Mountcastle, Bucy, Thompson on Probability and Uncertainty

D.B. Mountcastle, B.R. Bucy, J.R. Thompson
Student Estimates of Probability and Uncertainty in Advanced Laboratory and Statistical Physics Courses
Physics Education Research Conference Proceedings 2007

Equilibrium properties of macroscopic systems are highly predictable as n, the number of particles approaches and exceeds Avogadro's number; theories of statistical physics depend on these results. Typical pedagogical devices used in statistical physics textbooks to introduce entropy (S) and multiplicity () (where S = k ln()) include flipping coins and/or other equivalent binary events, repeated n times. Prior to instruction, our statistical mechanics students usually gave reasonable answers about the probabilities, but not the relative uncertainties, of the predicted outcomes of such events. However, they reliably predicted that the uncertainty in a measured continuous quantity (e.g., the amount of rainfall) does decrease as the number of measurements increases. Typical textbook presentations assume that students understand that the relative uncertainty of binary outcomes will similarly decrease as the number of events increases. This is at odds with our findings, even though most of our students had previously completed mathematics courses in statistics, as well as an advanced electronics laboratory course that included statistical analysis of distributions of dart scores as n increased.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 152-155