Investigating the dynamics of ontological reasoning across contexts in quantum physics

The ontologies students use—their conceptions about the nature of entities—impact the way they learn physics and reason through physics problems. We investigate students’ capacities for flexible use of ontologies in a modern physics context, focusing on students’ reasoning around two quantum entities (photons and electrons) for three canonical topics in introductory quantum physics (double slit experiment, Mach-Zehnder interferometer, and quantum tunneling). We present a description of a full framework to describe and distinguish between different kinds of dynamic ontologies. The framework identifies possible ontological structures in individual reasoning episodes, three of which we identify in our data set: unitary (applying a single stable ontology), parallel (switching back and forth between multiple ontologies), and blended (constructing a novel ontology by blending two or more input ontologies). These different ontological structures are applied to the specific ontologies used (e.g., wave or particle) for the specific entity (e.g., photon or electron). We demonstrate the utility of the framework by coding individual responses from a representative sample of an introductory modern physics course to an array of written and multiple-choice questions on homework, exams, and pre- and postsurveys. We present and explore the patterns of use of ontologies across the three topical contexts and these various modalities. We demonstrate that students use a variety of ontologies and ontological structures across entities and topic areas, even when not explicitly prompted to do so. In addition to providing evidence of students’ capacities for flexible use of ontologies, we find that the wording and framing of the question prompts impact students’ use of ontologies. Expanding on the aggregate data, we engage in analysis of a few notable examples to demonstrate how the wording, framing, and content of prompts can intersect to collectively impact students’ use of ontologies and ontological structures.

Figure 1

Typology of ontological structures for a given individual reasoning episode. Construction refers to when the ontologies are developed. Application refers to which (or how many) ontologies are applied.

Figure 2

Screenshots of the Quantum Wave PhET Simulation [44] showing the double slit experiment with (a) a beam of light, (b) a single photon, and (c) many photons over time.

Figure 3

Schematic of a Mach-Zehnder interferometer with a single photon source. $M_A$ and $M_B$ are mirrors, $B{S}_1$ and $B{S}_2$ are beam splitters, $P{M}_A$ and $P{M}_B$ are photomultiplier detectors, and $N_A$, $N_B$, and $N_C$ are counters for detectors $A$ and $B$, and coincidences between the two.

Figure 4

System of two wires with an air gap in between that we model as a finite square well. The potential energy is given by $V(x)$. The total energy, $E_{\mathrm{tot}}$, is greater than $V(x)$ inside the wires (regions I and III) and less than $V(x)$ in between the wires (region II) in the “classically forbidden region.”

Figure 5

Percentage of ontology codes, by entity.

Figure 6

Distribution of ontological structures among written responses (excluding MC).

Figure 7

Distributions of ontologies for leading and not leading questions. In each case, for prompts leading to a specific ontology, the percentage of codes for that ontology are statistically significantly different from the percentage of that ontology among nonleading questions (denoted by *).

Figure 8

Distribution of ontologies for one cluster of three double slit questions leading to particle, wave, and both particle and wave ontologies, respectively.

Figure 9

Distributions of ontological structures for leading and not leading questions. In each case, for prompts leading to a specific ontological structure, the percentage of codes for that structure are statistically significantly different from the percentage among nonleading questions (denoted by *).

Figure 10

Distribution of ontological structures for one cluster of three double slit questions leading to unitary and blended ontologies.

Figure 11

Distribution of ontologies for leading and nonleading questions within the Mach-Zehnder content domain.

Figure 12

Distributions of ontological structures for leading and nonleading questions within the Mach-Zehnder content domain area.

Figure 13

Comparisons between HW6 Q24-25 for distributions of (a) ontologies and (b) ontological structures.

Figure 14

Comparisons between HW6 Q21 and HW7 Q3 for distributions of ontologies.