Plasticity of intermediate mechanics students’ coordinate system choice

ion: The case of Ben, J. Math. Behav. 113, 1 2002 . 6 T. Dreyfus and P. Tsamir, Ben’s consolidation of knowledge structures about infinite sets, J. Math. Behav. 23, 271 2004 . 7 P. Tsamir and T. Dreyfus, How fragile is consolidated knowledge?, J. Math. Behav. 24, 15 2005 . 8 M. S. Sabella and E. F. Redish, Knowledge organization and activation in physics problem solving, Am. J. Phys. 75, 1017 2007 . 9 E. F. Redish, Proceedings of the International School of Physics Enrico Fermi, Course CLVI: Research on Physics Education, edited by E. F. Redish and M. Vicentini IOS, Amsterdam, 2004 , pp. 1–56. 10 A. A. diSessa, Towards an epistemology of physics, Cogn. Instruct. 10, 105 1993 . 11 B. L. Sherin, How students understand physics equations, Cogn. Instruct. 19, 479 2001 . 12 Forms are general mathematical elements of a structure, which students apply to specific situations. 13 D. Hammer and A. Elby, Tapping epistemological resources for learning physics, J. Learn. Sci. 12, 53 2003 . 14 D. Hammer, E. F. Redish, A. Elby, and R. E. Scherr, in Transfer of Learning: Research and Perspectives, edited by J. Mestre Information Age, Greenwich, CT, 2004 . 15 L. Lising and A. Elby, The impact of epistemology on learning: A case study from introductory physics, Am. J. Phys. 73, 372 2005 . 16 E. C. Sayre, M. C. Wittmann, and J. R. Thompson, Physics Education Research Conference Proceedings 2003, edited by K. C. Cummings, S. Franklin, and J. Marx Springer, New York/LLC, Secaucus, NJ, 2003 . 17 J. Tuminaro, Ph.D. thesis, University of Maryland, 2004. 18 M. C. Wittmann, Using resource graphs to represent conceptual change, Phys. Rev. ST Phys. Educ. Res. 2, 020105 2006 . 19 M. C. Wittmann and J. T. Morgan, Physics Education Research Conference Proceedings 2003, edited by S. Franklin, K. C. Cummings, and J. Marx Springer, New York/LLC, Secaucus, NJ, 2004 . 20 D. Hammer and A. Elby, Fourth International Conference of the Learning Sciences, edited by B. Fishman and S. O’ConnerDivelbiss Erlbaum, Mahwah, NJ, 2000 , pp. 4–5. 21 A. Elby and D. Hammer, On the substance of a sophisticated epistemology, Sci. Educ. 85, 554 2001 . 22 K. E. Black and M. C. Wittmann, Physics Education Research Conference 2007 AIP Conference Proceedings No. 951 AIP, New York, 2007 . 23 A. A. diSessa and B. L. Sherin, What changes in conceptual change, Int. J. Sci. Educ. 20, 1155 1998 . 24 J. Tuminaro and E. F. Redish, Elements of a cognitive model of physics problem solving: Epistemic games, Phys. Rev. ST Phys. Educ. Res. 3, 020101 2007 . 25 R. S. Russ, Ph.D. thesis, University of Maryland, 2006. 26 A. Elby, Helping physics students learn about learning, Am. J. Phys. 69, S54 1999 . 27 M. C. Wittmann and J. T. Morgan, Intuitive quantum physics, http://perlnet.umaine.edu/iqp/ 28 B. S. Ambrose, Investigating student understanding in intermediate mechanics: Identifying the need for a tutorial approach to instruction, Am. J. Phys. 72, 453 2004 . 29 M. C. Wittmann and B. S. Ambrose, Intermediate mechanics tutorials, http://perlnet.umaine.edu/imt/ 30 Though individual resources are held by individuals, their expression and use in a specific context may be socially negotiated. However, we wish to draw a distinction between resources held individually and their appropriate expression which may be socially determined . 31 This is, of course, a simplification. We do not discuss here an important third state—primed—for either neurons or resources. 32 D. Tannen and C. Wallat, in The Discourse Reader, edited by A. Jaworski and N. Coupland Routledge, New York, 1987 , pp. 346–366. 33 E. C. Sayre, M.S. thesis, University of Maine, 2005. 34 However, if a resource activates in two contexts, those contexts may or may not be near each other. Consider the conservation of stuff resource. In quantum mechanics, the energy of a particle is conserved as it passes through a barrier, though students may think the energy decreases Ref. 19 . In a classic Piagetian experiment, water is poured from a short fat glass to a tall skinny one, but its volume remains the same, though children may think the volume increases Ref. 51 . In both cases, conservation of stuff activates appropriately, but the cases bear no other resemblance. Thus, conservation of stuff could be nearby many otherwise disparate resources. Yet, if those other resources are disparate, they should not be near each other. To solve the addressing difficulty, resources need to be in two “places” at the same time. Obviously, ordinary buildings cannot have multiple locations. 35 For a overview, see McDermott and Redish, 1999 Ref. 52 . 36 B. L. Sherin, Ph.D. dissertation, University of California, 1996. 37 J. Minstrell, in Research in Physics Learning: Theoretical Issues and Empirical Studies, Proceedings of an International Workshop, Bremen, Germany, 1991, edited by R. Duit, F. Goldberg, and H. Niedderer IPN, Kiel, 1992 , pp. 110–128. 38 S. Demastes, R. Good, and P. Peebles, Patterns of conceptual change in evolution, J. Res. Sci. Teach. 33, 407 1996 . 39 Minsky Refs. 53,54 uses a similar but distinct definition for frames. He is much closer to what we call a resource graph, in which ideas are recruited into the frame system, and we do not discuss it further here. 40 For example, one might consider when certain framing activities are possible and how that depends on the readout strategies associated with a given resource graph. Perhaps only those resource graphs with appropriate readouts are available to the activity of framing. However, there is too little theoretical clarity on either end of the description for a connection to be made. Under what conditions is one unable to frame an activity in a PLASTICITY OF INTERMEDIATE MECHANICS... PHYS. REV. ST PHYS. EDUC. RES. 4, 020105 2008