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Millikan Lecture 1998: Building a Science of Teaching Physics
1.R. A. Millikan, Mechanics Molecular Physics and Heat (Ginn, Boston, 1903), p. 3.
2.P. Laws, “Millikan Lecture 1996: Promoting active learning based on physics education research in introductory physics courses,” Am. J. Phys. 65, 14–21 (1996).
3.R. A. Millikan, The Electron, Its Isolation and Measurement and the Determination of Some of its Properties (Univ. of Chicago, Chicago, 1917).
4.There is a more subtle interpretation to the Phillips quote. Even if we have solved a physics education problem, because physics education depends on the experiences of both students and teachers, the problems are a (fortunately slowly) moving target.
5.L. Carroll, Sylvie and Bruno (Garland, New York, 1976), p. 265.
6.Mathematically, this is even true of a sphere, which cannot be mapped by a single nonsingular map to a Euclidean plane. See, for example, H. Flanders, Differential Forms, with Applications to the Physical Sciences (Academic, New York, 1963).
7.Though note that a more accurate map is not necessarily more useful. A map constructed from aerial photographs can be very difficult to read. A map is more useful if it is constructed with an appropriate level of abstraction. Those New Yorkers “of a certain age,” will recall the old subway maps—embedded on a realistic map of the city with correct relative distances. The current subway maps are more symbolic, emphasizing the different lines and their topological relationships rather than accurately represented distances.
8.If you take two functions from far enough out in the sequence they will be as close together everywhere as you want. (Given any there is an N such that if for all x.)
9.This is called completing a Hilbert space. See, for example, M. Reed and B. Simon, Methods of Mathematical Physics: Functional Analysis (Academic, New York, 1980), p. 7.
10.Other goals are possible, such as helping an individual teacher understand the effectiveness of a particular educational innovation in her own classroom.
11.We try to make experiments as similar as possible, but it is not, of course, possible ever to reproduce an experiment exactly—even if the identical apparatus is used. These small variations help us understand what variables are important (e.g., the colored stripes on the resistors) and which are not (e.g., the color of the insulation on the wires).
12.Note from this example that wishful thinking does not necessarily imply a rosy view of a situation. It may be that the wishful thinking is that “the situation is so bad that there is nothing can do about it and therefore I don’t have to make an effort.”
13.Plato, “Meno,” in The Dialogues of Plato, Volume One, translated by B. Jowett (Random House, New York, 1937), pp. 349–380.
14.H. Gardner, The Mind’s New Science: A History of the Cognitive Revolution (Basic Books, New York, 1987).
15.This idea, in fact, goes back to Descartes. What Piaget added was the empirical observations that document the result in detail. See, for example, the discussion of Descartes’ work in S. Savage-Rumbaugh et al., Apes, Language, and the Human Mind (Oxford U.P., New York, 1998), p. 90.
16.A wonderful example of what happens when the brain doesn’t work properly to create the idea of objects from visual images is given in the title case study in O. Sacks, The Man Who Mistook his Wife for a Hat (Pan Books, London, 1985).
17.R. Van der Veer and J. Valsiner, The Vygotsky Reader (Blackwell, Oxford, UK, 1994);
17.D. W. Johnson, R. T. Johnson, and E. J. Holubec, Circles of Learning: Cooperation in the Classroom (Interaction Book, Edina, MN, 1993).
18.P. S. Churchland and T. J. Sejnowski, The Computational Brain (MIT, Cambridge, MA, 1992).
19.In addition to the work discussed below by physicists, I have found the work of many researchers in the education community to be of great value in understanding what is happening in my classes, in particular, John Clement, Andrea diSessa, David Hammer, Pat Heller, Peter Hewson, and Alan Schonfeld, among others,. For specific references to work on physics education by both physicists and educators, see L. C. McDermott and E. F. Redish, “Resource Letter on Physics Education Research,” Am. J. Phys. (to be published).
20.E. F. Redish, “Implications of cognitive studies for teaching physics,” Am. J. Phys. 62, 796–803 (1994).
21.D. Halliday and R. Resnick, Physics (Wiley, New York, 1961).
22.Astronaut and astrophysicist George Nelson has remarked: “Education is not rocket science—it’s much harder.” Shaping the Future Conference, University System of Maryland, College Park, MD, Nov. 30, 1998.
23.Zeno’s paradox is an old proof that motion is impossible. To reach any distance you must first go halfway. To cover the second half of the remaining distance you must go half the remaining way, etc. To go any distance you must therefore cover infinitely many distances. Since this is obviously (sic!) impossible in a finite time, you cannot cover any finite distance in a finite time, hence motion is impossible.
24.Except, in the case of the sine function, for a discrete set of particular angles where the result can be calculated exactly.
25.W. Thirring, Classical Field Theory (Springer, New York, NY, 1979), pp. 87–99;
25.P. Dirac “Classical theory of radiating electrons,” Proc. R. Soc. London 167, 148–169 (1938).
26.An excellent discussion of these difficulties can be found in A. Cromer, Connected Knowledge (Oxford U.P., Oxford, 1997).
27.The problem occurs when a physical system we are supposed to be measuring permits a number of different results. If we describe the system of to be measured by a quantum wave function, the time evolution of the state will lead to a wave function in which the system to be observed, the apparatus, and the observer all simultaneously coexist in states having different results. See, for example, John Gribben, In Search of Schrödinger’s Cat (Bantam Books, New York, 1985).
28.Some approaches that have been considered include the randomization of uncontrollable phases and the coherent build up of minuscule time-irreversible pieces of the Hamiltonian over macroscopic times leading to collapse of the wave packet, among others.
29.The use of constructivism in education has bifurcated into a wide variety of groups, with acrimonious arguments as to who are the “true” constructivists. Among this panoply of competing views there are some similar to those we describe here. See, for example, D. I. Dykstra, Jr., C. F. Boyle, and I. A. Monarch, “Studying Conceptual Change in Learning Physics,” Science Education 76 (6), 615–652 (1992);
29.E. von Glasersfeld, “A Constructivist Approach to Teaching,” in Constructivism in Education, edited by L. P. Steffe and J. Gale (Erlbaun, Hillsdale, NJ, 1995), pp. 3–16.
30.L. C. McDermott and the Physics Education Group at the University of Washington, Physics by Inquiry, Vols. I and II (Wiley, New York, 1996).
31.L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice- Hall, Upper Saddle River, NJ, 1998).
32.P. Laws, Workshop Physics Activity Guide (Wiley, New York, 1997).
33.R. Thornton and D. Sokoloff, Tools for Scientific Thinking (Vernier Software, Ortland, OR, 1995);
33.D. Sokoloff, P. Laws, and R. Thornton, Real Time Physics (Wiley, New York, 1998).
34.K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, “Development and assessment of a research-based tutorial on light and shadow,” Am. J. Phys. 66, 906–913 (1998).
35.B. Thacker, E. Kim, K. Trefz, and S. M. Lea, “Comparing problem solving performance of physics students in inquiry-based and traditional introductory physics courses,” Am. J. Phys. 62, 627–633 (1994).
36.These are similar to constraints in medical research.
37.In a demonstration interview a student is shown a physical apparatus and asked to explain what they think will happen in a particular circumstance. Such interviews were used by Piaget and have become a crucial element in the observations of McDermott and her colleagues.
38.In a think-aloud protocol a student is presented a task (such as a physics problem to solve) and asked to “think out loud.” See K. Ericsson and H. Simon, Protocol Analysis: Verbal Reports as Data (Revised Edition) (MIT, Cambridge, MA, 1993).
39.This is a common problem even at the University level and is well known to math education researchers. See, for example, S. Vinner, and T. Dreyfus, “Images and definitions for the concept of a function,” Journal for Research in Mathematics Education 20 (4), 356–366 (1989).
40.M. Wittmann, “Making sense of how students come to an understanding of physics: An example from mechanical waves,” Ph.D. dissertation, University of Maryland, 1998.
41.A. Arons, A Guide to Introductory Physics Teaching (Wiley, New York, 1990).
42.P. A. Krause, P. S. Shaffer, and L. C. McDermott, “Using research on student understanding to guide curriculum development: An example from electricity and magnetism,” AAPT Announcer 25, 77 (Dec., 1995).
43.Arons does include citations to education research, especially in the sections on mechanics, but the book focuses on raising issues and offering solutions, not documenting them.
44.Note further that this result had been known previously and even published, but not in a journal which I looked at regularly or which was conveniently available. D. P. Maloney, “Charged poles,” Physics Education 20, 310–316 (1985).
45.R. K. Thornton and D. R. Sokoloff, “Learning motion concepts using real-time microcomputer-based laboratory tools,” Am. J. Phys. 58, 858–867 (1990).
46.J. M. Saul, “Beyond Problem Solving, Evaluating Introductory Physics Courses Through the Hidden Curriculum,” Ph.D. Dissertation, University of Maryland, 1998
47.D. Hestenes, M. Wells, and G. Swackhammer, “Force Concept Inventory,” Phys. Teach. 30 (3), 141–158 (1992).
48.R. R. Hake, “Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses,” Am. J. Phys. 66, 64–74 (1998).
49.It was important to confirm this since Hake solicited results after the fact and those classes with poor results might have chosen not to report them.
50.The Workshop Physics classes tested were early secondary implementations. The well-established primary implementation at Dickinson College consistently scores well above this level.
51.P. Bak, How Nature Works (Springer Verlag, New York, 1996).
52.D. Hestenes, “Modeling games in the Newtonian world,” Am. J. Phys. 60, 732–748 (1992).
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