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The Interaction of Geometric and Spatial Reasoning: Student Learning of 2D Isometries in a Special Dynamic Geometry Environment

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2018, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
The relationship between spatial reasoning and success in mathematics has been well established. However, the ways in which spatial reasoning is used in mathematics learning is not clearly understood. Many current studies investigating spatial reasoning in mathematics quantitatively correlate aspects of students’ mathematical proficiency with standardized measures of spatial reasoning. To extend the research that connects spatial ability and the learning of mathematics, there is a need for studies that elaborate the ways in which students use spatial reasoning while learning specific mathematics content. The present study examines the relationship between spatial reasoning and geometric reasoning in the context of 2D isometries, specifically reflections and rotations. Rotations and reflections are often included in spatial reasoning assessments. Moreover, isometries are important formal mathematical concepts, which have properties, specific parameters, and lend themselves to analytic reasoning. Thus, isometries are a foundational topic for studying the link between spatial reasoning and the learning of mathematics. The present study investigated student learning of reflections and rotations using a special dynamic geometry environment. Drawing on a constructivist view of learning, the environment integrates dynamic motion with a grid in which students can learn the geometric properties of isometries while using visualization and analytic reasoning. The methodology of the study is one-on-one teaching experiments. The research questions motivating the study are the following: (1) What types of spatial reasoning do students use while learning about reflections and rotations in the special dynamic computer environment? (2) How do students’ analytic and mental imagery strategies interact while learning about reflections and rotations in the environment? (3) In the context of learning about reflections and rotations in the environment, how is property-based knowledge related to analytic and spatial reasoning? The results of this study show how spatial visualization and spatial-analytic reasoning were interrelated in students' problem solving on a variety of tasks. Students used both static and dynamic mental models to support their visual reasoning with varying levels of success depending on the problem type. Students also showed evidence of implicit and explicit property knowledge. The study describes the mental models students used when solving problems about reflections and rotations and proposes four new configurations describing the inter-relationship between spatial visualization and spatial analytic reasoning. The study also outlines how the processes of coordination and integration were used as students constructed and employed their mental models for solving problems about isometries. The results provide new models and theory that can describe more clearly how students come to understand new ideas in geometry.
Michael Battista (Advisor)
Patricia Brosnan (Committee Member)
Theodore Chao (Committee Member)
351 p.

Recommended Citations

Citations

  • Frazee, L. M. (2018). The Interaction of Geometric and Spatial Reasoning: Student Learning of 2D Isometries in a Special Dynamic Geometry Environment [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531862080144028

    APA Style (7th edition)

  • Frazee, Leah. The Interaction of Geometric and Spatial Reasoning: Student Learning of 2D Isometries in a Special Dynamic Geometry Environment. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1531862080144028.

    MLA Style (8th edition)

  • Frazee, Leah. "The Interaction of Geometric and Spatial Reasoning: Student Learning of 2D Isometries in a Special Dynamic Geometry Environment." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531862080144028

    Chicago Manual of Style (17th edition)