Context affects student thinking about sources of uncertainty in classical and quantum mechanics

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students’ procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study upper-level students’ thinking about sources of measurement uncertainty across experimental contexts, with a particular focus on classical and quantum mechanics contexts. We developed a survey to probe students’ thinking in the generic question “What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?” as well as in a range of specific experimental scenarios and interpreted student responses through the lens of availability and accessibility of knowledge pieces. We found that limitations of the experimental setup were most accessible to students in classical mechanics while principles of the underlying physics theory were most accessible to students in quantum mechanics, even in a context in which this theory was not relevant. We recommend that future research probe which sources of uncertainty experts believe are relevant in which contexts and how instruction in both classical and quantum contexts can help students draw on appropriate sources of uncertainty in classical and quantum experiments.

Figure 1

The four experimental scenarios included in the survey: projectile motion, Stern-Gerlach, Brownian motion, and single slit. These four experiments span the possible combinations of physics paradigm (classical or quantum) and the theoretical expected outcome (single value or distribution).

Figure 2

The descriptive text, diagram, and histogram of fictitious experimental data for the projectile motion scenario.

Figure 3

Respondent comfort with the experimental scenarios in the survey.

Figure 4

Codes applied to sources of uncertainty listed for each experiment in response to the prompt “What is causing the shape of the distribution? List as many causes as you can think of.” Physics paradigm is denoted by color ($\mathrm{purple}=\text{classical}$, $\mathrm{green}=\text{quantum}$), while theoretical expected outcome is denoted by pattern ($\mathrm{solid}=\text{single}$ value, $\mathrm{striped}=\text{distribution}$). Error bars represent the standard error on the proportions.

Figure 5

Codes applied to student responses to the question “What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?” Error bars represent the standard error on the proportions. Physics paradigm is denoted by color ($\mathrm{purple}=\text{classical}$, $\mathrm{green}=\text{quantum}$).

Figure 6

The descriptive text, diagram, and histogram of fictitious experimental data for the upper-level experimental scenarios.

Figure 7

Codes of sources listed by students with different comfort levels for the Brownian motion and Stern-Gerlach experiments, the two experiments with the lowest comfort levels. Error bars represent the standard error.

Figure 8

Codes for responses to the generic uncertainty questions, separated by what upper-level experiment each respondent saw during the survey. Physics paradigm is denoted by color ($\mathrm{purple}=\text{classical}$, $\mathrm{green}=\text{quantum}$), while theoretical expected outcome is denoted by pattern ($\mathrm{solid}=\text{single}$ value, $\mathrm{striped}=\text{distribution}$). Error bars represent the standard error.