### Abstract:

This study aimed to investigate students' models of probability in a modern
physics context. The study was divided into three phases. The first phase explored
student pre-knowledge about probability before modem physics instruction. The
second phase investigated student understanding of concepts related to probability
such as wave-particle behavior, the uncertainty principle, and localization. The
third phase probed how students used the wave function to interpret probability in
potential energy problems. The participants were students taking modem physics
at Oregon State University. In the first phase, we developed a diagnostic test to
probe mathematical probability misconceptions and probability in a classical
physics content. For the mathematical probability misconceptions part, we found
that students often used a randomly distributed expectancy resource to predict an
outcome of a random event. For classical probability, we found that students often
employed an object's speed to predict the probability of locating it in a certain
region, which we call a classical probability reasoning resource. In the second and
the third phases, we interviewed students in order to get more in-depth data. We
also report the findings from Fall 03 preliminary interviews which indicated the
need for a more detail theoretical framework to analyze student reasoning.
Therefore, we employed the framework proposed by Redish (2003) to analyze the
interview data into two perspectives - reasoning resources and epistemic
resources. We found that most students used a classical probability resource to
interpret the probability from the wave function. Additionally, we identified two
associated patterns that students used to describe the traveling wave function in the
potential step and barrier. Finally, we discuss some teaching implications and
future research that the findings suggested.