Making connections among representations of eigenvector: what sort of a beast is it?

Abstract

Many studies provide insights into students’ conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students’ initial conceptions, students’ transfer of learning of these conceptions to subsequent courses can provide additional information to structure meaningful curricular materials. This study explores physics students’ transfer of learning of eigenvalues and eigenvectors from prerequisite experiences to quantum mechanics. Data analysis focused on three task-based interviews with undergraduate students, observations of physics courses, and students’ course artifacts. Existing studies on students’ conceptions of linear algebra topics indicate the necessity of developing flexible shifts between different modes of thinking in order to grasp linear algebra. This study’s participants, who had initial learning experiences of linear algebra, were also observed to struggle with such shifts prior to quantum courses. It seems that various contexts in quantum courses, and explicit instructional methods, provided opportunities for students to enhance this initial learning of eigenvalues and eigenvectors. In particular, the explicit reasoning of one of the quantum courses’ instructors concerning the choice of certain representations during problem solving in class, seemed to facilitate students’ construction of similarities, thus providing evidence for actor-oriented transfer. Results of this study align with goals for recently developed instructional materials and interventions that emphasize opportunities for students to inquire and connect multiple modes of thinking.