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Development Process of a Praxeology for Supporting the Teaching of Proofs in a CAS Environment Based on Teachers’ Experience in a Professional Development Course

  • Nurit Zehavi
  • Giora Mann
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Abstract

This paper presents the development process of a praxeology (theory-of-practice) for supporting the teaching of proofs in a CAS environment. The characteristics of the praxeology were elaborated within the frame of a professional development course for teaching analytic geometry with CAS. The theoretical framework draws on Chevallard’s anthropological approach to the didactics of mathematics and Duval’s analysis of transformations within and between registers of semiotic representations. The teachers (n = 43) were asked (a) to draw conjectures regarding unfamiliar behavior of tangents to hyperbola, before and after exploration using given slider bars; and (b) to prove their conjectures after being exposed to the algebraic expressions underlying the slider bars. The teachers were also asked twice, before and after (b), to rate the need to ask students for an algebraic proof in similar tasks. Three types of proofs are presented in an increasing order of the level of mathematical maturity exhibited in each proof. Based on results coming from the empirical study, we propose a praxeology for preparing teachers to teach proofs consisting of Task design, Techniques, and Didactical discourse.

Keywords

Computer algebra systems Proof Analytic geometry Praxeology Semiotic representations Slider bars 
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Notes

Acknowledgment

The authors thank the editors-in-charge and the reviewers for their encouragement and constructive comments in shaping this paper.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Science Teaching DepartmentThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Beit ChananRehovotIsrael

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