Analogical scaffolding and the learning of abstract ideas in physics: An example from electromagnetic waves

Physical Review Special Topics - Physics Education Research

Volumn 3, Issue 1, 2007, Pages

  Podolefsky, Noah S ^a   Finkelstein, Noah D ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250700482     PISSN: 15549178     EISSN: 15549178     Source Type: Journal    
DOI: 10.1103/PhysRevSTPER.3.010109     Document Type: Article

References (50)

1. E. Rutherford, The scattering of α and β particles by matter and the structure of the atom, Philos. Mag. 6, 21 (1911).
2. J. C. Maxwell, in The Scientific Papers of James Clerk Maxwell, edited by W. D. Niven aCambridge University Press, Cambridge, U.K., 1890; Dover, New York, 1952), pp. 367-369.
3. M. K. Iding, How analogies foster learning from science texts, Instr. Sci. 25, 233 (1997).
4. D. Gentner, Structure-mapping: A theoretical framework for analogy, Cogn. Sci. 7, 155 (1983).
5. A. B. Markman and D. Gentner, Structure mapping in the comparison process, Am. J. Psychol. 113, 501 (2000).
6. D. E. Brown and J. Clement, Overcoming misconceptions via analogical reasoning: Abstract transfer versus explanatory model construction, Instr. Sci. 18, 237 (1989).
7. K. J. Holyoak and P. Thagard, The analogical mind, Am. Psychol. 52, 35 (1997).
8. R. J. Spiro, P. J. Feltovich, R. L. Coulson, and D. K. Anderson, in Similarity and Analogical Reasoning, edited by S. Vosniadou and A. Ortony (Cambridge University :Press, Cambridge, U.K., 1989).
9. N. S. Podolefsky and N. D. Finkelstein, Use of analogy in learning physics: The role of representations, Phys. Rev. ST Phys. Educ. Res. 2, 020101 (2006).
10. D. Gentner and D. R. Gentner, in Mental Models, edited by D. Gentner and A. Stevens (Lawrence Erlbaum Press, Hillsdale, NJ, 1983).
11. G. Lakoff, in Metaphor and Thought, 2nd ed., edited by A. Ortony (Cambridge University Press, Cambridge, U.K., 1993).
12. G. Fauconnier and M. Turner, The Way We Think: Conceptual Blending and the Mind's Hidden Complexities (Basic Books, New York, 2003).
13. M. Turner and G. Fauconnier, Conceptual integration and formal expression, Metaphor Symbol. Act. 10, 183 (1995).
14. G. Fauconnier, In The Analogical Mind, edited by D. Gentner, K. J. Holyoak, and B. N. Kokinov (MIT Press, Cambridge, MA, 2001).
15. W. M. Roth and G. M. Bowen, Complexities of graphical representations during lectures: A phenomenological approach, Learn. Instr. 9, 235 (1999).
16. G. Lakoff and R. Nunez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (Basic Books, New York, 2001).
17. D. E. Brown, Facilitating conceptual change using analogies and explanatory models, Int. J. Sci. Educ. 16, 201 (1994).
18. M. L. Gick and K. J. Holyoak, Analogical problem solving, Cogn. Psychol. 12, 306 (1980).
19. M. L. Gick and K. J. Holyoak, Schema induction and analogical transfer, Cogn. Psychol. 15, 1 (1983).
20. A. A. diSessa, in Constructivism in the Computer Age, edited by G. Forman and P. B. Pufall (Lawerence Erlbaum, Hillsdale, NJ, 1988).
21. D. Hammer, A. Elby, R. F. Scherr, and E. F. Redish, in Transfer of Learning from a Modern Multidisciplinary Perspective, edited by J. Mestre aInformation Age Publishing, Greenwich, CT, 2005), pp. 89-120.
22. M. Chi, P. Feltovich, and R. Glaser, Categorization and representation of physics problems by experts and novices, Cogn. Sci. 5, 121 (1981).
23. K. J. Kurtz, C. Mao, and D. Gentner, Learning by analogical bootstrapping, J. Learn. Sci. 10, 417 (2001).
24. L. L. Namy and D. Gentner, Making a silk purse out of two sow's ears: Childrens' use of comparison in category learning, J. Exp. Psychol. Gen. 131, 5 (2002).
25. R. L. Goldstone and Y. Sakamoto, The transfer of abstract principles governing complex adaptive systems, Cogn. Psychol. 46, 414 (2003).
26. V. M. Sloutsky, J. A. Kaminsky, and A. F. Heckler, The advantage of simple symbols for learning and transfer, Psychon. Bull. Rev. 12, 508 (2005).
27. 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).
28. D. E. Meltzer, Relation between students' problem-solving performance and representational mode, Am. J. Phys. 73, 463 (2005).
29. We note that this objectlike reasoning may also apply when the sign is in the form of words, and e.g., interpreting the phrase "step function" as describing a stair-step-like object. See, for example, D. T. Brookes and E. Etkina, Do our words really matter? Case Studies From Quantum Mechanics, Proceedings of the 2005 Physics Education Research Conference (AIP, Melville, NY, 2006).
30. M. Reiner, J. D. Slotta, M. T. H. Chi, and L. B. Resnick, Naïve physics reasoning: A commitment to substance-based conceptions, Cogn. Instruct. 18, 1 (2000).
31. D. L. Schwartz, Reasoning about the referent of a picture versus reasoning about the picture as the referent: An effect on visual realism, Mem. Cognit. 23, 709 (1995).
32. A. Elby, What students' learning of representation tells us about constructivism, J. Math. Behav. 19, 481 (2000).
33. S. Tornkvist, K. A. Pettersson, and G. Transtromer, Confusion by representation: On students' comprehension of the electric field concept, Am. J. Phys. 61, 335 (1993).
34. 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).
35. L. C. McDermott and P. S. Schaffer, Tutorials in Introductory Physics (Prentice-Hall, Upper Saddle River, NJ, 2001).
36. Alternatively, one might hypothesize that this approach would lead to more confusion for students. The string and sound analogies may interfere in problematic ways, or there may be simply too much information for students to learn at once.
37. N. Podolefsky and N. Finkelstein, http://per.colorado.edu/analogy/ index.htm
38. In common physics parlance, sign and representation share the same meaning. In other sciences, representation often refers to internal or mental representations, along the lines of mental models or schemata.
39. D. E. Rumelhart, in Theoretical Issues in Reading Comprehension, edited by R. J. Spiro, B. C. Bruce, and W. F. Brewer (Lawrence Erlbaum, Hillsdale, NJ 1980), pp. 35-38.
40. This was the state of scientific knowledge prior to Rutherford.
41. M. Turner, Compression and representation, Lang. Lit. 15, 17 (2006).
42. In the language of blending theory, this is referred to as a "single scope" blend, where the organizing frame of one mental space (solar system) is applied to the elements of another (atom). For more, see Ref. 12.
43. One might ask why an external representation is contained within a mental space. We side with the view that artifacts of the environment, such as pictures on paper, are key components of cognition, and hence mental spaces. See M. Wilson, Six views of embodied cognition, Psychon. Bull. Rev. 9, 625 (2002).
44. Each of these sign-schema-referent triangles may be considered a blend, whereby the sign, referent, and schema are connected by vital relations. In the case of the solar system, a picture of the solar system (sign) may be connected to the real solar system (referent) via the vital relation representation. In the Rutherford atom blend, the size of both the solar system and atom referents are scaled to a human scale (the actual size of the sign) via the vital relation space. Role and value vital relations may be involved, whereby the role central object takes the values sun or nucleus, and the role outer object takes the values planet or electron.
45. In this case, the historical progression happens to match a pedagogy that may be productive. We do not mean to suggest, however, that pedagogy should, in general, follow historical accounts of discovery.
46. These changes to sign-schema-referent relations may be along the lines of changes to Wittmann's resource graphs. See M. C. Wittmann, Using resource graphs to represent conceptual change, Phys. Rev. ST Phys. Educ. Res. 2, 020105 (2006).
47. It might be more accurate to say Planck's quantization of energy, which Bohr blended with Rutherford's model.
48. The delineation of abstract and concrete may depend on the level of expertise. To an expert physicist, an electron is a particular type of particle, and thus the electron is more concrete. To a student, to whom an electron may be an unfamiliar idea, "particle" may be more concrete in the sense of being connected to a real object, like a dust particle. In this sense, students' prior knowledge plays a role in our model to the extent that we can determine which ideas are already concrete for students, and which remain abstract. For a detailed analysis of levels of abstraction, see S. I. Hayakawa, Language in Thought and Action, 3rd ed. (Harcourt Brace Jovanovich, New York, 1972).
49. Such a notion of abstraction being a series of blends is consistent with Lakoff and Nunez's notion of layering (Ref. 16). The level of perceived abstraction may depend on the student, in that as students become increasingly familiar with abstract sign-schema relations, these relations may become increasingly treated as concrete. In this case, nodes may become so tightly coupled for an expert that the sign-schema link is compressed and the nodes disappear. For instance, to the expert physicist, the notions of "light" and "wave" are not separate ideas - to this expert, light is a wave.
50. Saalih Allie (private communication).