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An Exploration of the Interplay among Teacher Intervention, Dynamic Geometry Software and Students’ Mathematical Generalizing Practices about Properties of Geometric Transformations

Yao, Xiangquan, Yao
http://rave.ohiolink.edu/etdc/view?acc_num=osu1530616428632192

Abstract Details

2018, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
Making generalization is fundamental to mathematics and a crucial component of mathematical thinking. Developing learners’ capacity towards making and justifying generalizations about mathematical relationships has been a pivotal goal of mathematics education for decades. The purpose of this study was to examine how students construct generalizations in a technology-rich instructional environment and the teacher’s role in supporting students’ generalizing practices. A design research was used to study seven middle school students’ work when they engaged in learning geometric transformations in the presence of dynamic geometry software. Data processing and analysis consisted of five phases. In Phase I, generalizing episodes were identified within those mathematical activities. In Phase II, Pirie-Kieren’s (1994) theory for growth of mathematical understanding was utilized to trace the development of each generalizing episode. Critical interactional moments and how technology was used were recorded. In Phase III, all the observations, conjectures, and generalizations the participants shared in each generalizing episode were identified and categorized based on their level of generality and their connection to a broader mathematical structure. Phase IV involved analysis of teacher interventions and technological mediations. Phase V of analysis considered folding back activities among the generalizing episodes. Data analysis revealed: (1) three types of mathematical generalizations; (2) nine categories of teacher interventions that promote productive generalizing practices; (3) five types of technological mediations; and (4) a framework for categorizing folding back activities. Analysis of the generalizing episodes and the associated event maps suggested that: (1) students’ construction of mathematical generalizations were shaped by mathematical tasks, teacher interventions, and technological tools; (2) although property-based, construction-based, and theory-based generalizations became observable only at the stage of Property Noticing or Formalizing, understanding activities at the stage of Image Making and Image Having were crucial in the construction of generalizations; and (3) different categories of teacher interventions and technological mediations occurred at different stages of understanding. This study described how instructional interactions and technology might impact the construction and refinement of mathematical generalizations.
Azita Manouchehri (Advisor)
Michael Battista (Committee Member)
Patricia Brosnan (Committee Member)
Lin Ding (Committee Member)
307 p.
Mathematics Education

Recommended Citations

Citations

  • Yao, Yao, X. (2018). An Exploration of the Interplay among Teacher Intervention, Dynamic Geometry Software and Students’ Mathematical Generalizing Practices about Properties of Geometric Transformations [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1530616428632192

    APA Style (7th edition)

  • Yao, Yao, Xiangquan. An Exploration of the Interplay among Teacher Intervention, Dynamic Geometry Software and Students’ Mathematical Generalizing Practices about Properties of Geometric Transformations. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1530616428632192.

    MLA Style (8th edition)

  • Yao, Yao, Xiangquan. "An Exploration of the Interplay among Teacher Intervention, Dynamic Geometry Software and Students’ Mathematical Generalizing Practices about Properties of Geometric Transformations." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1530616428632192

    Chicago Manual of Style (17th edition)

osu1530616428632192
469
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This open access ETD is published by The Ohio State University and OhioLINK.