Pedagogical Moves Related to Analogy: Supporting Students' Sensemaking at the Interface of Eigentheory and Quantum Mechanics

Eigentheory concepts are central in mathematics and physics, serving purposes such as mathematizing physical phenomena and facilitating computations. In quantum mechanics, students are expected to reason about eigentheory concepts in various contexts, such as spin, energy, and position. In this talk, I will summarize research findings (Serbin & Wawro, 2024, PRPER) focused on a quantum mechanics professor's pedagogical moves related to analogy that support students in developing a unified understanding of eigenequations across quantum contexts. Some moves that engaged students in analogical reasoning include soliciting and scaffolding student participation, using deictic gestures and inscriptions, juxtaposing symbols, and explicitly highlighting sameness. I will use the same analytical framework to share ways that a quantum mechanics textbook employs analogizing activity to support its transition from the discrete to the continuous as it introduces the wave function. Discussion will highlight how analogical activity can help instruction and instructional tools promote students' sensemaking at the interface of mathematics and physics. This work comes from a broader research project on student understanding of linear algebra in quantum mechanics.