CAREER: An Interdisciplinary Study of Learning: Student Understanding of Linear Algebra in Physics

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

Title: CAREER: An Interdisciplinary Study Of Learning: Student Understanding Of Linear Algebra In Physics Consistent with the national charge for the advancement of Science, Technology, Engineering, and Mathematics (STEM) disciplines, the National Research Council's (NRC's) report (2012) "Discipline-Based Education Research: Understanding and Improving Learning in Undergraduate Science and Engineering" describes a need for interdisciplinary studies regarding learning and the transfer of knowledge for students in upper division STEM courses. This project will contribute towards this national need for basic research by investigating students' learning and understanding of key topics and ideas from linear algebra - a fundamental mathematics topic for STEM majors in multiple disciplines - as applied to undergraduate upper-division physics. In connection with this, the project will provide new insights in improving undergraduate education within the STEM disciplines. The results of this study will not only extend the research base of what is known about student understanding of mathematics and physics across disciplines, but it will also contribute to pedagogical implications at the undergraduate level by leveraging the synergy between mathematics and physics education research on teaching and learning. The project will also contribute to the development of innovative assessment instruments for undergraduate mathematics learning. The project will integrate research and education to investigate eigentheory and related key ideas from linear algebra within the framework of quantum physics. The research focal points will be to: (1) characterize the various ways in which students reason about and symbolize concepts related to eigentheory in quantum physics; (2) determine how students' language and symbols for concepts related to eigentheory compare and contrast across mathematics contexts and quantum physics contexts; and (3) explore how instructors' use of language and mathematical symbols relates to students' understanding, symbolization, and interpretation of eigentheory in quantum physics. To help foster and diversify the research investigations, data will be collected from the quantum physics courses at three academic institutions: Virginia Polytechnic Institute and State University; Oregon State University; and the University of Maine. The project will also produce and vet a conceptually oriented multiple-choice extension (MCE) assessment instrument for eigentheory. Included in the research to address items (1)-(3) listed above will be textbook analysis, the MCE eigentheory instrument creation and implementation, interview protocol development and implementation, classroom observations and interviews with participating instructors, and bridging sequences development. To enhance and expand the overall infrastructure and collaborations for research and education across disciplines, this instrument together with research results from the investigations will be disseminated widely through research and practitioner publications, presentations, and workshops in mathematics and physics education.