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 approaches that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.Students taking upper-level quantum mechanics often develop survival strategies for performing reasonably well in their course work. For example, they become proficient at solving algorithmic problems such as the time-independent Schrödinger equation with a complicated potential energy and boundary conditions. However, research suggests that they often struggle to make sense of the material and build a robust knowledge structure. They have difficulty mastering concepts and applying the formalism to answer qualitative questions, e.g., questions related to the properties of Review of Student Difficulties in Upper-Level Quantum Mechanics

Self-efficacy can affect performance, career goals, and persistence. Prior studies show that female students have lower self-efficacy than male students in various science, technology, engineering, and mathematics (STEM) domains, and the self-efficacy gap is a factor that contributes to the low representation of female students in STEM. However, prior research has not decoupled self-efficacy differences from performance differences. This study examines the self-efficacy of male and female students with similar performance in introductory physics courses and investigates whether gender gaps in self-efficacy are persistent across different instructors and course formats. Students filled out a self-efficacy in physics survey before physics 1, before physics 2, and at the end of physics 2. Students' achievement was measured by their performance on research-based conceptual physics tests and course grades. The physics courses were taught by several instructors and varied in the type of pedagogy used, with some using a "flipped" format and others using a traditional, lecture-based format. We found that female students had lower self-efficacy than male students at all performance levels in both physics 1 and physics 2. The selfefficacy gaps continued to grow throughout the introductory physics course sequence, regardless of course format (i.e., traditional or flipped) and instructor. The findings suggest that female students' self-efficacy was negatively impacted by their experiences in introductory physics courses, and this result is persistent across various instructors and course formats. Female students' lower self-efficacy compared to similarly performing male students can result in detrimental short-term and long-term impacts.

The lack of diversity and the under-performance of underrepresented students in STEM courses have been the focus of researchers in the last decade. In particular, many hypotheses have been put forth for the reasons for the under-representation and under-performance of women in physics. Here, we present a framework for helping all students learn in science courses that takes into account four factors: (1) the characteristics of instruction and learning tools, (2) student characteristics, (3) implementation of instruction and learning tools, and (4) the students’ environments. While there has been much research on factor 1 (characteristics of instruction and learning tools), there has been less focus on factor 2 (students’ characteristics, and in particular, motivational factors). Here, we focus on the baseline characteristics of introductory physics students obtained from survey data to inform factor 2 of the framework. A longitudinal analysis of students’ motivational characteristics in two-semester introductory physics courses was performed by administering pre- and post-surveys that evaluated students’ self-efficacy, grit, fascination with physics, value associated with physics, intelligence mindset, and physics epistemology. We found that female students reported lower levels of self-efficacy, fascination, and value associated with physics, and held a more “fixed” view of intelligence in the context of physics compared to male students. Female students’ fascination and value associated with physics decreased significantly more than males’ after an introductory physics course sequence. In addition, females’ view of physics intelligence became more “fixed” compared to males’ by the end of an introductory physics course sequence. Grit was the only factor on which females reported averages that were equal to or higher than males throughout introductory physics courses. The findings inform the framework and have implications for the development and implementation of effective pedagogies and learning tools to help all students learn.

Gender differences in students' physics identity in introductory physics courses can influence students' interest in science, technology, engineering, and mathematics and their career decisions. Exploring the components that influence these identities is critical to developing a better understanding of the underrepresentation of women in physics courses and physics-related majors. We used a revised version of the physics identity framework developed by Hazari et al. [J. Res. Sci. Teach. 47, 978 (2010)] to investigate whether the relation between gender and physics identity was mediated by motivational factors, such as competency belief, interest, and perceived recognition by others. We surveyed approximately 500 students in introductory level calculus-based physics courses in which 30% of the students are women. Analysis revealed that the relation between gender and physics identity was mediated by students' selfreported motivation at the end of the semester. The model showed that perceived recognition by others played a major role in students' endorsement of physics identity with female students less likely to endorse statements that others perceived them as a "physics person."

Students' intentions to persevere and their career choices in science, technology, engineering, and math fields can be impacted by their physics identities. Women are severely underrepresented at all levels in physics and engineering. Physics in particular has stereotypes about being a discipline for brilliant men. Therefore, it is particularly difficult for women who do not fit the description of a stereotypical physicist to develop a physics identity. Thus, understanding the factors underlying physics identity in introductory physics classrooms is important for creating an equitable and inclusive physics learning environment and has the potential to at least partly explain the current underrepresentation of women in physics-related majors and careers. In this study, we examined physics identity and several other motivational constructs of male and female students by administering a survey in introductory calculus-based physics courses at a large research university. We found gender differences in how students identify as a physics person and how their perceived recognition from others, such as their teaching assistants or instructors, peers, or family members relates to their physics identities. We tested separate models by gender that examined how different motivational constructs relate to students' physics identities. We found that the perception of being recognized by influential others such as the course instructor or teaching assistants was differentially related to female and male students' physics self-efficacy and sense of belonging in the physics classroom. These findings call for improving the physics learning environments to make them equitable so that all students have a high sense of belonging and self-efficacy and opportunity to develop a strong physics identity.

In diverse classrooms, stereotypes are often “in the air,” which can interfere with learning and performance among stigmatized students. Two studies designed to foster equity in college science classrooms ( Ns = 1,215 and 607) tested an intervention to establish social norms that make stereotypes irrelevant in the classroom. At the beginning of the term, classrooms assigned to an ecological-belonging intervention engaged in discussion with peers around the message that social and academic adversity is normative and that students generally overcome such adversity. Compared with business-as-usual controls, intervention students had higher attendance, course grades, and 1-year college persistence. The intervention was especially impactful among historically underperforming students, as it improved course grades for ethnic minorities in introductory biology and for women in introductory physics. Regardless of demographics, attendance in the intervention classroom predicted higher cumulative grade point averages 2 to 4 years later. The results illustrate the viability of an ecological approach to fostering equity and unlocking student potential.

Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics. I. INTRODUCTIONA solid grasp of the fundamental principles of quantum physics is essential for many scientists and engineers. However, quantum physics is a technically difficult and abstract subject. The subject matter makes instruction quite challenging, and even capable students constantly struggle to develop expertise and master basic concepts.In order to help students develop expertise in quantum mechanics, one must first ask how experts compare to novices in terms of their knowledge structure and their problem-solving, reasoning, and metacognitive skills. According to Sternberg [1], some of the characteristics of an expert in any field include: 1) having a large and well organized knowledge structure about the domain; 2) spending more time in determining how to represent problems than searching for a problem strategy (i.e., more time spent analyzing the problem before implementing the solution); 3) working forward from the given information in the problem and implementing strategies to find the unknowns; 4) developing representations of problems based on deep, structural similarities between problems; 5) efficient problemsolving; when under time constraints, experts solve problems more quickly than novices, and 6) accurately predicting the difficulty in sol...

We have developed and evaluated a Quantum Interactive Learning Tutorial (QuILT) on a Mach-Zehnder Interferometer with single photons to expose upper-level students in quantum mechanics courses to contemporary quantum optics applications. The QuILT strives to help students develop the ability to apply fundamental quantum principles to physical situations in quantum optics and explore the differences between classical and quantum ideas. The QuILT adapts visualization tools to help students build physical intuition about counter-intuitive quantum optics phenomena with single photons including a quantum eraser setup and focuses on helping them integrate qualitative and quantitative understanding. We discuss findings from in-class evaluations. PACS: 01.40.Fk, 03.65.-w, 03.67.-a, 07.60.Ly I.