.|
|Keywords:||pedagogy, curriculum, teaching, learning, mathematics, geometric, geometrical, deductive reasoning, proof, proving, school, national curriculum, euclid, euclidean, classroom, student, teacher, interaction, socio-mathematical norms, variation, instructional exchange, theory, theories, variation theory, teaching with variation|
|Subjects:||L Education > LB Theory and practice of education > LB2361 Curriculum
Q Science > QA Mathematics
|Divisions:||University Structure - Pre August 2011 > School of Education > Mathematics and Science Education
Faculty of Social and Human Sciences > Southampton Education School > Mathematics, Science & Health Education (MSHE)
|Date Deposited:||03 May 2011 08:21|
|Last Modified:||15 Jan 2015 09:20|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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