TY - JOUR

T1 - When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers

AU - Herbst, Patricio

AU - Miyakawa, Takeshi

N1 - Funding Information:
Acknowledgments The research reported in this article is supported by NSF grant ESI-0353285 to the first author. Opinions expressed here are the sole responsibility of the authors and do not necessarily reflect the views of the Foundation. The authors acknowledge valuable conversations with Daniel Chazan and with members of the GRIP (Geometry Reasoning and Instructional Practices) research group at the University of Michigan, in particular, valuable suggestions from Michael Weiss.

PY - 2008

Y1 - 2008

N2 - While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner's perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.

AB - While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner's perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.

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U2 - 10.1007/s11858-008-0082-3

DO - 10.1007/s11858-008-0082-3

M3 - Article

AN - SCOPUS:79953869610

SN - 1863-9690

VL - 40

SP - 469

EP - 486

JO - ZDM - International Journal on Mathematics Education

JF - ZDM - International Journal on Mathematics Education

IS - 3

ER -