Type of Document Dissertation Author Kobiela, Marta Anna URN etd-11302012-143043 Title Mathematical defining as a practice: Investigations of characterization, investigation, and development Degree PhD Department Teaching and Learning Advisory Committee

Advisor Name Title Richard Lehrer Committee Chair Ilana Horn Committee Member Leona Schauble Committee Member Philip Crooke Committee Member Keywords

- mathematical defining
- mathematical definition
- mathematical practices
Date of Defense 2012-08-09 Availability unrestricted AbstractIn recent years, the field of mathematics education has advocated for an expanded view of what it means to know mathematics and participate in mathematics as a practice. Here, I present three papers that describe my investigations of how students participate in the important mathematical practice of defining. The first paper consists of a review of research about how K-16 students participated in establishing and refining mathematical definitions. Analysis of the forms of activity revealed by this research led to the construction of a synthetic framework to more closely describe the practice of defining, which I termed Aspects of Definitional Practice. These aspects included asking definitional questions, constructing and/or evaluating examples, and constructing definitional explanations or arguments. In the second paper, the Aspects framework served as a lens for investigating how defining was initially established in one middle school classroom. The analysis focused on how defining was realized in interactions among students and between the teacher and students. The third paper describes how studentsâ€™ participation in Aspects of Definitional Practice developed over time, and how change in participation influenced the development of mathematical knowledge. Collectively, the three papers provide: (a) an analytic and theoretical framework for examining the mathematical practice of defining as it might be constituted in classrooms; (b) an analysis of the initial establishment of this form of practice as instantiated in interaction among students and their teacher; and (c) an investigation of how knowledge, practice and the interactions that contribute to their co-constitution develop and change over time.Files

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