Students' Understanding and Application of the Area under the Curve Concept in Physics Problems

• Published in: Physical review special topics. Physics education research Vol. 7; no. 1; pp. 010112 - 10128
• Main Authors: Nguyen, Dong-Hai, Rebello, N. Sanjay
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 28.06.2011
• Subjects: Calculus; College Science; Concept Formation; Curriculum Design; Education; Geometric Concepts; Graphs; Integrals; Interviews; Introductory Courses; Mathematical Concepts; Mathematics Education; Physics; Science Education; Science Instruction; Scientific Concepts; Students
• ISSN: 1554-9178; 1554-9178; 2469-9896
• DOI: 10.1103/PhysRevSTPER.7.010112

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. (Contains 2 tables and 6 figures.)