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Typically, physics education research addresses alternatives to transmission-based models of instruction. In light of critical pedagogy, I argue that the more relevant model to address is the banking model of education as identified by Paulo Freire, which subjects students to the colonialist consciousness and obedience to authority. In doing so, we can better identify root structural issues that plague the physics community. I argue that the Western conception of objectivity in science is motivated by the colonialist consciousness. The rigidity of what is considered science limits the identity of scientists to those of European descent, erasing the historical scientific knowledge of other peoples, such as the Indigenous peoples. I demonstrate a framework in which physics education is informed by critical pedagogy, as shaped by bell hooks and Sandy Grande, principled upon respect, reciprocity, and the human experience.

AAPT SM 22

The Banking Model of Physics Education

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Epistemic agency, or agency over knowledge, is well-studied in K-12 STEM learning environments and an area of current research within university physics laboratories. However, it has not been explored in upper division and major courses. In this talk, we explore how students engage in practices mirroring those of professional physicists in a project-based computational physics course designed to support students' epistemic agency. We introduce the overlapping yet distinct concept of pragmatic agency, or agency over practical decisions, to understand how students work evolves. We focus on a project where they also engage in making: they build physical and computational models in parallel. We argue for the importance of students having extensive agency over what to model and how to model for developing a grasp of computational physics practice.

Pragmatic and Epistemic Agency in A Project-based Computational Physics Course

As part of an effort to examine students’ mathematical sensemaking in a spins-first quantum mechanics course, students were asked to construct an eigenvalue equation for an operator that represents the position of a particle constrained to exist along a line. A subset of student responses took the general form of an eigenvalue equation written in Dirac notation. These responses were indicative of a few different ways of thinking about eigenvalue equations: a standard geometric interpretation, operating as measuring, and the eigenvalue equation as it relates to potential outcomes of measurement. In the context of Sherin’s symbolic forms framework, these data suggest three different symbolic forms for an eigenvalue equation that all share a single symbol template but have different conceptual schemata.

Student-Constructed Eigenvalue Equations in Quantum Mechanics: A Symbolic Forms Analysis

One important outcome of physics instruction is for students to be capable of relating physical concepts to multiple mathematical representations. In quantum mechanics (QM), students are asked to work across multiple symbolic notations, including some not encountered in previous coursework. To investigate student understanding of the relationships between expressions used in these various notations and generic vector expressions, a survey was distributed to students in upper-division QM courses at multiple institutions. The courses surveyed included those structured both as “spins-first” and “wave functions-first.” Network analysis techniques were used to compare student understanding of common expressions used in these courses, in both Dirac notation and wave function notation. Preliminary analysis suggests that, in addition to more distinct morphological grouping, students in “spins-first” courses also appear to conceptualize Dirac expressions as more vector-like than those in “wave-functions first” courses, consistent with the instructional emphasis.

Network Analysis of Student Interpretations of Dirac Expressions Across Curricula

We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom’s taxonomy (revised version) [1-3]. It was then used to code exam problems. We are now using this rubric to analyze the thinking skills of students taught online during covid vs. students taught in class after covid. We analyzed exams from different sections of the algebra-based physics course taught online during covid and in class after covid. We discuss the instrument, present results and future research plans.

Assessing Thinking Skills in Free-response Exam Problems: Covid vs. Non-covid

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”.

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

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*

Over the past several years, the Partnership for Integrating Computation into Undergraduate Physics (PICUP) has curated a collection of materials to help instructors add in computational modeling to their courses. I’ll discuss the various resources and how you can contribute to the community.

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

The Partnership for the Integration of Computation into Undergraduate Physics (PICUP) has had numerous successes since its beginning. However, challenges do remain as change is a slow process. This talk, by the external evaluator for PICUP, provides an overview of the summative evaluation featured in the PICUP Capstone Conference Report. Potential future avenues are also discussed.

Success and Remaining Challenges for PICUP and Integrating Computation

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration is working towards the detection and study of low-frequency gravitational waves using an array of rapidly rotating, highly stable radio pulsars distributed across the galaxy as accurate and precise clocks. A significant amount of research is driven by students from the high school to the graduate level. Students new to the field find themselves engaging with a large cross-section of many fields of astronomy, learning about stellar evolution, compact objects, galaxy evolution, gravitational waves, the interstellar medium, and more, and we strive to make our science accessible to them. I will describe our research program and specifically highlight the efforts within the collaboration to make our science more accessible to new students at many levels, getting them involved in cutting-edge science as quickly and easily as possible.

Simplifying Pulsar Timing Array Science for Students

Pulsars were discovered in 1967 and quickly identified as highly magnetized, fast rotating neutron stars. They are remnants of the explosion of a star known as a supernova. A neutron star has a diameter of about 7 miles and about twice as much mass as our Sun. Pulsars spin several times per second and have a magnetic field that can be a trillion times stronger than the one on Earth. As they age they emit electromagnetic radiation ranging from radio waves, visible light possibly up to gamma-rays. Their rotation causes their emission to be received in the form of pulses on Earth. The regularity of these pulses is the reason why they are often referred to as clocks in the sky. Some of them are more regular than others.

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