Abstract
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students' problem-solving and metacognitive skills in these courses. Some of these studies were multi-university investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to over-generalizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approached that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.
Highlights
Research suggests that students in upper-level quantum mechanics have common difficulties independent of their background, teaching style, textbook, and institution that are analogous to the patterns of difficulties observed in introductory physics courses, and many students in these courses have not acquired a functional understanding of the fundamental concepts [7,24]
Research on student reasoning difficulties in learning upper-level quantum mechanics and on students’ problemsolving and metacognitive skills in these courses is inspired by cognitive theories that point to the importance of knowing student difficulties in order to help them develop a functional understanding of relevant concepts
Some of these studies were conducted at several universities simultaneously while others were conducted at typical state universities where the student population in the upper-level quantum mechanics courses is likely to be representative of students in similar courses at other typical state universities
Summary
Helping students learn to “think like a physicist” is a major goal of many physics courses from the introductory to the advanced level [1,2,3,4,5,6,7,8,9]. In order to become an expert in physics, the development of problem-solving, reasoning, and metacognitive skills must go hand in hand with learning content and building a robust knowledge structure [4,5,6,10,11,12]. Much research in physics education has focused on investigating students’ reasoning difficulties in learning introductory physics and on the development of researchbased curricula and pedagogies that can significantly reduce these difficulties and help students develop a robust knowledge structure [3,4]. Of upper-level physics students and strategies that can be effective in such courses to help students learn physics and develop their problem-solving, reasoning, and higher-order thinking skills further [13,14]. The task of evaluating upper-level students’ learning and selfmonitoring skills should involve physics topics at the periphery of their own understanding
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