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What the Integral Does: Physics Students' Efforts at Making Sense of Integration
written by Joseph F. Wagner
Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when trying to make sense of integration, as well as some discomforts and skepticism some students maintain even after constructing useful conceptions of the integral. In particular, many students attempt to explain what integration does by trying to interpret the algebraic manipulations and computations involved in finding antiderivatives. This tendency, perhaps arising from their past experience of making sense of algebraic expressions and equations, suggests a reluctance to use their understanding of "what a Riemann sum does" to interpret "what an integral does."
Physics Education Research Conference 2015
Part of the PER Conference series
College Park, MD: July 29-30, 2015
Pages 355-358
Subjects Levels Resource Types
Education Foundations
- Alternative Conceptions
- Cognition
- Problem Solving
= Representational Use
- Student Characteristics
= Affect
= Skills
Mathematical Tools
- Calculus
= Integral
- Lower Undergraduate
- Upper Undergraduate
- Reference Material
= Research study
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- Educators
- Researchers
- application/pdf
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Mirror:
http://dx.doi.org/10.1119/perc.20…
Access Rights:
Free access
License:
This material is released under a Creative Commons Attribution 3.0 license. Further distribution of this work must maintain attribution to the published article's author(s), title, proceedings citation, and DOI.
Rights Holder:
American Association of Physics Teachers
DOI:
10.1119/perc.2015.pr.084
NSF Number:
1405616
PACSs:
01.40.Ha
01.40.Fk
Keywords:
PERC 2015, Riemann sums, integration, student understanding
Record Creator:
Metadata instance created December 16, 2015 by Lyle Barbato
Record Updated:
December 18, 2015 by Lyle Barbato
Last Update
when Cataloged:
December 18, 2015
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Record Link
AIP Format
J. Wagner, presented at the Physics Education Research Conference 2015, College Park, MD, 2015, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324).
AJP/PRST-PER
J. Wagner, What the Integral Does: Physics Students' Efforts at Making Sense of Integration, presented at the Physics Education Research Conference 2015, College Park, MD, 2015, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324>.
APA Format
Wagner, J. (2015, July 29-30). What the Integral Does: Physics Students' Efforts at Making Sense of Integration. Paper presented at Physics Education Research Conference 2015, College Park, MD. Retrieved December 14, 2017, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324
Chicago Format
Wagner, Joseph. "What the Integral Does: Physics Students' Efforts at Making Sense of Integration." Paper presented at the Physics Education Research Conference 2015, College Park, MD, July 29-30, 2015. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324 (accessed 14 December 2017).
MLA Format
Wagner, Joseph. "What the Integral Does: Physics Students' Efforts at Making Sense of Integration." Physics Education Research Conference 2015. College Park, MD: 2015. 355-358 of PER Conference. 14 Dec. 2017 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324>.
BibTeX Export Format
@inproceedings{ Author = "Joseph Wagner", Title = {What the Integral Does: Physics Students' Efforts at Making Sense of Integration}, BookTitle = {Physics Education Research Conference 2015}, Pages = {355-358}, Address = {College Park, MD}, Series = {PER Conference}, Month = {July 29-30}, Year = {2015} }
Refer Export Format

%A Joseph Wagner
%T What the Integral Does: Physics Students' Efforts at Making Sense of Integration
%S PER Conference
%D July 29-30 2015
%P 355-358
%C College Park, MD
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324
%O Physics Education Research Conference 2015
%O July 29-30
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Wagner, Joseph
%D July 29-30 2015
%T What the Integral Does: Physics Students' Efforts at Making Sense of Integration
%B Physics Education Research Conference 2015
%C College Park, MD
%P 355-358
%S PER Conference
%8 July 29-30
%U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13906&DocID=4324


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