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University student and K-12 teacher reasoning about the basic tenets of kinetic-molecular theory, Part I: Volume of an ideal gas
1.Some authors have argued that, at the introductory/elementary level, these aspects are the essence of the particle nature of matter. See, for example, O. Lee, D. C. Eichinger, C. W. Anderson, G. D. Berkheimer, and T. D. Blakeslee,“Changing middle school students' conceptions of matter and molecules,” J. Res. Sci. Teach. 30(3), 249–270 (1993).
2.See, for example, P. A. Tipler, Physics for Scientists and Engineers, 3rd ed. (Worth Publishers, New York, NY, 1991) and
2. S. S. Zumdahl, Chemical Principles, 6 ed. (Houghton Mifflin Company, Boston, MA, 2009).
3.The research also included an examination of the extent to which students related the temperature of an ideal gas to the microscopic motion of the gas particles. The findings were consistent with those from other studies. [See, for example, Ref. 10, Ref. 25, and M. E. Loverude, C. H. Kautz, and P. R. L. Heron, “Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of a gas,” Am. J. Phys. 70(2), 137–148 (2002).]
4.Students in the advanced introductory chemistry course at the UW are required to have completed at least one quarter of calculus and the equivalent of a one-year high school chemistry course. The Chemistry Department estimates that the advanced course represents the top 10% of all students taking introductory chemistry.
5. J. Piaget and B. Inhelder, The Child's Construction of Quantities: Conservation and Atomism (Routledge & Kegan Paul, London, 1974).
6. M. C. Linn and B. Eylon, “Knowledge Integration and Displaced Volume,” J. Sci. Ed. Tech. 9(4), 287–310 (2000);
6. C. Dawson and J. Rowell, “Displacement of Water: Weight or Volume? An Examination of Two Conflict Based Teaching Strategies,” Res. Sci. Ed. 14, 69–77 (1984);
6. 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(11), 1178–1187 (2003).
8. C. H. Kautz, P. R. L. Heron, M. E. Loverude, and L. C. McDermott, “Student understanding of the ideal gas law, Part I: A macroscopic perspective,” Am. J. Phys. 73(11), 1055–1063 (2005);
8. M. G., “The Gaseous State,” in Children's Ideas in Science, edited by R. Driver, E. Guesne, and A. Tiberghien (Open U.P., 1985);
9. K. C. deBerg, “Student understanding of the volume, mass, and pressure of air within a sealed syringe in different states of compression,” J. Res. Sci. Teach. 32(8), 871–884 (1995).
10. M. L. Rosenquist, “Improving preparation for college physics of minority students aspiring to science-related careers: Investigation of student difficulties and development of appropriate curriculum,” Ph.D. dissertation, Department of Physics, University of Washington, 1982 (unpublished).
11. C. Kautz, “Identifying and addressing student difficulties with the ideal gas law,” Ph.D. dissertation, Department of Physics, University of Washington, 1999 (unpublished).
12. F. M. Lorenzo-Barral and J. Mendozo-Rodriguez, “Changing Students' Conceptions about Non-Conservation of Volume in Solutions,” presented at the Third International Seminar on Misconceptions and Educational Strategies in Science and Mathematics, 1993 (unpublished).
14.See, for example, D. L. Benson, M. C. Wittrock, and M. E. Baur, “Students' preconceptions of the nature of gases,” J. Res. Sci. Teach. 30(6), 587–597 (1993).
16. M. B. Nakleh, “Are our students conceptual thinkers or algorithmic problem solvers?: Identifying conceptual students in general chemistry,” J. Chem. Ed. 70(1), 52–55 (1993).
17. M. J. Sanger and A. J. Phelps, “What are students thinking when they pick their answer? A content analysis of students' explanations of gas properties,” J. Chem. Ed. 84(5), 870–874 (2007).
18. S. C. Nurrenbern and M. Pickering, “Concept learning versus problem solving: Is there a difference?,” J. Chem. Ed. 64(6), 508–510 (1987).
19.The lack of consistency in the number of particles in the tanks in Fig. 1 from the original Nurrenbern and Pickering study was corrected in the Sanger and Phelps (2007) paper (see Ref. 16).
20. M. J. Sanger, E. Campbell, J. Felker, and C. Spencer, “"Concept learning versus problem solving": Does particle motion have an effect?,” J. Chem. Ed. 84(5), 875–879 (2007).
21.In this follow-up study, the authors illustrated the motion of the original gas and the four answer choices in the following way: the original distribution of the gas was represented by “nine red circles… [that] moved in rapid, straight-line motions unless undergoing a collision with another He atom or the walls of the circular container.” The particles in distribution (a) were also shown moving in straight lines (until they collided with a wall or another particle) and occupying the entire container, but the particles moved slower than in the original distribution. Particles in distribution (b) never moved “more than half of the container's radius away from the center and no particles ever collided with the container walls; if the particles moved too far from the center, they turned around in mid-air.” The same was true of the particles in distribution (d), but these never moved more than a half-radius away from the wall. In distribution (c), the particles occupied the bottom part of the container and would turn around mid-air if they moved “too far up in the container.”
22.The types of reasoning given by students in response to the written and online questions were similar and are not distinguished in the text.
23.The physical situation for the macroscopic density question is nearly identical to that of the macroscopic volume question. The differences are as follows: the rigid container is square (in the density context) rather than round, the container is said to be placed into an ice-water bath (rather than an unspecified method for lowering the temperature of the gas), and the final temperature is 0 °C instead of –20 °C. Students are asked whether the density (rather than the volume) of the gas increases, decreases, or remains the same as the gas cools.
24.On the microscopic volume question the percentages ranged from: ∼20%–35% for the introductory chemistry students, ∼20% for the advanced introductory chemistry students and ∼40% for the introductory physics students. On the microscopic volume question, the percentages were ∼15% for the introductory chemistry students and ∼5% for the advanced introductory chemistry students.
25.Although there is in fact an effect on the gas particles due to gravity, it is essentially negligible.
27.Approximately one-third of the teachers enrolled in the course were interviewed. The sample included elementary, middle, and high school teachers. The course grades earned by the teachers who were interviewed varied from below to above average.
28.In other words, the tank was ‘made bigger’– these holes did not provide access to ‘the outside,’ they only provided another space for particles to occupy.
29.Recall that many of the university students in the Sanger, et al. (2007) study articulated that they expected the particles in distributions (b), (c), and (d) to occupy the full volume of the container.
30.Two of these teachers received above-average grades in the course, and the remaining teacher received a below-average grade.
31.Reprinted with permission from Ref. 18. Copyright 1987 American Chemical Society.
32.Adapted with permission from Ref. 17. Copyright 2005 American Chemical Society.
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