**ERIC Number:**EJ931975

**Record Type:**Journal

**Publication Date:**2011

**Pages:**17

**Abstractor:**As Provided

**Reference Count:**20

**ISBN:**N/A

**ISSN:**ISSN-1554-9178

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

Nguyen, Dong-Hai; Rebello, N. Sanjay

Physical Review Special Topics - Physics Education Research, v7 n1 p010112-1-010112-17 Jan-Jun 2011

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.)

Descriptors: Science Instruction, Mathematical Concepts, Physics, Calculus, Scientific Concepts, College Science, Introductory Courses, Concept Formation, Geometric Concepts, Graphs, Interviews

American Physical Society. One Physics Ellipse 4th Floor, College Park, MD 20740-3844. Tel: 301-209-3200; Fax: 301-209-0865; e-mail: assocpub@aps.org; Web site: http://prst-per.aps.org

**Publication Type:**Journal Articles; Reports - Research

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A