Mathematical sense-making-looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world-is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level-upper division physics students-especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sensemaking can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

Problem solving in groups can be rich with tension for students. This tension may arise from conflicting approaches (conceptual and/or epistemological) and/or from conflict emerging in the social relations among group members. Drawing on video records of undergraduate students working collaboratively, we use three cases to illustrate the multifaceted ways in which conflict arises—combining conceptual, epistemological, and socioemotional dynamics—and a specific way of managing the tension that can emerge from the multifaceted conflict, “taking an escape hatch.” An escape hatch is a set of discourse moves through which participants close the conversational topic, thereby relieving tension, but before a conceptual resolution is achieved. We describe how epistemological twists and turns can be recruited as a means of managing the strong emotions experienced by the students, showing the coupling of emotion and epistemology in students’ conceptual sense making during group work. We help to provide the groundwork necessary for instructors to notice, understand, and respond to one way in which conceptual–epistemological–social–emotional aspects of interaction are coupled in the emergence of tension, rather than narrowly targeting instructional moves based on only conceptual or epistemological considerations. Instead, instructors should often respond to—and help students become aware of—the emotional component of peer interactions and its entanglement with the “cold cognitive” conceptual and epistemological components.

Abstract. Quantum mechanics can seem like a departure from everyday experience of the physical world, but constructivist theories assert that learners build new ideas from their existing ones. To explore how students can navigate this tension, we examine video of a focus group completing a tutorial about the "particle in a box." In reasoning about the properties of a quantum particle, the students bring in elements of a classical particle ontology, evidenced by students' language and gestures. This reasoning, however, is modulated by metacognitive moments when the group explicitly considers whether classical intuitions apply to the quantum system. The students find some cases where they can usefully apply classical ideas to quantum physics, and others where they explicitly contrast classical and quantum mechanics. Negotiating this boundary with metacognitive awareness is part of the process of building quantum intuitions. Our data suggest that (some) students bring productive intellectual resources to this negotiation.

Abstract. In collaborative small-group work, physics students need to both manage social conflict and grapple with conceptual and epistemological differences. In this paper, we document several outlets that students use as tools for managing social conflict when addressing quantum mechanics tutorials in clinical focus groups. These resources include epistemic distancing, humor, playing on tutorial wording and looking ahead to subsequent questions. We present preliminary analysis of episodes where students work through a Particle in a Box tutorial. Each episode highlights a different manner of navigating social tension: through shared epistemic humor in one case, and reinterpretation of the question in the other.

We focus on a student Chad's sense-making with representations (inscriptions) of both standard forms found in quantum textbooks and emergently constructed non-standard forms. Through fine-timescale analysis of video from a clinical interview, we document the different ways in which the inscription becomes embedded in the student's reasoning. Our findings show that the inscriptional system generated by Chad shapes, and is shaped by, his sense-making and causal reasoning, and that the standard forms recruited can provide a space for action, beyond that of simple read-out. We briefly touch on some guiding instructional design choices and directions of future research.