Elements of a cognitive model of physics problem solving: Epistemic games

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13. Note that we do not claim here that the structures we are developing somehow represent the “true” structure of the students’ internal cognitive processes. At present, these are undetectable. Rather, what we offer is a way for observers of student behavior to organize and categorize their observations in what appears to be a sensible and productive fashion.
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38. The argument is sometimes made that “any software can be run on any computer” and therefore abstract arguments made about the nature of software apply to all computational systems. While this may be true in principle, in practice, hardware and time constraints strongly affect what kind of structures produce results efficiently and effectively (in time, for example, to escape a leaping tiger). For a phenomenological analysis of a real system, it is appropriate to take into account properties and constraints on the actual computing system—in this case, a human being.
39. This term is used in the psychology literature as described here. See, for example, Ref. [49].
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44. Fuster refers to such a network representing a basic element of knowledge as a cognit (short for cognitive bit). We will not use this term here as it does not appear to be in widespread use.
45. The term “activate” here plays the role of the term more commonly used in physics education research, “elicit.”
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53. The metaphor here is of computer code. Code that is written in a high level language, such as fortran or c, must be interpreted into a form that the computer’s processor can use. The translation of code into machine language is typically referred to as compilation and results in much faster processing than line-by-line translation (viz., interpreted vs compiled code).
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60. Indeed, all reasoning in the end may depend on such phenomenologically developed intuitions; See, for example, G. Lakoff and M. Johnson, Metaphors We Live By (University of Chicago Press, Chicago, 1980); and L. Carroll, What the Tortoise Said to Achilles, Mind 4, 278 (1895).
61. In cognitive neuroscience such phenomenological bound resources are referred to as “reflexive reasoning” (Ref. [42]).
62. S. Dehaene, The Number Sense: How the Mind Creates Mathematics (Oxford University Press, New York, 1997).
63. G. Lakoff and R. E. Núñez, Where Mathematics Comes From (Basic Books, New York, 2000).
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67. We talk about these expectations and categorizations in terms of control structures we call epistemological framing. This process is discussed in Ref. [14].
68. We may not have seen some common games as a result of the fact that our class de-emphasized the use of a textbook. None was required and few students bought the recommended one.
69. We use the terms “conceptual” and “concepts” here loosely to mean any collection of interpretive ideas about a physical quantity or mechanism.
70. In some sense, Pictorial Analysis is a collection of games rather than a single game. Each distinct kind of diagram—free-body diagram, circuit diagram, phase diagram, etc.—represents a distinct epistemic form and has its own distinct moves, conceptual resources, and end state. Refinement of this general game into more specific games will require further research.
71. T. Ben-Zeev, When Erroneous Mathematical Thinking is Just as ‘Correct’: The Oxymoron of Rational Errors, in The Nature of Mathematical Thinking, edited by R. Sternberg and T. Ben-Zeev (Lawrence Erlbaum, 1996), pp. 55–79.
72. T. Ben-Zeev, Rational Errors and the Mathematical Mind, General Review of Psychology 2, 366 (1998).
73. American Heritage Dictionary (Houghton Mifflin, Boston, 2000).
74. This relies on the measurement of aspects of the epistemological state using pre-post MPEX and measurement of aspects of the conceptual state using fractional gains on the FCI. Strong gains were obtained in both measures. These results will be documented elsewhere.
75. D. Hestenes, M. Wells, and G. Swackhamer, Force Concept Inventory, Phys. Teach. 30, 141 (1992) [SPIN].
76. R. K. Thornton and D. R. Sokoloff, Assessing student learning of Newton’s laws: The Force and Motion Conceptual Evaluation, Am. J. Phys. 66, 338 (1998) [SPIN][INSPEC].
77. E. F. Redish, J. M. Saul, and R. N. Steinberg, Student Expectations In Introductory Physics, Am. J. Phys. 66, 212 (1998) [SPIN][INSPEC].
78. E. F. Redish, Teaching Physics with the Physics Suite (John Wiley & Sons, Inc., New York, 2003).
79. F. Marton and S. Booth, Learning and Awareness (Lawrence Erlbaum Associates, 1997), Chap. 6.
80. A fourth student (a male) is present during this session but he contributes little and does not speak during the selected excerpts.
81. This illustrates the fact that these students, having only recently learned Newton’s laws and the use of forces, are not only solving the problem at hand in their discussion; they are taking steps in the process of compiling their Newtonian knowledge. See Ref. [55] for more discussion of this point.
82. At the time of the instructional intervention, Tuminaro was not consciously attempting to nudge “the students into playing a different epistemic game.” It is only in the analysis, not in the actual event, that he used the concept of epistemic games to describe this episode.
83. At an earlier point in the discussion, she accepts the idea that the temperature needed in the gas formula should be room temperature, even though it is not given. She says, “I’m assuming it’s room temperature since it’s not specified.” This may not contradict our hypothesis since many classes in chemistry and physics take standard temperature and pressure as the assumed value when it is unspecified.
84. E. Kim and S.-J. Pak, Students do not overcome conceptual difficulties after solving 1000 traditional problems, Am. J. Phys. 70, 759 (2002) [SPIN].
85. This problem is adapted from D. P. Maloney, T. L. O’Kuma, C. J. Hieggelke, and A. Van Heuvelen, Surveying Students’ Conceptual Knowledge of Electricity and Magnetism, Am. J. Phys. 69, S12 (2001) [SPIN][INSPEC][CAS].