Free-Body Diagrams and Problem Solving in Mechanics: An Example of The Effectiveness of Self-Constructed Representations
Earlier research has found that it is useful to distinguish situations in which students construct external representations on their own from situations in which they are expected to interpret already provided external representations. One type of representations that is particularly important for teaching mechanics is the free-body diagram. In this study, we investigated how inclusion of free-body diagrams into problem statements influences students' performance in solving mechanics problems. To that end two versions of a five-problem assessment instrument that only differed with respect to the inclusion/non-inclusion of free-body diagrams (FBDs) were administered to two groups of first year physics students. It was found that inclusion of free-body diagrams into the problem statements not only did not facilitate problem solving, but also impeded it significantly. Particularly large between group differences, in favor of the group not provided with FBDs, were detected for problems that required use of free-body diagrams showing resolution of forces into components. The results of our study indicate that consistency between internal and external representations of knowledge is a very important requirement for effective problem solving and effective learning of physics, in general. This consistency is most easily established when students use self-constructed external representations.
Aviani, I., Erceg, N., & Mešić, V. (2015). Drawing and using free body diagrams: Why it may be better not to decompose forces. Physical Review Special Topics-Physics Education Research, 11, 020137. DOI: https://doi.org/10.1103/PhysRevSTPER.11.020137
Bransford, J., Brown, A. L., & Cocking, R.R. (2000). How People Learn: Brain, Mind, Experience, and School. Washington: NAP.
Brookes, D. T., & Etkina, E. (2007). Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning. Physical Review Special Topics-Physics Education Research, 3, 010105. DOI: https://doi.org/10.1103/PhysRevSTPER.3.010105
Cox, R. (1999). Representation construction, externalized cognition and individual differences. Learning and instruction, 9, 343-363. DOI: http://dx.doi.org/10.1016/S0959-4752(98)00051-6
Draxler, D. (2006). Aufgabendesign und basismodellorientierter Physikunterricht. Ph.D. thesis, Universitaet Duisburg-Essen.
Field, A. (2013). Discovering statistics using IBM SPSS statistics. London: SAGE Publications, Inc.
Gall, M.D., Gall, J.P., & Borg, W.R. (2003). Educational Research: An Introduction. Boston: Pearson Education.
Girwidz, R. (2015). Medien im Physikunterricht. In E. Kircher, R. Girwidz, & P. Haeussler (Hrsg), Physikdidaktik: Theorie und Praxis (pp. 193-247). Berlin-Heidelberg: Springer-Verlag.
Johnson, R.B. & Christensen, L.B. (2012). Educational Research: Quantitative, Qualitative, and Mixed Approaches. Thousand Oaks, CA: SAGE Publications, Inc.
Kohl, P. B. (2007). Towards an understanding of how students use representations in physics problem solving. Ph.D. thesis, Western Washington University.
Kondratyev, A. S., & Sperry, W. (1994). Direct use of vectors in mechanics’ problems. The Physics Teacher, 32, 416-418. DOI: http://doi.org/10.1119/1.2344061
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive science, 11, 65-100.
McDonald, J.H. 2014. Handbook of Biological Statistics. Baltimore, Maryland: Sparky House Publishing.
Meltzer, D. (2002). Student learning of physics concepts: efficacy of verbal and written forms of expression in comparison to other representational modes. Online:
Nersessian, N. (2008). Creating Scientific Concepts. Cambridge, MA: MIT Press.
Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational psychologist, 38, 1-4. DOI: http://dx.doi.org/10.1207/S15326985EP3801_1
Reisberg, D. (1987). External representations and the advantages of externalizing one’s thoughts. In Proceedings of the 9th Annual Conference of the Cognitive Science Society (pp. 281-293). Hillsdale, NJ: Lawrence Erlbaum Associates.
Rosengrant, D., Van Heuvelen, A., & Etkina, E. (2009). Do students use and understand free-body diagrams? Physical Review Special Topics-Physics Education Research, 5, 010108. DOI: https://doi.org/10.1103/PhysRevSTPER.5.010108
Rosnow, R. L., Rosenthal, R., & Rubin, D. B. (2000). Contrasts and correlations in effect-size estimation. Psychological science, 11, 446-453. DOI: https://doi.org/10.1111/1467-9280.00287
Rutherford, A. (2011). ANOVA and ANCOVA: A GLM Approach. Hoboken, NJ: John Wiley & Sons.
Saghaei, M. (n.d.). Randomization. Retrieved February 16, 2017, from http://mahmoodsaghaei.tripod.com/Softwares/randalloc.html
Schweder, R.A. (1982). Beyond Self-Constructed Knowledge: The Study of Culture and Morality. Merrill-Palmer Quarterly, 28, 41-69.
Sweller, J., Van Merrienboer, J. J., & Paas, F. G. (1998). Cognitive architecture and instructional design. Educational psychology review, 10, 251-296. DOI: https://doi.org/10.1023/A:1022193728205
van den Berg, E., & van Huis, C. (1998). Drawing forces. The Physics Teacher, 36, 222-223. DOI: http://dx.doi.org/10.1119/1.880046
Wetzels, S. A. J., Kester, L., & van Merriënboer, J.J. G (2010). Use of external representations in science: Prompting and reinforcing prior knowledge activation. In L. Verschaffel, E. de Corte, T. De Jong, & J. Elen, Use of representations in reasoning and problem solving: Analysis and improvement (pp. 225-241). Abingdon: Routledge.
Wong, E. D. (1993). Self‐generated analogies as a tool for constructing and evaluating explanations of scientific phenomena. Journal of Research in Science Teaching, 30, 367-380.
Woolfolk, A. (2013). Educational Psychology. NJ, Upper Saddle River: Pearson.
Zou, B.S.X. (2000). The use of multiple representations and visualizations in student learning of introductory physics: an example from work and energy. Ph.D. thesis, The Ohio State University.
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