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Student Teachers’ Argumentation 1 DRAFT – Please do not cite or distribute – DRAFT Running Head: ARGUMENTATION PRACTICES AND CONCEPTIONS OF PROOF Student Teachers’ Argumentation Practices in View of Their Conceptions of Proof AnnaMarie Conner University of Georgia AnnaMarie Conner, Department of Mathematics and Science Education, University of Georgia. This paper is based in part on the author’s doctoral dissertation, completed at The Pennsylvania State University under the direction of Rose Mary Zbiek, supported in part by the National Science Foundation under Grant ESI0083429 to the University of Maryland with a major subcontract to The Pennsylvania State University and by a research initiation grant from The Pennsylvania State University College of Education Alumni Society. Any opinions, findings, and conclusions or recommendations expressed in this document are those of the author and do not necessarily reflect the views of the National Science Foundation or the College of Education Alumni Society. I would like to thank Andrew Izsák, Eric Knuth, Rose Mary Zbiek, Glen Blume, and Susan Peters for their valuable critiques of this manuscript. Correspondence concerning this article should be addressed to AnnaMarie Conner, Department of Mathematics and Science Education, University of Georgia, Athens, Georgia 30602. E-mail: [email protected] Teachers’ Argumentation 2 DRAFT – Please do not cite or distribute – DRAFT Abstract Student teachers’ conceptions of the purpose and need for proof in mathematics were found to align with their support for argumentation in secondary mathematics classes. Student teachers’ conceptions of proof were inferred from interviews, while classroom observations provided most of the data about support for argumentation. A modification of Toulmin’s argument diagrams was used to analyze the argumentation. The student teachers provided and elicited different kinds of warrants in arguments of differing complexity within discourse that, on the surface, could be characterized as IRE. In addition, analysis of argumentation by means of Toulmin’s diagrams is shown to be useful even in classrooms where effective argumentation is not the focus of the teacher.Student Teachers’ Argumentation 3 DRAFT – Please do not cite or distribute – DRAFT Student Teachers’ Argumentation Practices in View of Their Conceptions of Proof While the nature of the relationship between argumentation and proof is difficult to articulate, one can view proof as a specific kind of argumentation, as is described by Pedemonte (2007). Argumentation and proof share a similar dependence on justification, which Yackel and Hanna (2003) describe as giving reasons for a mathematical action or statement “in an attempt to communicate the legitimacy of one’s mathematical activity” (p. 229). In a proof1, these reasons must be mathematical in nature, building upon one another deductively with an axiom system. In argumentation within a classroom, however, the reasons given for an action or statement may not be mathematical in nature. The collective argumentation that occurs in mathematics classrooms has been shown to influence student learning (Krummheuer, 1995), and the role of the teacher within this argumentation is very important (Yackel, 2002). In this study, I investigated a possible relationship between how a teacher thinks about proof and how he or she supports collective argumentation in a secondary mathematics class. Much of the research on argumentation in mathematics education has investigated the phenomenon in classes in which the teacher is part of the research team or is working closely with the research team to design lessons and facilitate argumentation among students. These studies were generally conducted in elementary and middle school classrooms with a conscious emphasis on argumentation on the part of the teacher, and the collective argumentation that is described is characterized by rich student-to-student (and student-and-teacher) interactions (e.g., Forman & Ansell, 2002; Krummheuer, 1995; Zack & Graves, 2001). One goal of this study is to provide a picture of what argumentation looks like in regular public high school classrooms where its facilitation is not an explicit goal of instruction. 1 I consider a proof to be a logically correct deductive argument built up from given conditions, definitions, and theorems within an axiom system.Student Teachers’ Argumentation 4 DRAFT – Please do not cite or distribute – DRAFT A definition of proof as a logically correct deductive argument highlights the connection between proof and argumentation as one thinks about a proof as a particular kind of argument. However, considering the relationship implied by this definition does not clarify whether engaging in collective argumentation might lead to improved ability to construct proofs or how a teacher’s knowledge of proof may influence his or her practice with respect to argumentation. Given the dependence of argumentation and proof on justification (as described by Yackel & Hanna, 2003), it is reasonable to believe that a teacher’s conceptions of proof may relate to how he or she facilitates argumentation in his or her classroom. A second goal of this study is to explore a possible connection between one aspect of a student teacher’s conception of proof and his or her support for collective argumentation. This study extends the current literature on argumentation and attempts to connect the work on proof with research on collective argumentation by examining the following questions. • How do prospective secondary mathematics teachers support collective argumentation in secondary mathematics classrooms? • What characterizes the relationship between the argumentation observed in a particular classroom and the prospective teacher’s conception of proof and justification? Conceptual underpinnings Krummheuer (1995) describes collective argumentation as “a social phenomenon, when cooperating individuals tried to adjust their intentions and interpretations by verbally presenting the rationale of their actions” (p. 229). Collective argumentation, as described by Krummheuer, embodies much of the spirit of both the Reasoning and Proof Standard and the Communication Standard in the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000). These two


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UGA EMAT 8990 - Conner_Arg_Proof_for_8990

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