Date of Award

Fall 12-15-2008

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Middle-Secondary Education and Instructional Technology

First Advisor

Christine D. Thomas, Ph.D

Second Advisor

Pier A. Junor Clarke, Ph.D

Third Advisor

Janice Fournillier, Ph.D

Fourth Advisor

Marla Bell, Ph.D

Abstract

The purpose of this grounded theory study was to explore the interplay of prospective secondary mathematics teachers’ affect, metacognition, and mathematical cognition in a problem-solving context. From a social constructivist epistemological paradigm and using a constructivist grounded theory approach, the main research question guiding the study was: What is the characterization of the interplay among prospective teachers’ mathematical beliefs, mathematical behavior, and mathematical knowledge in the context of solving mathematics problems? I conducted four interviews with four prospective secondary mathematics teachers enrolled in an undergraduate mathematics course. Participant artifacts, observations, and researcher reflections were regularly recorded and included as part of the data collection. The theory that emerged from the study is grounded in the participants’ mathematics problem-solving experiences and it depicts the interplay among affect, metacognition, and mathematical cognition as meta-affect, persistence and autonomy, and meta-strategic knowledge. For the participants, “Knowing How and Knowing Why” mathematics procedures work and having the ability to justify their reasoning and problem solutions represented mathematics knowledge and understanding that could empower them to become productive problem-solvers and effective secondary mathematics teachers. The results of the study also indicated that the participants interpreted their experiences with difficult, challenging problem-solving situations as opportunities to learn and understand mathematics deeply. Although they experienced fear, frustration, and disappointment in difficult problem-solving and mathematics-learning situations, they viewed such difficulty with the expectation that feelings of satisfaction, joy, pride, and confidence would occur because of their mathematical understanding. In problem-solving situations, affect, metacognition, and mathematics cognition interacted in a way that resulted in mathematics understanding that was productive and empowering for these prospective teachers. The theory resulting from this study has implications for prospective teachers, teacher education, curriculum development, and mathematics education research.

DOI

https://doi.org/10.57709/1363895

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