# Preservice Teachers Making Sense of Fraction Concepts and Operations in a Mathematics Education Content Course

2-13-2019

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Department of Mathematics

Jennifer Tobias

## Abstract

Twenty-five first-year preservice teachers attending a university in the Midwest of the United States of America participated in a whole-class-setting study aimed at investigating their knowledge of how they made sense of fraction concepts and operations, and how the development of this knowledge was facilitated during a mathematics education content course. Classroom mathematical practices of the content course that became “taken-as-shared” overtime were documented using the three-phase data analysis framework of Stephan and Rasmussen (2002, 2008). In the first phase of the analysis, whole-class discussion of fraction concepts and operations were transcribed and noted each time preservice teachers drew conclusions. Toulmin’s (2003) model (data, warrant, claim, and backing) was also used to code or draw up a claim or an argumentation scheme for each conclusion reached in each class period. The claims were identified from both video recordings and transcripts. An argumentation scheme was constructed for each claim so that each of the constituents of the argument can easily be identified. The data analysis generated a chronological argumentation log that documented each of the arguments which were made in whole discussions over the course of five weeks of time. The theoretical framework for this study derived from Cobb and Yackel’s (1996) emergent perspective. The emergent or social constructivist perspective supports a psychological constructive viewpoint by making it possible to analyze individual students’ constructive activities in social contexts (Cobb & Yackel, 1996). Two research questions were identified and answered after all the data had been collected and analyzed. The results indicate that only the sociomathematical norm of what constituted an acceptable solution was reestablished, and 16 mathematical ideas became taken-as-shared as the class developed strategies for making sense of fraction concepts and operations. Implications are discussed for the ways in which preservice teachers may be taught fraction concepts and operations.

KEYWORDS: fraction concepts; fraction operations; preservice teachers; sense-making

## DOI

http://doi.org/10.30707/ETD2019.Desta.D

308

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