Conceptual Understanding of Newtonian Mechanics Through Cluster Analysis of FCI Student Answers
The Force Concept Inventory is a multiple-choice test and is one of the most popular and most analyzed concept inventories. It is used to investigate student understanding of Newtonian mechanics. A structured approach to data analysis can transform it in a “diagnostic” instrument that can validate inferences about student thinking. In this paper, we show how cluster analysis methods can be used to investigate patterns of student conceptual understanding and supply useful details about the relationships among student concepts and misconceptions. The answers given to the FCI questionnaire by a sample of freshman engineering have been analyzed. The analysis takes into account the decomposition of the force concept into the conceptual dimensions suggested by the FCI authors and successive studies. Our approach identifies latent structures within the student response patterns and groups students characterized by similar correct answers, as well as by non-correct answers. These response patterns give us new insights into the relationships between the student force concepts and their ability to analyze motions. Our results show that cluster analysis proved to be a useful tool to identify latent structures within the student conceptual understanding. Such structures can supply diagnostic insights for classroom pedagogy and teaching approaches.
KeywordsAssessment Cluster analysis Engineering freshmen Force Concept Inventory
We wish to express our thanks to Prof. Rosa Maria Sperandeo-Mineo for her continuous advice and support during the development of this study.
- Battaglia, O. R., Di Paola, B., & Fazio, C. (2018). An unsupervised quantitative method to analyse students’ answering strategies to a questionnaire. In S. Magazu (Ed.), New trends in physics education research (pp. 19–46). New York, NY: Nova Science Publishers Inc.Google Scholar
- Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1–27.Google Scholar
- DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical Science, 11(3), 189–228.Google Scholar
- Di Paola, B., Battaglia, O. R., & Fazio, C. (2016). Non-Hierarchical Clustering to analyse an open-ended questionnaire on algebraic thinking. South African Journal of Education, 36(1), 1142.Google Scholar
- Fazio, C., Battaglia, O. R., & Di Paola, B. (2013). Investigating the quality of mental models deployed by undergraduate engineering students in creating explanations: The case of thermally activated phenomena. Physical Review Special Topics - Physics Education Research, 9(2), 020101.Google Scholar
- Fulmer, G. W. (2015). Validating proposed learning progressions on force and motion using the Force Concept Inventory: Finding from Singapore secondary schools. International Journal of Science and Mathematics Education, 13(6), 1235–1254. https://doi.org/10.1007/s10763-014-9553-x.CrossRefGoogle Scholar
- Grunspan, D. Z., Wiggins, B. L., & Goodreau, S. M. (2014). Understanding classrooms through social network analysis: A primer for social network analysis in education research. Cell Biology Education, 13(2), 167–179.Google Scholar
- Hestenes, D., & Jackson, J. (2007). Revised Table II for the Force Concept Inventory (Unpublished). Retrieved from http://modeling.asu.edu/R&E/Research.html. Accessed March 2016.
- Jammer, M. (1957). Concepts of force. Cambridge, England: Harvard University Press.Google Scholar
- MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In L. M. LeCam & J. Neyman (Eds.), Proc. 5th Berkely Symp. Math. Statist. Probab. 1965/66 (Vol. I, pp. 281–297). Berkely, CA: University of California Press.Google Scholar
- Nieminen, P., Savinainen, A., & Viiri, J. (2013). Gender differences in learning of the concept of force, representational consistency, and scientific reasoning. International Journal of Science and Mathematics Education, 11, 1137–1156. https://doi.org/10.1007/s10763-012-9363-y.CrossRefGoogle Scholar
- Saxena, P., Singh, V., & Lehri, S. (2013). Evolving efficient clustering patterns in liver patient data through data mining techniques. International Journal of Computer Applications, 66(16), 23–28.Google Scholar
- Scott, T. F., & Schumayer, D. (2017). Conceptual coherence of non-Newtonian worldviews in Force Concept Inventory data. Physical Review Physics Education Research, 13, 010126. https://doi.org/10.1103/PhysRevPhysEducRes.13.010126.CrossRefGoogle Scholar
- Scott, T. F., Schumayer, D., & Gray, A. R. (2012). Exploratory factor analysis of a Force Concept Inventory data set. Physical Review Special Topics Physics Education Research, 8, 020105.Google Scholar
- Semak, M. R., Dietz, R. D., Pearson, R. H., & Willis, C. W. (2017). Examining evolving performance on the Force Concept Inventory using factor analysis. Physical Review Physics Education Research, 13, 019903. https://doi.org/10.1103/PhysRevPhysEducRes.13.010103.CrossRefGoogle Scholar
- Steif, P. S., & Hansen, M. A. (2007). New practices for administering and analyzing the results of concept inventories. Journal of Engineering Education, 96, 205–212. https://doi.org/10.1002/j.2168-9830.2007.tb00930.x.CrossRefGoogle Scholar
- Stewart, J., Miller, M., Audo, C., & Stewart, G. (2012). Using cluster analysis to identify patterns in students’ responses to contextually different conceptual problems. Physical Review Special Topics Physics Education Research, 8, 020112.Google Scholar
- Struyf, A., Hubert, M., & Rousseeuw, P. J. (1997). Clustering in an object-oriented environment. Journal of Statistical Software, 1(4), 1–30.Google Scholar