• Open Access

Using cluster analysis to identify patterns in students’ responses to contextually different conceptual problems

John Stewart, Mayo Miller, Christine Audo, and Gay Stewart
Phys. Rev. ST Phys. Educ. Res. 8, 020112 – Published 4 October 2012

Abstract

This study examined the evolution of student responses to seven contextually different versions of two Force Concept Inventory questions in an introductory physics course at the University of Arkansas. The consistency in answering the closely related questions evolved little over the seven-question exam. A model for the state of student knowledge involving the probability of selecting one of the multiple-choice answers was developed. Criteria for using clustering algorithms to extract model parameters were explored and it was found that the overlap between the probability distributions of the model vectors was an important parameter in characterizing the cluster models. The course data were then clustered and the extracted model showed that students largely fit into two groups both pre- and postinstruction: one that answered all questions correctly with high probability and one that selected the distracter representing the same misconception with high probability. For the course studied, 14% of the students were left with persistent misconceptions post instruction on a static force problem and 30% on a dynamic Newton’s third law problem. These students selected the answer representing the predominant misconception slightly more consistently postinstruction, indicating that the course studied had been ineffective at moving this subgroup of students nearer a Newtonian force concept and had instead moved them slightly farther away from a correct conceptual understanding of these two problems. The consistency in answering pairs of problems with varied physical contexts is shown to be an important supplementary statistic to the score on the problems and suggests that the inclusion of such problem pairs in future conceptual inventories would be efficacious. Multiple, contextually varied questions further probe the structure of students’ knowledge. To allow working instructors to make use of the additional insight gained from cluster analysis, it is our hope that the physics education research community will make these methods available though their Web sites.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 23 February 2012

DOI:https://doi.org/10.1103/PhysRevSTPER.8.020112

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

John Stewart*, Mayo Miller, Christine Audo, and Gay Stewart

  • Physics Department, University of Arkansas, Fayetteville, Arkansas 72701, USA

  • *johns@uark.edu

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 8, Iss. 2 — July - December 2012

Reuse & Permissions
Access Options
CHORUS

Article part of CHORUS

Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×