Conceptions of Function Composition in College Precalculus Students

Autor/in	Bowling, Stacey
Titel	Conceptions of Function Composition in College Precalculus Students
Quelle	(2014), (222 Seiten) PDF als Volltext Verfügbarkeit Ph.D. Dissertation, Arizona State University
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
ISBN	978-1-3038-8105-3
Schlagwörter	Hochschulschrift; Dissertation; Mathematical Concepts; Semi Structured Interviews; Calculus; Mathematical Logic; Mathematics Instruction; Problem Solving; College Mathematics; College Students + Suchen Sie Ihr Suchwort? Thesis; Dissertations; Academic thesis; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematical logics; Mathematische Logik; Mathematics lessons; Mathematikunterricht; Problemlösen; Collegestudent
Abstract	Past research has shown that students have difficulty developing a robust conception of function. However, little prior research has been performed dealing with student knowledge of function composition, a potentially powerful mathematical concept. This dissertation reports the results of an investigation into student understanding and use of function composition, set against the backdrop of a precalculus class that emphasized quantification and covariational reasoning. The data were collected using task-based, semi-structured clinical interviews with individual students outside the classroom. Findings from this study revealed that factors such as the student's quantitative reasoning, covariational reasoning, problem solving behaviors, and view of function influence how a student understands and uses function composition. The results of the study characterize some of the subtle ways in which these factors impact students' ability to understand and use function composition to solve problems. Findings also revealed that other factors such as a students' persistence, disposition towards "meaning making" for the purpose of conceptualizing quantitative relationships, familiarity with the context of a problem, procedural fluency, and student knowledge of rules of "order of operations" impact a students' progress in advancing her/his solution approach. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.] (As Provided).
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Update	2020/1/01