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Candace_Joswick_ Dissertation.pdf (47.48 MB)

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Investigating the Relationship Between Classroom Discourse and Concept Development in Geometry Learning

Joswick, Candace Domenica
http://rave.ohiolink.edu/etdc/view?acc_num=osu1500237810722885

Abstract Details

2017, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
Mathematical classroom discourse has been identified as a key element in students’ cognitive development (e.g., Forman, 1996; Lampert & Cobb, 2003; Yackel, Cobb, & Wood, 1991). In constructivist-based, inquiry classrooms, discussions can be an important way for students to use interactions within their social environment to build personal mathematical understanding. This approach is also consistent with sociocultural views on learning. “Academic mathematical Discourse practices can be understood in general as using language and other symbols systems to talk, think, and participate in the practices that lead to literate mathematical Discourse practices that are the `the objective of school learning’” (Moskovich, 2007, p. 28). The iterative process of sending and receiving communications within the mathematics classroom can shape students’ learning and mathematical dispositions. Researchers argue that as students write about their thinking, talk about their thinking with others, and respond thoughtfully to others’ mathematical ideas, they build understandings of mathematics from these interactions (Empson, 2003; National Council of Teachers of Mathematics, 2001; Yackel, 2002). While researchers agree that mathematical classroom discourse is a crucial element in students’ cognitive development, exactly what role discourse plays in regulating students’ cognitive development is undefined. Given a cognitive continuum from the conceptual understanding and reasoning students bring to school to the standards or school learning outcomes of mathematics classrooms, learning progressions describe “the successively more sophisticated ways of thinking about an idea that follow one another as students learn” (Wilson & Bertenthal, 2005, p. 48). Battista’s research on geometry learning (1992, 2009) and Learning Progression for Geometric Shapes (2007) makes evident that increases in sophistication of conceptualization are marked by and coincide with changes in language. For example, initially, students may describe a rhombus by calling it a “diamond” or, students may talk about rectangles as shapes akin to “doors” and parallelograms as “tilted” or “slanted” doors (Battista, 2012). Such informal mathematical discourse (Moschkovich, 2007) “is typically used in lower levels of learning progressions” (Battista, unpublished manuscript). As students’ understanding of the parts and properties of shapes advances, they “explicitly and exclusively use formal geometric concepts and language to describe and conceptualize shapes in a way that attends to a sufficient set of properties to specify the shapes” (Level 2.3; Battista, 2007, 2012). Fittingly, no longer is a student describing a rectangle as a “door;” the student’s use of “rectangle” “refers to a class of shapes that possesses all the properties the student has come to associate with the set of rectangles” (Battista, 2007). Although language changes that occur in connection with conceptual changes in reasoning about shapes and their properties have been studied (Battista, 2007, 2012; van Hiele, 1986), the relationship between classroom discourse and the development of students’ conceptual understanding and geometric reasoning has not been thoroughly investigated. This study investigates how students’ geometry concept development is related to particular language use and how language changes over time as students’ understanding of geometry concepts becomes more sophisticated. Classroom discourse is foregrounded through analyses of data collected from a grade 5 classroom utilizing Battista’s (1999) Shape Makers.
Michael Battista, PhD (Advisor)
Theodore Chao, PhD (Committee Member)
Karen Irving, PhD (Committee Member)
728 p.
Mathematics Education
geometry; inquiry; dynamic geometry; learning progressions; Shape Makers; classroom interactions; discourse; language use

Recommended Citations

Citations

  • Joswick, C. D. (2017). Investigating the Relationship Between Classroom Discourse and Concept Development in Geometry Learning [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500237810722885

    APA Style (7th edition)

  • Joswick, Candace. Investigating the Relationship Between Classroom Discourse and Concept Development in Geometry Learning . 2017. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1500237810722885.

    MLA Style (8th edition)

  • Joswick, Candace. "Investigating the Relationship Between Classroom Discourse and Concept Development in Geometry Learning ." Doctoral dissertation, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1500237810722885

    Chicago Manual of Style (17th edition)

osu1500237810722885
207
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This open access ETD is published by The Ohio State University and OhioLINK.