Use of analogy in learning physics: The role of representations

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1. J. C. Maxwell, in The Scientific Papers of James Clerk Maxwell, edited by W. D. Niven (Cambridge University Press, Cambridge, 1890).
2. D. Bartlett, Analogies Between Electricity and Gravity, Metrologia 41, S115 (2004).
3. K. Dunbar, in Model-based Reasoning in Scientific Discovery, edited by L. Magnani, N. Nercessian, and P. Thagard (Plenum Press, New York, 1999).
4. A. Cho, Ultracold Atoms Spark a Hot Race, Science 301, 750 (2003) [CAS].
5. K. Chang, Big Step in Conductivity: More Sociable Particles (New York Times, New York, 2003).
6. E. Rutherford, The Scattering of α and β Particles by Matter and the Structure of the Atom, Philos. Mag. 6, 21 (1911).
7. D. Gentner, Structure-Mapping: A Theoretical Framework for Analogy, Cogn. Sci. 7, 155 (1983).
8. D. Gentner and D. R. Gentner, in Mental Models, edited by G. Gentner and A. Stevens (Lawrence Erlbaum Associates, Hillsdale, NJ, 1983).
9. K. J. Holyoak and P. Thagard, The Analogical Mind, Am. Psychol. 52, 35 (1997) [CAS].
10. G. Lakoff, The Contemporary Theory of Metaphor, 2nd ed., in Metaphor and Thought, edited by Ortony and Andrew (Cambridge University Press, Cambridge, 1993).
11. S. M. Glynn, in The Psychology of Learning Science, edited by S. Glynn, R. Yeany, and B. Beritton (Lawrence Erlbaum Associated, Hillsdale, NJ, 1991).
12. D. E. Brown and J. Clement, Overcoming Misconceptions via Analogical Reasoning: Abstract Transfer Versus Explanatory Model Construction, Instr. Sci. 18, 237 (1989).
13. D. E. Brown, Facilitating Conceptual Change Using Analogies and Explanatory Models, Int. J. Sci. Educ. 16, 201 (1994).
14. Throughout this paper, we will use the word representation to refer exclusively to external representations (e.g., graphs), rather than internal representation (e.g., mental models).
15. B. S. Ambrose, P. R. L. Heron, S. Vokos, and L. C. McDermott, Student Understanding of Light as An Electromagnetic Wave: Relating the Formalism to Physical Phenomena, Am. J. Phys. 67, 891 (1999) [SPIN].
16. Students are also taught that the fields exist in space even if the charges (and, hence, forces) are not present.
17. D. J. Chalmers, R. M. French, and D. R. Hofstadter, High-level Perception, Representation, and Analogy: A Critique of Artificial Intelligence Methodology, J. Exp. Theor. Artif. Intell. 4, 185 (1992).
18. G. Fauconnier and M. Turner, The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities (Basic Books, New York, 2003).
19. G. Lakoff and R. Nunez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (Basic Books, New York, 2001).
20. J. Clement, Observed Methods for Generating Analogies in Scientific Problem Solving, Cogn. Sci. 12, 563 (1988).
21. E. Mazur, Peer Instruction: A User’s Manual (Prentice-Hall, New Jersey, 1997).
22. H-ITT: see http://www.h-itt.com.
23. L. C. McDermott and P. S. Schaffer, Tutorials in Introductory Physics (Prentice-Hall, New Jersey, 2001).
24. D. Hestenes, M. Wells, and G. Swackhammer, Force Concept Inventory, Phys. Teach. 30, 141 (1992) [SPIN].
25. L. Bao and E. F. Redish, Model analysis: Representing and assessing the dynamics of student learning, Phys. Rev. ST Phys. Educ. Res. 2, 010103 (2006).
26. Sound waves are traveling waves, but this was not explicitly taught in the tutorial.
27. The following analogy may be helpful. During a presidential election, both Democrats and Republicans vote. There are equal numbers in each party, and in both parties more people vote for the Republican. The Republican wins overall, but people who voted for the Democrat were more likely Democrats, while people who voted for the Republican were more likely Republicans.
28. The two other answers were revised in the follow-up study to be more attractive, but neither proved to be strong distracters.
29. Post-test results were analyzed using a two-tailed z test of pair-wise comparisons.
30. Since the 3D characteristic was taught explicitly for EM waves in the no-analogy tutorial, students may well have chosen the distracter 1=2=4>3 more often based on memorization or recall.
31. Out of 6 in the spring, 8 in the fall.
32. At this point, we do not know whether representations influence student conceptions of sound, conceptions influence the choice of representation, or if they influence each other.
33. We could represent the string with some other representations, such as vectors, but this would not provide any additional important information about the string, nor would it be a typical representation used by an expert.
34. Z. Hrepic, D. Zollman, and S. Robello, Eliciting and Representing Hybrid Mental Models, Proceedings of the NARST 2005 Annual Meeting (NARST, Dallas, TX, 2005).
35. A. A. diSessa, in Constructivism in the Computer Age, edited by G. Foreman and P. Pufall, (Lawrence Erlbaum, 1998).
36. D. Hammer, A. Elby, R. E. Scherr, and E. F. Redish, in Transfer of Learning from a Modern Multidisciplinary Perspective, edited by J. Mestre (Information Age Publishing, Greenwich, CT, 2005), pp. 89–120.
37. J. Lemke, in Reading Science: Critical and Functional Perspectives on Discourses of Science, edited by J. R. Martin and R. Veels (Routledge, London, 1998).
38. E. Ochs, P. Gonzales, and S. Jacoby, in Interaction and Grammar, edited by E. Ochs, E. Schegloff, and S. Thompson (Cambridge University Press, Cambridge, 1996).
39. Metarepresentational competence describes the “full range of capabilities that students (and others) have concerning the construction and use of external representations,” (Ref. [40]).
40. A. A. diSessa and B. L. Sherin, Meta-representation: an Introduction, J. Math. Behav. 19, 385 (2000).
41. W. M. Roth and G. M. Bowen, Complexities of Graphical Representations during Lectures: A Phenomenological Approach, Learn. Instr. 9, 235 (1999).
42. P. B. Kohl and N. D. Finkelstein, Student Representational Competence and Self-Assessment When Solving Physics Problems, Phys. Rev. ST Phys. Educ. Res. 1, 010104 (2005).
43. M. Kozhevnikov, M. Hegarty, and R. E. Mayer, Revising the Visualizer-Verbalizer Dimension: Evidence for Two Types of Visualizers, Cogn. Instruct. 20, 47 (2002).
44. A. Elby, What Students’ Learning of Representation tells us about Constructivism, J. Math. Behav. 19, 481 (2000).
45. A. A. diSessa and B. L. Sherin, What Changes in Conceptual Change? Int. J. Sci. Educ. 20, 1155 (1998).
46. M. C. Wittman, The Object Coordination Class Applied to Wavepulses: Analysing Student Reasoning in Wave Physics, Int. J. Sci. Educ. 24, 97 (2002).