Dissertation/Thesis Abstract

Students' use of metaphor and gesture during collaborative work on tasks designed to foster students' covariational reasoning
by Hornbein, Peter, M.S., University of Colorado at Denver, 2015, 91; 1588190
Abstract (Summary)

Researchers have argued that gesture and speech, two elements of discourse, are neurologically related, and that language and mental imagery are intertwined. Because of this relationship between language, gesture and image, these discourse elements may allow a teacher to make inferences about the reasoning the student is using. In order for the teacher to make these inferences, students must engage in discourse, which I am initially defining here as written and spoken language and the accompanying gestures. This requires that students work on open ended, contextual problems that provide opportunities for discourse. An area that provides opportunities for discourse includes functions and the relationship between the covarying quantities that the function expresses.

By investigating discourse and covarying quantities, I will attempt to answer two, related research questions. What is the nature of students' use of metaphor and gesture when working collaboratively on tasks designed to provide opportunities for covariational reasoning? What information might the students' use of metaphor and gesture provide about the student's covariational reasoning? In order to answer these two questions, I analyzed data from four, ninth grade students during work on two task-based interviews in which the students completed a version of a widely-used bottle problem. The data analysis consisted of multiple passes coding for the quantitative operation, gesture and metaphor used by the students.

Gesture and metaphor helped make inferences about the quantitative operation the students were using and whether they were comparing or coordinating covarying quantities. The students' gesture allowed me to infer more about the underlying imagery they were using than did metaphor, however, the two were most powerful when considered together. Two of the four students were primarily comparing amounts of change in the two quantities and the other two students coordinated the two quantities. The results led me to a conjecture about the relationship of language, imagery and gesture, and how this relationship might be used in both educational and research settings.

I proposed a relationship between imagery, language and gesture that I referred to as the Language-Imagery-Gesture Triad with imagery and gesture forming the foundation supporting language. Linguistic structures such as metonymy and metaphor facilitate the relationship between imagery and language.

Indexing (document details)
Advisor: Johnson, Heather L.
Commitee: Ferrara, Michael, Tzur, Ron
School: University of Colorado at Denver
Department: Educational Studies and Research
School Location: United States -- Colorado
Source: MAI 54/04M(E), Masters Abstracts International
Subjects: Mathematics education
Keywords: Collaborative, Covariation, Gesture, Metaphor, Reasoning
Publication Number: 1588190
ISBN: 978-1-321-73163-7
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