An Analysis of Covariational Reasoning Pedagogy for the Introduction of Derivative in Selected Calculus Textbooks

Autor/in	Chen, Yixiong
Titel	An Analysis of Covariational Reasoning Pedagogy for the Introduction of Derivative in Selected Calculus Textbooks
Quelle	(2023), (163 Seiten) PDF als Volltext Verfügbarkeit Ed.D. Dissertation, Teachers College, Columbia University
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
ISBN	979-8-3795-4081-4
Schlagwörter	Hochschulschrift; Dissertation; Calculus; Mathematics Instruction; High School Students; Textbooks; Thinking Skills; Teaching Methods; Content Analysis; Abstract Reasoning; Undergraduate Students; Cross Cultural Studies; Change; Foreign Countries; China; United States + Suchen Sie Ihr Suchwort? Thesis; Dissertations; Academic thesis; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Textbook; Text book; Schulbuch; Lehrbuch; Denkfähigkeit; Teaching method; Lehrmethode; Unterrichtsmethode; Inhaltsanalyse; Abstraktes Denken; Denken; Cultural comparison; Kulturvergleich; Wandel; Ausland; USA
Abstract	Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that conceptually introduce derivatives in four calculus textbooks. One widely used calculus textbook was selected for the study in each of the four categories: U.S. college, U.S. high school, China college, and China high school. Two qualified investigators and I conducted the study. We used a framework of five developmental levels for covariational reasoning. The conceptual analysis of four calculus textbooks found that the U.S. college and the U.S. high school textbooks emphasize the average and instantaneous rate of change. However, both lack development of the direction and magnitude of change. On the other hand, this study's Chinese high school calculus textbook has a greater degree of development in the direction and magnitude of change while having a deficit in the average rate of change. This study's Chinese college calculus textbook does not have any meaningful development regarding covariational reasoning pedagogy. The relational analysis of the concepts previously identified in the conceptual analysis phase revealed that this study's U.S. college calculus textbooks provide abundant examples and exercises to transition between the average and instantaneous rate of change. On the other hand, all other calculus textbooks in this study lack any significant transition among passages that stimulate covariational reasoning. The textbook analysis in this study provides insights into the current focus of calculus textbooks in both the U.S. and China. In addition, the study has implications for learning and teaching calculus at both high school and college, as well as future editions of calculus textbooks. Finally, limitations and recommendations are discussed. [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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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01