Abstract
Quantum mechanics is a highly mathematical topic that many students struggle with. We studied the effect of initial mathematics knowledge and self-efficacy on student learning on an introductory (first to second-year) quantum mechanics course by administering a mathematics pre-test and a self-efficacy questionnaire (N = 50). We correlated the results with course performance (exercise and exam scores). The self-efficacy beliefs of different student groups differed, but correlations between self-efficacy, initial mathematics skills and performance on this course remained modest. In addition, the correlations between self-efficacy beliefs in different aspects of learning quantum mechanics were low to moderate, meaning that students’ self-efficacy beliefs in this topic are highly situational. We observed that first-year students with high self-efficacy were more likely to report theoretical physics as their study track. Their initial mathematics skills did not differ from their peers, but they scored slightly better in exercises and the exam than first-year physics students, as the (experimental) physics group also included lower performing individuals. Second-year students who reported physics as their study track scored lower than both first-year physics and theoretical physics students in all measures. The explanation is likely a selective effect: the physics students who take the course in their first year are more comfortable with more advanced physics and mathematics content.
Highlights
Quantum mechanics (QM) is a complex and often difficult topic for students of physical sciences
We studied the effect of initial mathematics knowledge and self-efficacy on student learning on an introductory quantum mechanics course by administering a mathematics pre-test and a self-efficacy questionnaire (N = 50)
We have studied the effects of students’ initial skills in mathematics on learning the basics of quantum mechanics in conjunction with a change in the timing of mathematics teaching
Summary
Quantum mechanics (QM) is a complex and often difficult topic for students of physical sciences. Enthusiastic students find studying QM exciting and motivating. In QM, both instructors and students face the difficulty of observing the examined phenomena, and the theory relies strongly on its mathematical constituents. To proceed deeper into the topic, the students need to grasp both the physical interpretation and the mathematical formulations [1, 2, 3]. QM is laid upon the theory of Hilbert spaces, and understanding of at least the basic axioms and features of vector spaces is important. This makes linear algebra part of the necessary mathematical toolbox
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