A research-based approach to improving student understanding of the vector nature of kinematical concepts

American Journal of Physics

Volumn 73, Issue 10, 2005, Pages 921-931

  Shaffer, Peter S ^a   McDermott, Lillian C ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27144439036     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2000976     Document Type: Article

References (35)

1. Results from these investigations are in D. E. Trowbridge and L. C. McDermott, "Investigation of student understanding of the concept of velocity in one dimension," Am. J. Phys. 48 (12), 1020-1028 (1980);
2. "Investigation of student understanding of the concept of acceleration in one dimension," 49 (3), 242-253 (1981);
3. and L. C. McDermott, M. L. Rosenquist, and E. H. van Zee, "Student difficulties in connecting graphs and physics: Examples from kinematics," ibid. 55 (6), 503-515 (1987).
4. Documentation of similar findings in the honors section of the introductory course are in P. C. Peters, "Even honors students have conceptual difficulties with physics," Am. J. Phys. 50 (6), 501-508 (1982).
5. L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice Hall, Englewood Cliffs, NJ, 2002).
6. L. C. McDermott and the Physics Education Group at the University of Washington, Physics by Inquiry (Wiley, New York, 1996).
7. For a list of references to studies at the precollege level, see R. Duit, "Students' and teachers' conceptions and science education, Bibliography," Leibniz Institute for Science Education at the University of Kiel, Olshausenstr. 62 24098 Kiel, Germany, or 〈http://www.ipn.uni-kiel. de/aktuell/stese/stese.html〉.
8. For a list of references to studies at the university level, see L. C. McDermott and E. F. Redish, "Resource letter: PER-1: Physics education research," Am. J. Phys. 67 (9), 755-767 (1999).
9. For example, Laws, Thornton, and Sokoloff have applied findings from research to the development of real-time microcomputer-based laboratory tools to help students make connections between real motions and their graphical representations. A discussion of the instructional approach appears in P. W. Laws, "Millikan lecture 1996: Promoting active learning based on physics education research in introductory physics courses," Am. J. Phys. 65 (1), 14-21 (1997);
10. and R. K. Thornton and D. R. Sokoloff, "Learning motion concepts using real-time microcomputer-based laboratory tools," ibid. 58 (9), 858-867 (1990).
11. P. Labudde, F. Reif, and L. Quinn, "Facilitation of scientific concept learning by interpretation procedures and analysis," Int. J. Sci. Educ. 10 (1), 81-98 (1988);
12. F. Reif and S. Allen, "Cognition for interpreting scientific concepts: A study of acceleration," Cogn. Instruct. 9 (1), 1-44 (1992).
13. This problem was used by Reif in the studies described in Ref. 7.
14. There are many problems of this type that students should be able to solve. Another example of the need to infer information about the acceleration from kinematical constraints is given in L. C. McDermott, P. S. Shaffer, and M. D. Somers, "Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood's machine," Am. J. Phys. 62 (1), 46-55 (1994). Students were presented with a problem involving two blocks of different mass connected by an inextensible string passing over a pulley. About 15% failed to recognize that the accelerations of the blocks were equal.
15. Most of the Ph.D. granting universities had similar results on the pretests and post-tests. The results have been combined and are presented in the tables and text. Footnotes to the tables give results from non-Ph.D. granting institutions, Harvard University, and a self-selected honors section of UW calculus-based physics, which had a higher percentage of physics and science majors than other sections.
16. For examples of research related to graphical interpretations of motion, see R. J. Beichner, "Testing student understanding of motion graphs," Am. J. Phys. 62 (8), 750-762 (1994);
17. F. M. Goldberg and J. H. Anderson, "Student difficulties with graphical representations of negative values of velocity," Phys. Teach. 27 (4), 254-260 (1989);
18. and the third paper in Ref. 1.
19. See, for example, S. Flores, S. E. Kanim, and C. H. Kautz, "Student use of vectors in introductory mechanics," Am. J. Phys. 72 (4), 460-468 (2004);
20. N. L. Nguyen and D. E. Meltzer, "Initial understanding of vector concepts among students in introductory physics courses," ibid. 71 (6), 630-638 (2003);
21. R. D. Knight, "The vector knowledge of beginning physics students," Phys. Teach. 33 (2), 74-78 (1995);
22. J. M. Aguirre, "Student preconceptions about vector kinematics," ibid. 26 (4), 212-216 (1988);
23. and J. M. Aguirre and G. Erickson, "Students' conceptions about the vector characteristics of three physics concepts," J. Res. Sci. Teach. 21, 437-457 (1984).
24. See the second paper in Ref. 13.
25. This result is similar to that obtained by Reif and Allen on a corresponding question in the small-scale study (N=5) described in the second article in Ref. 7.
26. Confusion between velocity and acceleration in one dimension has been documented previously. See, for example, the first two papers in Ref. 1.
27. We also have administered pretest questions involving open, curved trajectories. Most students do not claim that the acceleration is directed toward the center or the "foci"; however, the percentage of correct answers is similar to that on the oval pretest.
28. 0. Some students might have had difficulty with this approximation.
29. There is a common tendency to associate causes of motion only with active forces and not with passive forces. See, for example, J. Minstrell, "Explaining the 'at rest' condition of an object," Phys. Teach. 20 (1), 10-14 (1982);
30. L. C. McDermott, "Research on conceptual understanding in mechanics," Phys. Today 37 (7), 24-32 (1984).
31. Some of the generalizations, their basis, and an instructional strategy that can be summarized as "elicit, confront, and resolve" are discussed in greater detail in L. C. McDermott, "Oersted medal lecture 2001: Physics education research - The key to student learning," Am. J. Phys. 69 (11), 1127-1137 (2001)
32. and L. C. McDermott, "Millikan lecture 1990: What we teach and what is learned - Closing the gap," Am. J. Phys. 59 (4), 301-315 (1991).
33. Reif had observed a similar tendency. See, for example, Ref. 7.
34. Research on student understanding of 2D vertical motion has been con-ducted at the University of Washington, at the University of Maine (J. R. Thompson), and at Grand Valley State University (B. S. Ambrose).
35. For a description of these courses, see L. C. McDermott, "A perspective on teacher preparation in physics and other sciences: The need for special science courses for teachers," Am. J. Phys. 58 (8), 734-752 (2000).