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Student understanding of static equilibrium: Predicting and accounting for balancing
1.L. G. Ortiz, “Identifying and addressing student difficulties with rotational dynamics,” Ph.D. dissertation, Department of Physics, University of Washington, 2001 (unpublished).
2.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, 2002).
3.David Halliday, Robert Resnick, and Kenneth S. Krane, Physics, 4th ed. (Wiley, New York, 1992);
3.Douglas C. Giancoli, Physics for Scientists and Engineers, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 2000).
4.Reference 2, pp. 61–64.
5.For most questions, the results were the same before and after the tutorial on rigid body dynamics so we have combined the data. For one question, the results were affected by the tutorial on rigid body dynamics. We have omitted this data because that tutorial has changed considerably, and the results are probably not relevant for the typical classroom.
6.For similar results see C. Henderson, “Common concerns about the force concept inventory,” Phys. Teach. 40, 542–547 (2002).
7.A similar problem appeared in P. Hewitt, “Figuring physics,” Phys. Teach. 25, 109–110 (1987).
8.All of the percentages have been rounded to the nearest 5% to provide a sense of how well they are known, that is, differences on the order of 5%–10% are not considered significant.
8.For further discussion of this assessment, see P. R. L. Heron, M. E. Loverude, P. S. Shaffer, and L. C. McDermott, “Helping students develop an understanding of Archimedes’ principle, Part II: Development of research-based instructional materials,” Am. J. Phys. 71, 1188–1195 (2003).
9.It can be argued that the students should consider the beam as the system of interest in which case the relevant forces are contact forces exerted by each crate on the beam, not the gravitational forces exerted on the crates. However, the same conclusion is reached in either case, and we considered the choice of system to be of secondary importance.
10.The students did not need to distinguish between the gravitational force exerted on the clay and the force exerted by the clay on the board in order to be considered correct.
11.See M. L. Rosenquist, “Improving preparation for college physics of minority students aspiring to science-related careers,” Ph.D. dissertation, Department of Physics, University of Washington, 1982 (unpublished).
11.See also J. W. Renner and A. E. Lawson, “Promoting intellectual development through science teaching,” Phys. Teach. 11, 273–276 (1973);
11.M. E. Loverude, C. H. Kautz, and P. R. L. Heron, “Helping students develop an understanding of Archimedes’ Principle, Part I: Research on student understanding,” Am. J. Phys. 71, 1178–1187 (2003), and Ref. 8.
12.For related results in the context of position, velocity, and acceleration, see D. E. Trowbridge and L. C. McDermott, “Investigation of student understanding of the concept of velocity in one dimension,” Am. J. Phys. 48, 1020–1028 (1980)
12.and D. E. Trowbridge and L. C. McDermott, “Investigation of student understanding of the concept of acceleration in one dimension,” Am. J. Phys. 49, 242–253 (1981).
13.See Ref. 8 and the last article in Ref. 11.
14.See, for example, L. Viennot, “Spontaneous reasoning in elementary dynamics,” Eur. J. Sci. Educ. 1, 205–221 (1979);
14.A. Champagne, L. Klopfer, and J. Anderson, “Factors influencing the learning of classical mechanics,” Am. J. Phys. 48, 1074–1079 (1980);
14.J. Clement, “Students’ preconceptions in introductory mechanics,” Am. J. Phys. 50, 66–71 (1982).
15.Many equal-arm balances rely on the center of mass of the apparatus to provide sufficient torque to counter the effects of the additional masses. Some also rely on the change in the ratio of the distances from the points at which the pans are attached, if those points are above the pivot point of the balance.
16.For the two-piece bar the (smallest) angle formed between the position and gravitational force vectors (when placed tail-to-tail) of one piece supplements that of the other, that is,
17.For other evidence of little (or no) change in the prevalence of specific learning difficulties before and after instruction, see, for example, L. C. McDermott, “Millikan Lecture 1990: What we teach and what is learned–Closing the gap,” Am. J. Phys. 59, 301–315 (1991);
17.L. C. McDermott, “Guest comment: How we teach and how students learn–a mismatch?,” Am. J. Phys. 61, 295–298 (1993);
17.and R. R. Hake, “Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses,” Am. J. Phys. 66, 64–74 (1998).
18.Anthony Bedford and Wallace Fowler, Statics (Addison-Wesley, Reading MA, 1995).
19.A similar attempt by a different professor yielded essentially the same results. In the second class, the professor used the baseball bat problem as the basis for an in-class question on which students used a personal response system to indicate their predictions.
20.Other evidence that students often observe what they expect to see can be found in, for example, M. McCloskey, “Intuitive physics,” Sci. Am. 249 (4), 122–130 (1983).
21.A. A. diSessa, “Towards an epistemology of physics,” Cogn. Instruct. 10, 105–225 (1993).
22.Although a detailed analysis is beyond the scope of this paper, it is clear that some of the results reported here could be interpreted within this perspective. For example, many students stated that the bar will “go back to where it was initially” once it is released, but suggested no explanatory mechanism. Such answers are consistent with the apparent belief, reported by diSessa, in the universal tendency of systems to return to equilibrium once a presumed dis-equilibrating influence has been removed.
23.For a description of the tutorial system, see, for example, L. C. McDermott, “Response for the 2001 Oersted Medal, Physics education research: The key to student learning,” Am. J. Phys. 69, 1127–1137 (2001).
24.Reference 2, pp. 65–68.
25.Previously published findings by our group suggest that the somewhat greater emphasis on the topic in some classes in which the tutorial was used is probably not the determining factor. See the article in Ref. 8.
26.For a discussion of the pedagogical importance of operational definitions, see Arnold Arons, A Guide to Introductory Physics Teaching (Wiley, New York, 1990). A discussion of the usefulness of an operational definition of length can be found in R. E. Scherr, “An investigation of student understanding of basic concepts of special relativity,” Ph.D. dissertation, Department of Physics, University of Washington, 2001 (unpublished).
27.See Ref. 8 and the last article in Ref. 11.
28.This difficulty is taken into account in tutorials on forces and Newton’s laws in Ref. 2 as well as several other widely available instructional materials including those described in R. K. Thornton and D. R. Sokoloff, “Assessing student learning of Newton’s laws: The Force and Motion Conceptual Evaluation and the evaluation of active learning laboratory and lecture curricula,” Am. J. Phys. 66, 338–352 (1998).
28.Several current textbooks also include explicit discussions of this difficulty. See, for example, Randall D. Knight, Physics for Scientists and Engineers: A Strategic Approach (Addison-Wesley, San Francisco, CA, 2004).
29.For a discussion of this strategy see the first article in Ref. 17.
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