Date of Award

Spring 5-3-2024

Level of Access Assigned by Author

Open-Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor

John R. Thompson

Second Committee Member

MacKenzie Stetzer

Third Committee Member

Thomas Stone

Additional Committee Members

Megan Wawro

Peter Stechlinski

Abstract

Quantum mechanics (QM) is a fundamental theory in physics that was developed based on a series of experiments. Rather than being built up from first principles, QM is built on a series of postulates that describe the outcomes of those experiments. The postulates establish both the mathematical formalism and basic concepts used to model quantum systems. While different systems require varying degrees of complex mathematics to model, the basic principles remain.


“Spins-first” QM instruction takes advantage of these varying degrees of mathematical difficulty by first introducing students to spin-1 2 systems which can be modeled with relatively simple mathematics. These courses give students an opportunity to build intuition for QM principles prior to engaging with the more mathematically complex systems. Ideally, students
would use their knowledge from the context of spin to make sense of systems requiring functional representations. Due to the inextricable nature of the mathematics and physics in QM, it serves as an interesting context for studying students’ mathematical sensemaking (MSM).


This project set out to examine student reasoning and MSM, particularly in the transition from discrete to continuous systems in a spins-first QM course. Student responses to tasks that had them examine and construct quantum mechanical operator equations provided insight into student conceptions of eigenvalue equations and measurement. Student responses to written tasks were analyzed with modified grounded theory as well as the concept image, symbolic forms, and conceptual blending frameworks. The identification of symbolic forms accessed by students served as some of the first evidence of students engaging in MSM in the transition. Interview data were analyzed with a modeling framework as well as a categorical framework for MSM in physics. Utilizing the two frameworks in parallel allowed for the identification of some novel sensemaking behaviors as well as an exploration of the overlap of sensemaking and modeling. These findings were then leveraged in an effort to support student learning and sensemaking. An
in-class instructional sequence as well as an online instructional survey were developed and piloted. While both sets of materials do require further refinement, the preliminary results from both are promising.

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