**ERIC Number:**EJ1165693

**Record Type:**Journal

**Publication Date:**2017

**Pages:**13

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**EISSN-2469-9896

**EISSN:**N/A

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

Physical Review Physics Education Research, v13 n2 p020141-1-020141-13 Jul-Dec 2017

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level--upper division physics students--especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, "eigenvector eigenvalue," which is composed of multiple primitive symbolic forms.

Descriptors: Quantum Mechanics, Mathematics, Expertise, Introductory Courses, Problem Solving, Science Instruction, Undergraduate Students, Case Studies, Teaching Methods, Energy

American Physical Society. One Physics Ellipse 4th Floor, College Park, MD 20740-3844. Tel: 301-209-3200; Fax: 301-209-0865; e-mail: assocpub@aps.org; Web site: http://prst-per.aps.org

**Publication Type:**Journal Articles; Reports - Research

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**National Science Foundation (NSF), Division of Undergraduate Education (DUE)

**Authoring Institution:**N/A

**Grant or Contract Numbers:**1323129; 1625797