  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
semi-structured 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.
