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Physical Review Special Topics - Physics Education Research
written by Dong-Hai Nguyen and N. Sanjay Rebello
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.
Subjects Levels Resource Types
Education - Basic Research
- Problem Solving
= Heuristics
= Processes
- Student Characteristics
= Skills
Mathematical Tools
- Calculus
- Lower Undergraduate
- Graduate/Professional
- Reference Material
= Research study
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Format:
application/pdf
Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 3.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevSTPER.7.010112
NSF Number:
0816207
PACS:
01.50.Zv
Keywords:
Mathematical Concepts, Problem Solving, Student Understanding
Record Cloner:
Metadata instance created May 1, 2012 by Lyle Barbato
Record Updated:
May 9, 2012 by Vince Kuo
Last Update
when Cataloged:
June 28, 2011
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Record Link
AIP Format
D. Nguyen and N. Rebello, Phys. Rev. ST Phys. Educ. Res. 7 (1), 010112 (2011), WWW Document, (http://dx.doi.org/10.1103/PhysRevSTPER.7.010112).
AJP/PRST-PER
D. Nguyen and N. Rebello, Students' understanding and application of the area under the curve concept in physics problems, Phys. Rev. ST Phys. Educ. Res. 7 (1), 010112 (2011), <http://dx.doi.org/10.1103/PhysRevSTPER.7.010112>.
APA Format
Nguyen, D., & Rebello, N. (2011, June 28). Students' understanding and application of the area under the curve concept in physics problems. Phys. Rev. ST Phys. Educ. Res., 7(1), 010112. Retrieved October 25, 2014, from http://dx.doi.org/10.1103/PhysRevSTPER.7.010112
Chicago Format
Nguyen, Dong-Hai, and N. Sanjay Rebello. "Students' understanding and application of the area under the curve concept in physics problems." Phys. Rev. ST Phys. Educ. Res. 7, no. 1, (June 28, 2011): 010112, http://dx.doi.org/10.1103/PhysRevSTPER.7.010112 (accessed 25 October 2014).
MLA Format
Nguyen, Dong-Hai, and N. Sanjay Rebello. "Students' understanding and application of the area under the curve concept in physics problems." Phys. Rev. ST Phys. Educ. Res. 7.1 (2011): 010112. 25 Oct. 2014 <http://dx.doi.org/10.1103/PhysRevSTPER.7.010112>.
BibTeX Export Format
@article{ Author = "Dong-Hai Nguyen and N. Sanjay Rebello", Title = {Students' understanding and application of the area under the curve concept in physics problems}, Journal = {Phys. Rev. ST Phys. Educ. Res.}, Volume = {7}, Number = {1}, Pages = {010112}, Month = {June}, Year = {2011} }
Refer Export Format

%A Dong-Hai Nguyen
%A N. Sanjay Rebello
%T Students' understanding and application of the area under the curve concept in physics problems
%J Phys. Rev. ST Phys. Educ. Res.
%V 7
%N 1
%D June 28, 2011
%P 010112
%U http://dx.doi.org/10.1103/PhysRevSTPER.7.010112
%O application/pdf

EndNote Export Format

%0 Journal Article
%A Nguyen, Dong-Hai
%A Rebello, N. Sanjay
%D June 28, 2011
%T Students' understanding and application of the area under the curve concept in physics problems
%J Phys. Rev. ST Phys. Educ. Res.
%V 7
%N 1
%P 010112
%8 June 28, 2011
%U http://dx.doi.org/10.1103/PhysRevSTPER.7.010112


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