Accounting for Errors in Model Analysis Theory: A Numerical Approach

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written by Steven Sommer and Rebecca S. Lindell

By studying the patterns of a group of individuals' responses to a series of multiple-choice questions, researchers can utilize Model Analysis Theory to create a probability distribution of mental models for a student population. The eigenanalysis of this distribution yields information about what mental models the students possess, as well as how consistently they utilize said mental models. Although the theory considers the probabilistic distribution to be fundamental, there exists opportunities for random errors to occur. In this paper we will discuss a numerical approach for mathematically accounting for these random errors. As an example of this methodology, analysis of data obtained from the Lunar Phases Concept Inventory will be presented. Limitations and applicability of this numerical approach will be discussed.

Physics Education Research Conference 2003
Part of the PER Conference series
Madison, WI: August 6-7, 2003
Volume 720, Pages 49-52

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Published: September 9, 2004

Subjects	Levels	Resource Types
Astronomy - Astronomy Education = Education Research Education Foundations - Research Design & Methodology Mathematical Tools - Numerical Analysis	- Lower Undergraduate	- Reference Material = Research study

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Mirror:: https://doi.org/10.1063/1.1807251
Access Rights:: Available by subscription
Restriction:: © 2003 American Institute of Physics
Additional information is available.
DOI:: 10.1063/1.1807251
PACSs:: 01.40.Fk; 06.20.Dk
Keywords:: Lunar Phases Concept Inventory (LPCI), Model Analysis theory, PERC 2003, error analysis, human factors, modelling, statistical analysis, students' mental models
Record Creator:: Metadata instance created July 14, 2005 by Lyle Barbato
Record Updated:: April 11, 2024 by Lyle Barbato
Last Update when Cataloged:: September 9, 2004
Other Collections:: The PER-Central

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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=2913">Sommer, Steven, and Rebecca Lindell. "Accounting for Errors in Model Analysis Theory: A Numerical Approach." Paper presented at the Physics Education Research Conference 2003, Madison, WI, August 6-7, 2003.</a>

AIP Format

S. Sommer and R. Lindell, , presented at the Physics Education Research Conference 2003, Madison, WI, 2003, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411).

AJP/PRST-PER

S. Sommer and R. Lindell, Accounting for Errors in Model Analysis Theory: A Numerical Approach, presented at the Physics Education Research Conference 2003, Madison, WI, 2003, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411>.

APA Format

Sommer, S., & Lindell, R. (2003, August 6-7). Accounting for Errors in Model Analysis Theory: A Numerical Approach. Paper presented at Physics Education Research Conference 2003, Madison, WI. Retrieved May 3, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411

Chicago Format

Sommer, Steven, and Rebecca Lindell. "Accounting for Errors in Model Analysis Theory: A Numerical Approach." Paper presented at the Physics Education Research Conference 2003, Madison, WI, August 6-7, 2003. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411 (accessed 3 May 2025).

MLA Format

Sommer, Steven, and Rebecca Lindell. "Accounting for Errors in Model Analysis Theory: A Numerical Approach." Physics Education Research Conference 2003. Madison, WI: 2003. 49-52 Vol. 720 of PER Conference. 3 May 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411>.

BibTeX Export Format

@inproceedings{ Author = "Steven Sommer and Rebecca Lindell", Title = {Accounting for Errors in Model Analysis Theory: A Numerical Approach}, BookTitle = {Physics Education Research Conference 2003}, Pages = {49-52}, Address = {Madison, WI}, Series = {PER Conference}, Volume = {720}, Month = {August 6-7}, Year = {2003} }

Refer Export Format

%A Steven Sommer %A Rebecca Lindell %T Accounting for Errors in Model Analysis Theory: A Numerical Approach %S PER Conference %V 720 %D August 6-7 2003 %P 49-52 %C Madison, WI %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411 %O Physics Education Research Conference 2003 %O August 6-7 %O text/html

EndNote Export Format

%0 Conference Proceedings %A Sommer, Steven %A Lindell, Rebecca %D August 6-7 2003 %T Accounting for Errors in Model Analysis Theory: A Numerical Approach %B Physics Education Research Conference 2003 %C Madison, WI %V 720 %P 49-52 %S PER Conference %8 August 6-7 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=2913&DocID=3411

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