Students’ understanding and application of the area under the curve concept in physics problems
This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2011-06-01
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| Series: | Physical Review Special Topics. Physics Education Research |
| Online Access: | http://doi.org/10.1103/PhysRevSTPER.7.010112 |
| _version_ | 1818845587791937536 |
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| author | Dong-Hai Nguyen N. Sanjay Rebello |
| author_facet | Dong-Hai Nguyen N. Sanjay Rebello |
| author_sort | Dong-Hai Nguyen |
| collection | DOAJ |
| description | This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that “the integral equaled the area under the curve.” The findings in this study are consistent with those in previous mathematics education research and research in physics education on students’ use of the area under the curve. |
| first_indexed | 2024-12-19T05:32:02Z |
| format | Article |
| id | doaj.art-6b56d8bc1be84d06af182fd88b8f3ac3 |
| institution | Directory Open Access Journal |
| issn | 1554-9178 |
| language | English |
| last_indexed | 2024-12-19T05:32:02Z |
| publishDate | 2011-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Special Topics. Physics Education Research |
| spelling | doaj.art-6b56d8bc1be84d06af182fd88b8f3ac32022-12-21T20:34:13ZengAmerican Physical SocietyPhysical Review Special Topics. Physics Education Research1554-91782011-06-017101011210.1103/PhysRevSTPER.7.010112Students’ understanding and application of the area under the curve concept in physics problemsDong-Hai NguyenN. Sanjay RebelloThis study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that “the integral equaled the area under the curve.” The findings in this study are consistent with those in previous mathematics education research and research in physics education on students’ use of the area under the curve.http://doi.org/10.1103/PhysRevSTPER.7.010112 |
| spellingShingle | Dong-Hai Nguyen N. Sanjay Rebello Students’ understanding and application of the area under the curve concept in physics problems Physical Review Special Topics. Physics Education Research |
| title | Students’ understanding and application of the area under the curve concept in physics problems |
| title_full | Students’ understanding and application of the area under the curve concept in physics problems |
| title_fullStr | Students’ understanding and application of the area under the curve concept in physics problems |
| title_full_unstemmed | Students’ understanding and application of the area under the curve concept in physics problems |
| title_short | Students’ understanding and application of the area under the curve concept in physics problems |
| title_sort | students understanding and application of the area under the curve concept in physics problems |
| url | http://doi.org/10.1103/PhysRevSTPER.7.010112 |
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