ERIC Number: EJ1483296
Record Type: Journal
Publication Date: 2025
Pages: 21
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: EISSN-1464-5211
Available Date: 0000-00-00
How Do Widely-Used Calculus Textbooks Introduce the Concepts of Definite Integrals?
Dae S. Hong1; Dennis Kwaka1
International Journal of Mathematical Education in Science and Technology, v56 n9 p1669-1689 2025
This study explores opportunities to learn definite integrals in three widely-used textbooks in the US, Definitions, worked examples, and exercise problems were coded using research based cognitive resources in definite integrals to examine if widely-used textbooks provide students with opportunities to explore how two quantities are related to show area under a curve or other contexts. The results show that initial introduction, worked examples, and exercise problems all provide limited opportunities for students to explore the multiplicative relationship between two quantities (integrand and differential) and adding small pieces to understand definite integrals. Although students may be able to solve integral problems using anti - derivatives, it is possible that they may not understand the definite integral conceptually (knowing why the definite integral gives the area under a curve) or be able expand their understanding to other contexts. Implications of these results are also discussed.
Descriptors: Mathematics Education, Mathematics Instruction, Mathematics Materials, Textbook Evaluation, Calculus, Mathematical Concepts, College Mathematics
Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: 1Teaching and Learning, College of Education, University of Iowa, Iowa City, USA

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