Exploratory factor analysis of the QMCA

Abstract

This investigation is situated within an ongoing project which seeks to understand student thinking in upperdivision introductory quantum mechanics courses. Recently, the Quantum Mechanics Concept Assessment (QMCA) was revised to include additional items in spin-basis contexts to reflect the rising prevalence of the "spins-first" instructional paradigm. In this work, we utilize exploratory factor analysis to group items on the QMCA based on common variance. Student responses were collected from several large institutions over the 2018-2019 academic year, with the three largest institutions following a "spins-first" curriculum. In interpreting our factor structure, we focus on the placement of isomorphic questions and the original concept framework of the QMCA, as well as a tentative interpretation of factor groupings. We conclude by discussing how these groupings may be further investigated, as well as implications for subsequent iterations of the QMCA and research on student thinking in these two contexts.

Rasch Analysis of the Quantum Mechanics Concept Assessment

“…The factor loadings represent what percentage of the variance on that item can be accounted for by the assumed underlying factor. If an item has a factor loading greater than or equal to approximately 0.3 then it is said to be well described by the factor [14]. We see from the table that the items that There is a pattern here.…”

“…The QMCA consists of 38 multiple-choice items covering measurement, the time-independent Schrodinger equation, time evolution, wave functions, boundary conditions, probabilities, and expectation values. It was adapted from the free-response format Quantum Mechanics Assessment Tool (QMAT), and it has undergone many revisions and verifications of face and content validity including a CTT analysis [4], an exploratory factor analysis [14], and a modified module analysis [15]. However, there has yet to be a Rasch analysis of the QMCA or any quantum assessment for that matter.…”