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ERIC Number: EJ1436959
Record Type: Journal
Publication Date: 2024
Pages: 28
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: EISSN-1464-5211
Quantitative and Covariational Reasoning Opportunities Provided by Calculus Textbooks: The Case of the Derivative
Thembinkosi Peter Mkhatshwa
International Journal of Mathematical Education in Science and Technology, v55 n9 p2191-2218 2024
While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational reasoning, in the context of the derivative concept, provided by two textbooks commonly used in the teaching of calculus in the United States-a regular calculus textbook and an applied calculus textbook. Analysis of expository sections, examples, and exercises related to the derivative provided in these textbooks revealed three main results. First, the applied calculus textbook provides plenty of opportunities to engage in quantitative reasoning. Similar opportunities are limited in the regular calculus textbook. Second, opportunities to engage in covariational reasoning are not only minimal in both textbooks, but also limited to low levels of covariational reasoning, namely coordination, direction, and quantitative coordination. Third, the applied calculus textbook consistently defines ordinary and partial derivatives as rates of change while the regular calculus textbook consistently defines these concepts as limits of a difference quotient. Findings of this research have implications for several stakeholders, including calculus textbook authors and calculus instructors.
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A