Students’ flexible use of ontologies and the value of tentative reasoning: Examples of conceptual understanding in three canonical topics of quantum mechanics

As part of a research study on student reasoning in quantum mechanics, we examine students’ use of ontologies, or the way students’ categorically organize entities they are reasoning about. In analyzing three episodes of focus group discussions with modern physics students, we present evidence of the dynamic nature of ontologies, and refine prior theoretical frameworks for thinking about dynamic ontologies. We find that in a given reasoning episode ontologies can be dynamic in construction (referring to when the reasoner constructs the ontologies) or application (referring to which ontologies are applied in a given reasoning episode). In our data, we see instances of students flexibly switching back and forth between parallel stable structures as well as constructing and negotiating new ontologies in the moment. Methodologically, we use a collective conceptual blending framework as an analytic tool for capturing student reasoning in groups. In this research, we value the messiness of student reasoning and argue that reasoning in a tentative manner can be productive for students learning quantum mechanics. As such, we shift away from a binary view of student learning which sees students as either having the correct answer or not.

Figure 1

Sophomore level modern physics class ($N=88$) responses to When not being observed, an electron in an atom still exists at a definite (but unknown) position at each moment in time. (Following the work of Baily [6, 7]) Highly statistically significant ($p\ll 0.001$) shifts from pre- to post-survey with the Bhapkar test. These data were collected in the same course and semester as the focus group data presented in Sec. 5.

Figure 2

Baily’s [6] representation of classical versus quantum ontologies of an electron. The double headed arrow represents movement back and forth between parallel ontological structures of particle and wave, which are both subsumed within a broader ontology of “electron.”

Figure 3

Adapted from Ref. [61]. Example of a common conceptual blend in physics. Solar system and atom form the input spaces for the Rutherford model of the atom in which electrons revolve around the nucleus and the nucleus attracts the electrons.

Figure 4

Framework for the nature of ontologies. Within a given reasoning episode, ontologies can be dynamic in their construction or application. Blended ontologies are new structures constructed in the moment, as opposed to stable structures that a reasoner brings with them to a reasoning episode. Parallel ontologies occur when multiple stable structures are applied.

Figure 5

In episode 1, students were given the screenshot in (c) which shows a single photon as a point on the detection screen of a double slit experiment. (a), and (b) The PhET simulation [71] shown as a single photon is fired and travels toward the screen.

Figure 6

Conceptual blending diagram for episode 1—a discussion between Eric (blue), Tara (orange), and Bryan (pink) about the behavior of a single photon in a double slit experiment. Classical particle and classical wave form the input spaces for the Blob of EM wave blend space.

Figure 7

Schematic of a Mach-Zehnder interferometer with one beam splitter presented to students in episode 2. Point $A$ marks the point that Tara references in line 74 (this was not present in the diagram given to students). PMA, PMB are detectors, $N_A$, $N_B$, $N_C$ are counters, $M_A$, $M_B$ are mirrors, and $B{S}_1$ is a beam splitter.

Figure 8

We model the collective conversation in episode 2 between Eric (blue), Tara (orange), and Bryan (pink) as a conceptual blend. Superimposed photon is formed by input spaces of classical particle and classical wave. Eric and Tara run the shared blend to arrive at different interpretations of superposition. The elements indicated with gray were not spoken by any one individual, but rather implied by statements from various group members.

Figure 9

We model the conversation between Fernando (blue), Zach (orange), and Jacob (pink) in episode 3 as a collective conceptual blend, where classical particle and (semiclassical or quantum) wave form the input spaces for the fuzzy ball of probability blend. Part of the wave input includes the material anchor [77] of a simulation that the students recall (elements indicated in italics). The elements indicated with a gray circle were not spoken by any one individual, but rather implied by statements from various group members.

Figure 10

Preliminary model of four different ontological approaches to QM sense making. Classical mechanics (CM).