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.
Highlights
Though probability and simple statistics are common in our societyranging from baseball batting averages to polling data with its statistical measures, we rarely teach the concepts in our introductory physics courses
The learning of the concept of probability has been studied in great detail in the area of mathematics and statistics—for example, in Refs. 1 and 2—and there is a thoroughthough slightly outdatedbibliography on the topic.[3]
Because probability is rarely taught in introductory physics, it has not been studied much by physics education researchers
Summary
Though probability and simple statistics are common in our societyranging from baseball batting averages to polling data with its statistical measures, we rarely teach the concepts in our introductory physics courses. We have created a set of activities for teaching probability in a way that can help non-science-major students later learn concepts of quantum physics. We describe the effect of our course on student understanding of probability and probability density in classical situations for a population that, anecdotally, has little mathematical confidence or science background. A goal of our course has been to make physics concepts accessible to students who are on their way to learning the introductory ideas of quantum physics. To help students understand this concept, we begin by teaching about probability in nonphysics situations and move into discussions of probability density in physical situations such as a ball toss or oscillating glider. Research data are given based on the Fall, 2005, semester in which we were best able to track student learning on the topic of probability density. We describe data from several ungraded pre- and post-tests and two examination questions, as well as informal observations which are consistent with our research data
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