written by
Michael C. Wittmann,
Jeffrey Morgan, and
Roger Feeley

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.

<a href="http://www.compadre.org/quantum/items/detail.cfm?ID=4846">Wittmann, M, J. Morgan, and R. Feeley. "Laboratory-tutorial activities for teaching probability." Phys. Rev. ST Phys. Educ. Res. 2, no. 2, (August 2, 2006).</a>

M. Wittmann, J. Morgan, and R. Feeley, Laboratory-tutorial activities for teaching probability, Phys. Rev. ST Phys. Educ. Res. 2 (2), (2006), <http://dx.doi.org/10.1103/PhysRevSTPER.2.020104>.

Wittmann, M., Morgan, J., & Feeley, R. (2006, August 2). Laboratory-tutorial activities for teaching probability. Phys. Rev. ST Phys. Educ. Res., 2(2). Retrieved January 17, 2017, from http://dx.doi.org/10.1103/PhysRevSTPER.2.020104

Wittmann, M, J. Morgan, and R. Feeley. "Laboratory-tutorial activities for teaching probability." Phys. Rev. ST Phys. Educ. Res. 2, no. 2, (August 2, 2006), http://dx.doi.org/10.1103/PhysRevSTPER.2.020104 (accessed 17 January 2017).

@article{
Author = "Michael Wittmann and Jeffrey Morgan and Roger Feeley",
Title = {Laboratory-tutorial activities for teaching probability},
Journal = {Phys. Rev. ST Phys. Educ. Res.},
Volume = {2},
Number = {2},
Month = {August},
Year = {2006}
}

%A Michael Wittmann %A Jeffrey Morgan %A Roger Feeley %T Laboratory-tutorial activities for teaching probability %J Phys. Rev. ST Phys. Educ. Res. %V 2 %N 2 %D August 2, 2006 %U http://dx.doi.org/10.1103/PhysRevSTPER.2.020104 %O application/pdf

%0 Journal Article %A Wittmann, Michael %A Morgan, Jeffrey %A Feeley, Roger %D August 2, 2006 %T Laboratory-tutorial activities for teaching probability %J Phys. Rev. ST Phys. Educ. Res. %V 2 %N 2 %8 August 2, 2006 %U http://dx.doi.org/10.1103/PhysRevSTPER.2.020104

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