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Model analysis of fine structures of student models: An example with Newton’s third law
1.L. C. McDermott and E. F. Redish, “Resource letter PER-1: Physics education research,” Am. J. Phys. 67 (9), 755–767 (1999).
2.L. Bao, “Dynamics of student modeling: A theory, algorithms, and application to quantum mechanics,” Ph.D. dissertation, University of Maryland, December 1999.
3.G. Gliner, “College students organization of math word problems in relation to success in problem solving,” School Sci. Math. 89 (5), 392–404 (1989).
4.G. Gliner, “College students organization of math word problem solving in terms of mathematical structure versus surface structure,” School Sci. Math. 91 (3), 105–110 (1991).
5.How People Learn: Brain, Mind, Experience, and School, edited by J. D. Bransford, A. L. Brown, and R. Cocking (National Academy Press, Washington, DC, 1999).
6.D. Palmer, “The effect of context on students reasoning about forces,” Int. J. Sci. Educ. 19 (6), 681–696 (1997).
7.E. Engel Clough and R. Driver, “A study of consistency in the use of students conceptual frameworks across different task contexts,” Sci. Educ. 70 (4), 473–496 (1986).
8.In research, we generally consider three major domains of context factors: content-based factors, educational settings, and certain student internal status such as views and motivations on learning.
9.L. Bao and E. F. Redish, “Concentration analysis: A quantitative assessment of student states,” PERS of Am. J. Phys. 69 (7), S45–53(2001);
9.“Model analysis: Assessing the dynamics of student learning,” Cognit. Instruction (submitted).
10.For example: D. Hestenes and M. Wells, “Mechanics baseline test,” Phys. Teach. 30, 159–169 (1992);
10.D. Hestenes, M. Wells, and G. Swackhammer, “Force concept inventory,” Phys. Teach. 30, 141–153 (1992).
11.Reference 2, Chap. 4.
12.See Refs. 2 and 9.
13.J. Minstrell, “Facets of students knowledge and relevant instruction,” Research in Physics Learning: Theoretical Issues and Empirical Studies, Proceedings of an International Workshop, Bremen, Germany, 4–8 March, 1991, edited by R. Duit, F. Goldberg, and H. Niedderer (IPN, Kiel, Germany, 1992), pp. 110–128.
14.S. Vosniadou, “Capturing and modeling the process of conceptual change,” Learning Instruction 4, 45–69 (1994).
15.Ronald K. Thornton, “Conceptual dynamics: Changing student views of force and motion,” in The Changing Role of Physics Departments in Modern Universities, Proceedings of the International Conference on Undergraduate Physics Education, edited by E. F. Redish and J. S. Rigden (Wiley, New York, 1997), pp. 241–266.
16.Detailed definitions and discussions can be found in Refs. 2 and 9.
17.Supporting evidence and method of investigations can be found in Refs. 2 and 9.
18.A detailed formulation is discussed in Refs. 2 and 9.
19.See Ref. 2 and I. A. Halloun and D. Hestenes, “Common sense concepts about motion,” Am. J. Phys. 53 (11), 1056–1065, 1985;
19.I. A. Halloun and D. Hestenes, “The initial knowledge state of college physics students,” Am. J. Phys. 53 (11), 1043–1055 (1985).
20.Reference 7 and D. P. Maloney, “Rule-governed approaches to physics—Newton s third law,” Phys. Educ. 19, 37 (1984).
21.Reference 7 and D. Palmer, “How consistently do students use their alternative conceptions?,” Res. Sci. Educ. 23, 228–235 (1993).
22.See Ref. 6.
23.See Refs. 2, 7, and 9. In addition, our experience also suggests that it is sometimes possible for students to have different considerations for an object that is speeding up and one that is moving at a constant speed.
24.D. A. Zollman, “Preparing future science teachers: The physics component of a new program,” J. Phys. Educ. 29, 271–275 (1994);
24.D. A. Zollman, “Learning cycles for a large enrollment class,” Phys. Teach. 28, 20–25 (1990).
25.When dealing with the mixing of student models, we consider two different types of mixed states: explicit mixing and implicit mixing. Explicit mixing describes the situation where a single context setting activates a student to explicitly consider two different models at the same time. Implicit mixing describes the situation where a single context setting always activates a student to use one model, but different equivalent context settings will cue the same student to use different models. More details on how to study and assess the different types of mixing are discussed in Ref. 9 and in a manuscript in preparation.
26.Here, although students consider the acceleration irrelevant, it doesn’t mean that these students have the correct expert model on this issue. It only reflects that most students don’t associate this issue in their reasoning.
27.We are currently studying this issue.
28.See Ref. 2 for more details on physical features.
29.See Ref. 2.
30.The numbering tradition of the common models is different from the one used in Ref. 2. The system used in this paper makes it more convenient to represent model space when the number of common models with different physical features may vary. The superscript is used to represent the dimension related to pushing.
31.See Ref. 2, Chap. 5.
32.Strictly speaking, the development of the survey and the interviews were done in the same time frame. The interviews were conducted over a period of two weeks and the results from the earlier ones were used to make slight modifications to the survey questions. Our initial design of the survey was largely based on the existing research in the literature as well as our own empirical experience. However, based on the interview results, this initial guess seems to have been quite successful, which saved much time in our research.
33.See Ref. 9.
34.See Refs. 9, 13, 14, Ref. 2, Chap. 5, and D. P. Maloney and R. S. Siegler, “Conceptual competition in physics learning,” Int. J. Sci. Educ. 15 (3), 283–295(1993).
35.See Ref. 2 for more details.
36.For more details, see Ref. 9 and Ref. 2, Chap. 4.
37.See Ref. 2 for details on model plots and class model states.
38.Quite interestingly, the results also indicate that more students in higher level classes change their ideas on this issue. Our preliminary results indicate that this can happen when students get into confusing/transitional stages (often with mixed model states). We are looking further into the mechanisms behind this phenomenon.
39.See Refs. 2 and 14.
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