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Abstract Title: Student-Constructed Eigenvalue Equations in Quantum Mechanics: Symbolic Forms and Mathematical Sensemaking Analysis
Abstract Type: Contributed Poster Presentation
Abstract: As part of an effort to examine students' mathematical sensemaking (MSM) in a spins-first quantum mechanics (QM) course, students were asked to construct an eigenvalue equation (EE) for a one-dimensional position operator. A subset of responses took the general form of an EE written in Dirac notation. Sherin's symbolic forms and Gifford and Finklestein's categorical framework for MSM were used in analysis. The data suggest three different symbolic forms for an EE, all sharing a single symbol template but each having a unique conceptual schema: a transformation which reproduces the original, an operation taking a measurement of state, and a statement about the potential results of measurement. The first two are consistent with prior work, while the third is novel and aligned with an expert QM interpretation. The variety of symbolic forms identified and MSM-focused analysis suggest that students engage in MSM during the transition between discrete and continuous systems.
Session Time: Poster Session 2
Poster Number: II-39

Author/Organizer Information

Primary Contact: Anthony Pina
University of Maine
Orono, ME 04473
Phone: 5629003387
and Co-Presenter(s)
John Thompson (he, him), University of Maine
Zeynep Topdemir (she, her) University of Maine