Theses Doctoral

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

Chen, Yixiong

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.

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More About This Work

Academic Units
Mathematics, Science, and Technology
Thesis Advisors
Smith, J. Philip
Ed.D.C.T., Teachers College, Columbia University
Published Here
June 14, 2023