Real problem solving is an additional teaching tool that requires each student to examine his or her own mental connections. This process can be difficult, time consuming, and frustrating. Most human beings work very hard to avoid engaging in this process, as illustrated in the problem-solving flow chart that circulated around the internet some years ago (shown on cover page to Part 1, page 11). The vast majority of students entering our introductory physics courses do not engage in real problem solving. Without instruction in problem solving, those who survive tend to use a pattern-matching strategy while unsuccessful students engage in the plug-and-chug strategy.
In the classroom, it is useful to remember the old practice of miners using canaries to detect poisonous gasses underground. Unsuccessful students are more sensitive
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to weak teaching practices, so like the canaries in mines, it is easy to see their failure. If a significant number of students are dropping out or failing a course, then it is probable that the successful students who, like the miners survive, are also being harmed.
Good teaching practices most obviously benefit the typically unsuccessful students, but they equally benefit the best students. In the next three chapters in Part 1, we describe some teaching practices that benefit both the typically successful and unsuccessful students.
Endnotes
1 There is a vast literature on college students’ personal physics ideas -- also called alternative conceptions, preconceptions, naive conceptions, and misconceptions.
A sampling of articles include: Trowbridge, D.E. & McDermott, L. C. (1981), Investigation of student understanding of the concept of acceleration in one dimension, American Journal of Physics, 49(3), 242-253; Clement, J. (1982), Students' preconceptions in introductory mechanics, American Journal of Physics, 50(1), 66-71; McCloskey, M. (1983), Naive theories about motion, in Mental Models, D.S. Gentner and A. Stevens (Eds), Hillsdale, New York: Lawrence Elbraum; McDermott, L.C. (1984), Research on conceptual understanding in mechanics, Physics Today, 37(7), 24-32; Goldberg, F.M. & McDermott, L.C.
(1987), An investigation of student understanding of the real image formed by a converging lens or concave mirror, American Journal of Physics, 55(2), 108 –11;
Cohen, R., Eylon, B. & Ganiel, U. (1983), Potential difference and current in simple electric circuits, American Journal of Physics, 51, 407 - 412; Guth, J. (1995), An in-depth study of two individual students’ understanding of electric and magnetic fields, Research in Science Education, 25(4), 479-490; Furio, C. &
Guisasola, J. (1998), Difficulties in learning the concept of electric field, Science Education, 82(4), 511-26; Loverude, M.E., Kautz, C.H., & Heron, P.R.L. (2002), Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas, American Journal of Physics, 70(2), 137; and Kautz, C.H., Heron, P.R.L., Shaffer, P.S. and McDermott, L.C. (2005), Student understanding of the ideal gas law, Part II: A microscopic perspective, American Journal of Physics, 73(11), 1064-1071. For an overview of some of these studies, see McDermott, L.C. & Redish, E.F. (1999), Resource letter PER-1: Physics education research, American Journal of Physics, 67, 755-767.
2 There is a growing research base about students’ expectations or beliefs about the nature of physics knowledge and how to learn physics that affect student learning in a class. See, for example: Redish, E.F., Saul, J.M., & Steinberg, R.N. (1998), Student expectations in introductory physics, American Journal of Physics, 66, 212-224; Hammer, D. (2000), Student resources for learning introductory physics, American Journal of Physics, Physics Education Research Supplement, 68(S1), S52-S59; Elby, A., and Hammer, D. (2001). On the substance of a sophisticated
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Part 1:Teaching Physics Through Problem Solvingepistemology. Science Education, 85, 554-567; Hammer, D. (1994), Epistemological beliefs in introductory physics. Cognition and Instruction, 12 (2), 151-183; and Perkins, K. Adams, W. K., Finkelstein, N. D., Pollock, J. S., & Wieman, C. E.
(2005), Correlating student attitudes with student learning using the Colorado Learning Attitudes about Science Survey, Proceedings of the 2004 Physics Education Research Conference, Rochester, NY: PERC Publishing
3 Directly from an article by Jonathan Tuminaro and Edward Redish (2007), Elements of a cognitive model of physics problem solving: Epistemic games, Physical Review ST Physics Education Research, 3, 020101. There are many books about the emerging models of cognition. See, for example, Anderson, J.R.
(2004), Cognitive science and its implications, 6th Ed, Worth Publishing; Fuster, J.
(1999), Memory in the cerebral cortex: An empirical approach to neural networks in the human and nonhuman primate, MIT Press; and Fuster, J. (2003), Cortex and mind:
Unifying cognition, Oxford University Press.
4 In this brief presentation, we are using the more familiar term, ideas, rather than the smaller elements of knowledge with which students think. For a brief
discussion of these elements of knowledge, see the introduction to an article by Jonathan Tuminaro and Edward Redish (2007), Elements of a cognitive model of physics problem solving: Epistemic games, Physical Review ST Physics Education Research, 3, 020101.
5 For some seminal papers about how experts and novice solve problems, see Chi, M.T.H., Feltovich, P. J., & Glaser, R. (1981), Categorization and representation of physics problems by experts and novices, Cognitive Science, 5, 121-152; Eylon, B.
& Reif, R (1984), Effects of knowledge organization on task performance, Cognition and Instruction, 1(1), 5-44; and Larkin, J., McDermott, J., Simon, D. and Simon, H. (1980), Expert and novice performance in solving physics problems, Science, 208, 1335-1342.
6 Schoenfeld, A. H. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and meta-cognitions as driving forces in intellectual performance, Cognitive Science, 8, 173-190
7 Of course, there are more than two novice strategies for solving problems.
Different researchers use different research methodologies (e.g., videotaping individual students thinking aloud while solving a problem with structured or semi-structured questions by the interviewer; videotaping groups of students solving homework problems), students from classes with different pedagogies, and describe the novice strategies in different ways. See, for example: Tuminaro, J & Redish E.F. (2007), Elements of a cognitive model of physics problem solving: Epistemic games, Physical Review ST Physics Education Research, 3, 020101;
Walsh, L.N., Howard, R.G., and Bowe, B. (2007), Phenomenographic study of students’ problem solving approaches in physics, Physical Review ST Physics Education Research, 3, 020108.
8 See, for example, Chi, M., Feltovich, P.J., & Glaser, R. (1981), Categorization
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and representation of physics problems by experts and novices, Cognitive Science, 5, 121-152; Reif, F., & Heller, J.I (1982), Knowledge structure and problem solving in physics, Educational Psychologist, 17, 102-127; Ferguson-Hessler, M.G.M., & de Jong, T. (1987), On the quality of knowledge in the field of electricity and magnetism, American Journal of Physics, 55(6), 492-497; Elio, R. &
Scharf, P.B. (1990), Modeling novice-to-expert shifts in problem solving strategy and knowledge organization, Cognitive Science, 14(4), 579-639; and Zajchowski, R.,
& Martin, J. (1993), Differences in the problem solving of stronger and weaker novices in physics: Knowledge, strategies, or knowledge structure? Journal of Research in Science Teaching, 30, 459-470.
9 For reviews of expert-novice research, see Maloney, D.P. (1994), Research on problem solving in physics. In D.L. Gabel (Ed.), Handbook of Research in Science Teaching and Learning, (pp. 327-354), NY, Macmillan. See also, Hsu, L., Brewe, E., Foster, T. M., & Harper, K. A. (2004), Resource letter RPS-1: Research in problem solving. American Journal of Physics, 72(9), 1147-1156.