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Pre-Service Teachers’ Understandings of Isometries

Clayton, Emanuel
http://rave.ohiolink.edu/etdc/view?acc_num=osu1597915853566819

Abstract Details

2020, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
The purpose of the present study was to examine: 1) the nature of pre-service elementary and middle school teachers’ knowledge of isometries; 2) the relationship between visualization, analytic strategies, and knowledge of the prototypical defining properties of isometries; and 3) how the use of the isometry modules in the iDGi dynamic geometry environment can improve these pre-service teachers’ understanding of isometries and use of spatial visualization. The participants for the study consisted of four volunteer pre-service elementary and middle childhood teachers from the Department of Teacher Education working towards a Bachelor of Science in Education degree at a public research university in the midwestern United States. Each pre-service teacher participated in one-on-one, video-recorded teaching experiments implemented with instructional modules on isometries in the Individualized Dynamic Geometry Instruction (iDGi) environment. iDGi is a computer/iPad-implemented, learning-progression-based, dynamic geometry learning system for intermediate/middle school that can be used by students independently or in classrooms with teacher guidance. Individual case studies for each participant detail the development of knowledge of isometries exhibited by participants while completing iDGi isometry modules and how their visualization and analytic, property-based reasoning interacted. Overall, the findings of the study indicate that the iDGi environment enhanced participants' understanding of isometries. In general, students moved away from Level 1 visual-holistic reasoning toward Level 2.3 formal property-based reasoning, with the largest shifts in reasoning occurring for rotations and reflections (although some students continued to struggle with reflections about obliques lines). Even though participants used various configurations of spatial visualization, analytic strategies, and knowledge of properties when reasoning about isometries, the iDGi isometry modules helped participants develop analytic strategies that were more consistent with prototypical defining properties of isometries based on their parameters, and seemed to increase participant links between visualization and properties. The results of the study may help in developing a more detailed learning progression for isometries, and they suggest possible improvements in instructional task design and follow-up research.
Michael Battista (Advisor)
Azita Manouchehri (Committee Member)
Patricia Brosnan (Committee Member)
Mathematics Education
isometries; geometry; reflections; translations; rotations; spatial reasoning; geometric reasoning; education; mathematics education; pre-service teachers; prospective teachers

Recommended Citations

Citations

  • Clayton, E. (2020). Pre-Service Teachers’ Understandings of Isometries [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1597915853566819

    APA Style (7th edition)

  • Clayton, Emanuel. Pre-Service Teachers’ Understandings of Isometries. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1597915853566819.

    MLA Style (8th edition)

  • Clayton, Emanuel. "Pre-Service Teachers’ Understandings of Isometries." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1597915853566819

    Chicago Manual of Style (17th edition)

osu1597915853566819
207
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This open access ETD is published by The Ohio State University and OhioLINK.