How Do Widely-Used Calculus Textbooks Introduce the Concepts of Definite Integrals?
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| Title: | How Do Widely-Used Calculus Textbooks Introduce the Concepts of Definite Integrals? |
|---|---|
| Language: | English |
| Authors: | Dae S. Hong (ORCID |
| Source: | International Journal of Mathematical Education in Science and Technology. 2025 56(9):1669-1689. |
| Availability: | 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 |
| Peer Reviewed: | Y |
| Page Count: | 21 |
| Publication Date: | 2025 |
| Document Type: | Journal Articles Reports - Research |
| Education Level: | Higher Education Postsecondary Education |
| Descriptors: | Mathematics Education, Mathematics Instruction, Mathematics Materials, Textbook Evaluation, Calculus, Mathematical Concepts, College Mathematics |
| DOI: | 10.1080/0020739X.2024.2348145 |
| ISSN: | 0020-739X 1464-5211 |
| Abstract: | 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. |
| Abstractor: | As Provided |
| Entry Date: | 2025 |
| Accession Number: | EJ1483296 |
| Database: | ERIC |
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| Abstract: | 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. |
|---|---|
| ISSN: | 0020-739X 1464-5211 |
| DOI: | 10.1080/0020739X.2024.2348145 |
