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Quantum mechanics is increasingly being taught “spins-first”: using systems with spin as examples before systems with wave functions. It is important for spins-first instructors to understand how students apply knowledge from spin systems to understand the continuous quantum systems that they study later. We are studying the ideas that students have about discrete bases, continuous bases, and the connections between them. We interviewed six students who were enrolled in a spins-first quantum mechanics course and asked them to participate in a card-sorting task where they organized twenty cards with a variety of quantum mechanics content and representations including braket notation, matrix notation, function notation, and code snippets. In this talk, we will discuss the reasoning participants used to organize cards into “discrete” and “continuous” categories as well as how students described the different types of representations as communicating “discreteness”.

AAPT SM 22

How Students Compare and Contrast the “Discreteness” of Quantum Representations

AAPT meetings are a great way to reflect on your teaching, recommit to best practices and re-energize your career with new research, products, and techniques. Listen to internationally known plenary speakers, attend sessions, workshops, and special activities. This meeting is an excellent opportunity to share your expertise and learn from and network with leaders in the field.



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Previous research has shown that students who demonstrate sufficient skills and conceptual understanding to reason productively may perform inconsistently on analogous questions. Such inconsistencies can be explained via dual process theories of reasoning (DPToR). To gain insight into students’ reasoning trajectories, we developed an exploratory sequence of DPToR-aligned metacognitive prompts and administered the sequence immediately after students answered a physics question containing salient distracting features. The metacognitive prompts asked students to reflect on their initial ideas, the extent to which they had doubts about those ideas, the extent to which their final answer differed from those ideas, the nature of their reasoning approach, and their confidence in their own understanding. In this talk, we describe how we use student responses to these prompts, along with timing data and a measure of cognitive reflection skills, to investigate students’ reasoning trajectories.

Using Metacognitive Prompts to Explore Student Reasoning Trajectories*

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Exercise Sets, Faculty Commons, and Resources of the PICUP Website

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How Students Compare and Contrast the “Discreteness” of Quantum Representations

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Using Metacognitive Prompts to Explore Student Reasoning Trajectories*

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