Making expert processes visible: How and why theorists use assumptions and analogies in their research

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists ($N=11$) to gain insight into the cognitive processes and skills that they use in their professional research. Among numerous activities that theorists described, here we elucidate two activities that theorists commonly characterized as being integral to their work: making assumptions and using analogies. Theorists described making assumptions throughout their research process, especially while setting their project’s direction and goals, establishing their model’s interaction with mathematics, and revising their model while troubleshooting. They described how assumptions about their model informed their mathematical decision making, as well as instances where mathematical steps fed back into their model’s applicability. We found that theorists used analogies to generate new project ideas as well as overcome conceptual challenges. Theorists deliberately sought out or constructed analogies, indicating this is a skill students can practice. When mapping knowledge from one system to another, theorists used systems that shared a high degree of mathematical similarity; however, these systems did not always share similar surface features. We conclude by discussing connections between the ways theorists use assumption and analogy and offering potential new avenues of research regarding applications to instruction.

Figure 1

A visual representation of the space of analogy types that we use to classify theorists’ analogies, based on the extent to which structural (vertical axis) and surface (horizontal axis) are mapped from base to target. Colors demonstrate that this space is a spectrum rather than a set of distinct categories. Concept for figure adapted from Gentner and Markman [56].

Figure 2

A flowchart summarizing the rounds of analysis performed on the interview data.

Figure 3

A sample process diagram that was generated using the actions, cues, and sensemaking process codes, with callouts indicating representative examples of the different subprocesses. Rectangles represented actions, circles represented cues, and hexagons represented instances of sensemaking. Shapes shaded yellow indicate that they are related to assumptions while blue indicates a relation to analogy. Visually, arrows connecting the action-cue-sensemaking bubbles point in all directions on the diagram, indicating that theorists frequently jump between different points in their overall process. In this specific diagram, the prevalence of yellow shapes illustrates that this theorist frequently described aspects of their process related to making effective assumptions. Figure generated with Lucidchart [70].

Figure 4

Several instances of analogy usage that we identified, mapped onto the analogy space presented in Fig. 1. Analogies in the upper left corner labeled high structure and low surface were mathematical analogies between systems from “distant” domains of physics (e.g., electrostatics and galactic dynamics). The upper right side of the diagram illustrates analogies between highly similar systems on both levels (e.g., adapting previously solved calculations from within the theorist’s subfield). Other analogies fell on a spectrum between the upper right and lower right corner, depending on the degree to which the theorist needed to change their mathematical approach to the new problem.