- Open Access
Laboratory-tutorial activities for teaching probability
Phys. Rev. ST Phys. Educ. Res. 2, 020104 – Published 2 August, 2006
DOI: https://doi.org/10.1103/PhysRevSTPER.2.020104
Abstract
We report on the development of students’ ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We describe a set of activities used to teach concepts of probability and probability density. Rudimentary knowledge of mechanics is needed for one activity, but otherwise the material requires no additional preparation. Extensions of the activities include relating probability density to potential energy graphs for certain “touchstone” examples. Students have difficulties learning the target concepts, such as comparing the ratio of time in a region to total time in all regions. Instead, they often focus on edge effects, pattern match to previously studied situations, reason about necessary but incomplete macroscopic elements of the system, use the gambler’s fallacy, and use expectations about ensemble results rather than expectation values to predict future events. We map the development of their thinking to provide examples of problems rather than evidence of a curriculum’s success.
Article Text
References (16)
- J. Garfield and A. Ahlgren, Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research, J. Res. Math. Educ.19, 44 (1988).
- C. Konold, Issues in Assessing Conceptual Understanding in Probability and Statistics, J. Educ. Stat. 3, http://www.amstat.org/publications/jse/v3n1/konold.html (1995).
- H. Sahai, A. Khurshid, and S. C. Misra, A Second Bibliography of the Teaching of Probability and Statistics, J. Educ. Stat. 4, http://www.amstat.org/publications/jse/v4n3/sahai.html (1996).
- L. Bao and E. F. Redish, Understanding probabilistic interpretations of physics systems: A prerequisite to learning quantum physics, Am. J. Phys. 70, 210 (2002).
- B. S. Ambrose et al., An investigation of student understanding of single-slit diffraction and double-slit interference, Am. J. Phys. 67, 146 (1999).
- D. Domert, C. J. Linder, and Å. Ingerman, Probability as a conceptual hurdle to understanding one-dimensional quantum scattering and tunnelling, Eur. J. Phys. 26, 47 (2005).
- P. Jolly et al., Visualizing motion in potential wells, Am. J. Phys. 66, 57 (1998).
- M. C. Wittmann et al., http://www.arxiv.org/abs/physics/0602141
- R. R. Harrington and E. E. Prather, in The Changing Role Of Physics Departments In Modern University, AIP Conf. Proc. No. 399, edited by E. F. Redish and J. Rigden (AIP, Woodbury, 1997), p. 797. Available online at http://perlnet.umaine.edu/bio/harrington/ICUPE.html
- M. C. Wittmann, Lab-Tutorials fur den Quantenphysik Unterricht, Prax. Naturwiss., Phys. Sch. 55, 16 (2006), http://arxiv.org/abs/physics/0604115
- E. F. Redish and T. McCaskey (personal communication).
- E. F. Redish, J. M. Saul, and R. N. Steinberg, Student expectations in introductory physics, Am. J. Phys. 66, 212 (1998).
- B. S. Ambrose, Student Understanding of Probability in Classical and Modern Physics, AAPT Announcer 31 (2), 81 (2001).
- B. S. Ambrose, Student Understanding of Probability in the Classical and Semiclassical Regimes, AAPT Announcer 32 (2), 134 (2002).
- Video available at http://perlnet.umaine.edu/abt/v2video.htm
- L. Bao, Ph.D. thesis, available at http://physics.umd.edu/perg/dissertations/, University of Maryland, 1999.