arXiv subjects

Eric Kuo

Publications and source records attributed to Eric Kuo.

16 recordsLinked to original sources

arXiv2026

Teacher Leader Identity Development in a Physics Teaching Community of Practice: A Narrative Case Study

This longitudinal narrative case study examines the leadership identity development of Kayla, a female high school physics teacher, across five years of participation in a community of practice (CoP). Drawing on multiple data sources, we trace how her participation evolved from classroom-level practice to broader institutional influence. Four interconnected dimensions of leadership identity development were identified: personal, social, practice, and institutional culture change. Findings show how CoP membership provided collective legitimacy and relational support that enabled Kayla to move beyond identity negotiation toward transformation , successfully advocating for an AP Physics course and increasing female student participation. This study contributes to teacher professional learning literature by demonstrating the value of an identity lens for understanding teacher leadership as a gradual, socially enabled process. The longitudinal design reveals transformative conditions that cross-sectional studies often obscure, highlighting narrative case study as a productive methodology for capturing teacher leadership identity development over time.

physics.ed-ph↗

arXiv2025

"I forgot the formula:" How students can use coherence to reconstruct a (partially) forgotten equation

Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments when answering qualitative E&M problems in interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases that show how coherence-seeking approaches were employed to overcome this problem-solving challenge. In attempts to reconstruct these equations, participants were guided by identifying and chaining qualitative dependencies and seeking coherence between qualitative and mathematical understanding of the physical system. These moments of forgetting and reconstructing equations are a useful site for studying broader physics learning goals. While prior work investigates the use of mathematical sensemaking by examining how students respond to explicit prompts, our cases illustrate how students can spontaneously use mathematical sensemaking strategies. We reflect on these cases to consider how such adaptive reasoning can be a target for instruction and assessment.

physics.ed-ph↗

arXiv2025

Thematic analysis of student perceptions of resources and demands experienced in introductory physics

The current work aims to better understand student course experiences for those who reported negative perceptions in introductory physics. We conducted semi-structured interviews with 24 students who reported negative perceptions of their class on a screening survey. Participants were asked to share general reflections on challenges and successes they experienced, as well as their reflections on specific aspects of the course (e.g., experiences with instructors and peers). Interview transcripts were then coded to identify the types of experiences students reported, whether they were experienced as positive or negative, as well as the themes and features associated with those experiences. Experiences with the classroom, course structure, instructors, and exams were most frequently reported as negative. Experiences with peers, help-seeking, course curriculum, and specific learning activities were the most positive, though only experiences with peers had more positive reports than negative. We then used a resources vs. demands framework [Soc Personal Psychol Compass 7, 637 (2013)] to interpret the common instructional, cognitive, and motivational themes and features reported across multiple contexts. We discuss the implications of the results for theory and practice.

physics.ed-ph↗

arXiv2024

Teachers' Experiences with Implementing Open-ended Labs in High School Physics Classe

Although most teachers acknowledge the importance of taking investigative approached in students' science learning experiences, implementing them in high-school classes can be challenging for teachers. In this work, we analyzed data from multiple sources from a teaching Community of Practice (CoP) to investigate (a) barriers to using open-ended labs in physics classes, (b) shifts in teachers' beliefs about the use of open-ended labs in their classes during teachers' engagement in a physics teacher CoP in a partnership program, and (c) a case study of one teachers whose shifts in perceptions about open-ended labs led to her successful implementation of an open-ended lab in her class. The findings confirm the existence of well-known psychological and structural barriers that can prevent teachers from adopting investigative approaches in teaching physics labs. Moreover, we learned how the interaction of these barriers further complicates the adoption of open-ended approaches in physics classes. The study also revealed a significant gap between teachers' current practices and their desired method for conducting labs, particularly in terms of structured versus open-ended approaches. The case study offered deeper insights into how shifts in teaching practices occur through changes in perceptions within a supportive CoP.

physics.ed-ph↗

arXiv2023

Navigating Socio-Emotional Risk through Comfort-Building in a Physics Teaching Community of Practice: A Case Study

In teacher professional development (PD), grouping teachers with varying levels of experience can be a productive and empowering way to stimulate the exchange and co-generation of content and pedagogical knowledge. However, less experienced teachers can face socio-emotional risks when engaging in collaborative science content reasoning tasks with more experienced colleagues (Finkelstein, Jaber, & Dini, 2018), and these risks may impact the collaborative experience of both parties and the learning environment in teacher PD. This descriptive case study examines the process of productively navigating socio-emotional risks and interpersonal tensions encountered by a veteran and pre-service physics teacher during one episode of discussing physics content. We use a single term, comfort-building, to encapsulate discursive moves that result in increased feelings of comfort and safety by the participants. Comfort-building includes moves that serve to mitigate social risk, ease tension, and avoid discomfort, as well as those geared toward finding common ground and co-navigating challenges. These moves can carve out conversational space for teachers to more confidently face risks associated with being accountable to the physics content knowledge and engage in discipline-based conversations more deeply. The presented episode in this study was followed by video-stimulated individual interviews to determine how consciously the teachers connected their participation to explicit risk and comfort. This case study highlights an affective dimension for consideration in the continued study and facilitation of science teaching communities of practice, especially ones that bring together teachers with a variety of backgrounds and skill sets.

physics.ed-ph↗

arXiv2023

Responsive Professional Development: A Facilitation Approach for Teachers' Development in a Physics Teaching Community of Practice

Creating learning environments that can accommodate teachers' diverse needs is challenging because responsive elements are not clearly defined or identified. This study identified responsive teacher professional development (PD) elements by taking a phenomenological approach. Using surveys and interviews with 13 high school physics teachers in a PD program at a Midwestern university, we identified responsive features such as practicality, flexibility, and accessibility core to the enactment of a responsive PD. Other features were opportunities for community engagement, pedagogical support, and professional growth, which were aligned with the benefits of engagement in a Community of Practice model incorporated in this work.

physics.ed-ph↗

arXiv2023

Statistical causal inference methods for observational research in PER: a primer

Recent critiques of Physics Education Research (PER) studies have revoiced the critical issues when drawing causal inferences from observational data where no intervention is present. In response to a call for a "causal reasoning primer", this paper discusses some of the fundamental issues underlying statistical causal inference. In reviewing these issues, we discuss well-established causal inference methods commonly applied in other fields and discuss their application to PER. Using simulated data sets, we illustrate (i) why analysis for causal inference should control for confounders but not control for mediators and colliders and (ii) that multiple proposed causal models can fit a highly correlated data set. Finally, we discuss how these causal inference methods can be used to represent and explain existing issues in quantitative PER. Throughout, we discuss a central issue: quantitative results from observational studies cannot support a researcher's proposed causal model over other alternative models. To address this issue, we propose an explicit role for observational studies in PER that draw statistical causal inferences: proposing future intervention studies and predicting their outcomes. Mirroring a broader connection between theoretical motivating experiments in physics, observational studies in PER can make quantitative predictions of the causal effects of interventions, and future intervention studies can test those predictions directly.

stat.ME↗

arXiv2019

Using causal networks to represent the targets of resource coordination

The resources framework emphasizes the potential productivity of student intuitions for constructing a canonical understanding of physics. It models learning as the progressive coordination and refinement of these resources. Yet, there is a lack of theoretical clarity about how resources should be coordinated and refined to align with canonical physics. We present causal network diagrams as a tool for representing the targets of research coordination. As an example, we compare student reasoning about projectile motion to the causal network describing that motion. We argue that the causal networks make manifest and explicit two types of resource coordination required to achieve a correct physical understanding: (i) integrating additional causal influences and mediators and (ii) using qualitative logic to draw valid inferences.

physics.ed-ph↗

arXiv2019

A new approach for uncovering student resources with multiple-choice questions

The traditional approach to studying student understanding presents a question and uses the student answers to make inferences about their knowledge. However, this method does not capture the range of possible alternative ideas available to students. We use a new approach, asking students to generate a plausible explanation for every choice of a multiple-choice question, to capture a range of explanations that students can generate in answering physics questions. Asking 16 students to provide explanations in this way revealed alternative possibilities for student thinking that would not have been captured if they only provided one solution. The findings show two ways these alternatives can be productive for learning physics: (i) even students who ultimately chose the wrong answer could often generate the correct explanation and (ii) many incorrect explanations contained elements of correct physical reasoning. We discuss the instructional implications of this multiple-choice questioning approach and of student alternative ideas.

physics.ed-ph↗

arXiv2019

Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory Physics

What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal mathematics and conceptual understanding, is a key target of successful physics problem-solving instruction. However, typical assessments tend to measure understanding in more disjoint ways. To capture coherence-seeking practices in student problem solving, we introduce an assessment framework that highlights opportunities to use these problem-solving approaches more flexibly. Three assessment items embodying this calculation-concept crossover framework illustrate how coherence can drive flexible problem-solving approaches that may be more efficient, insightful, and accurate. These three assessment items were used to evaluate the efficacy of an instructional approach focused on developing mathematical-sensemaking skills. In a quasi-experimental study, three parallel lecture sections of first-semester, introductory physics were compared: two mathematical sensemaking sections, with one having an experienced instructor (MS) and one a novice instructor (MS-nov), and a traditionally-taught section acted as a control group (CTRL). On the three crossover assessment items, mathematical sensemaking students used calculation-concept crossover approaches more and generated more correct solutions than CTRL students. Student surveyed epistemological views toward problem-solving coherence at the end of the course predicted their crossover approach use but did not fully account for the differences in crossover approach use between the MS and CTRL groups. These results illustrate new instructional and assessment frameworks for research on mathematical sensemaking and adaptive problem-solving expertise.

physics.ed-ph↗

arXiv2018

Nothing's plenty: The significance of null results in physics education research

A central aim of physics education research is to understand the processes of learning and use that understanding to inform instruction. To this end, researchers often conduct studies to measure the effect of classroom interventions on student learning outcomes. Many of these intervention studies have provided an empirical foundation of reformed teaching techniques, such as active engagement. However, many times there is not sufficient evidence to conclude that the intervention had the intended effect, and these null results often end up in the file drawer. In this paper, we argue that null results can contribute significantly to physics education research, even if the results are not statistically significant. First, we review social sciences and biomedical research that has found widespread publication bias against null results, exploring why it occurs and how it can hurt the field. We then present three cases from physics education research to highlight how studies that yield null results can contribute to our understanding of teaching and learning. Finally, we distill from these studies some general principles for learning from null results, proposing that we should evaluate them not on whether they reject the null hypothesis, but according to their potential for generating new understanding.

physics.ed-ph↗

arXiv2015

Seeking instructional specificity: an example from analogical instruction

Broad instructional methods like interactive engagement have been shown to be effective, but such general characterization provides little guidance on the details of how to structure the instructional materials. In this study, we seek instructional specificity by comparing two ways of using an analogy to learn a target physical principle: (i) applying the analogy to the target physical domain on a Case-by-Case basis and (ii) using the analogy to create a General Rule in the target physical domain. In the discussion sections of a large, introductory physics course (N = 231), students who sought a General Rule were better able to discover and apply a correct physics principle than students who analyzed the examples Case-by-Case. The difference persisted at a reduced level after subsequent direct instruction. We argue that students who performed Case-by-Case analyses are more likely to focus on idiosyncratic problem-specific features rather than the deep structural features. This study provides an example of investigating how the specific structure of instructional materials can be consequential for what is learned.

physics.ed-ph↗

arXiv2014

Language of physics, language of math: Disciplinary culture and dynamic epistemology

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don't just use math, we make meaning with it in a different way than mathematicians do. In this reflective essay, we explore math as a language and consider the language of math in physics through the lens of cognitive linguistics. We begin by offering a number of examples that show how the use of math in physics differs from the use of math as typically found in math classes. We then explore basic concepts in cognitive semantics to show how humans make meaning with language in general. The critical elements are the roles of embodied cognition and interpretation in context. Then we show how a theoretical framework commonly used in physics education research, resources, is coherent with and extends the ideas of cognitive semantics by connecting embodiment to phenomenological primitives and contextual interpretation to the dynamics of meaning making with conceptual resources, epistemological resources, and affect. We present these ideas with illustrative case studies of students working on physics problems with math and demonstrate the dynamical nature of student reasoning with math in physics. We conclude with some thoughts about the implications for instruction.

physics.ed-ph↗

arXiv2011

How students blend conceptual and formal mathematical reasoning in solving physics problems

Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual reasoning in two ways: for selecting relevant equations (before manipulating them), and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending conceptual and formal mathematical reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended mathematical operations with conceptual reasoning about physical processes, reflecting a view - expressed earlier in his explanation of the equation - that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal mathematical reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

physics.ed-ph↗

arXiv2006

Graphical Condensation Generalizations Involving Pfaffians and Determinants

Graphical condensation is a technique used to prove combinatorial identities among numbers of perfect matchings of plane graphs. Propp and Kuo first applied this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang later applied graphical condensation to nonbipartite graphs to prove more complex identities. Here we generalize some of the identities of Yan, Yeh, and Zhang. We also describe the latest generalization of graphical condensation in which the number of perfect matchings of a plane graph is expressed as a Pfaffian or a determinant where the entries are also numbers of perfect matchings of subgraphs.

math.CO↗

arXiv2001

Ununfoldable Polyhedra with Convex Faces

Unfolding a convex polyhedron into a simple planar polygon is a well-studied problem. In this paper, we study the limits of unfoldability by studying nonconvex polyhedra with the same combinatorial structure as convex polyhedra. In particular, we give two examples of polyhedra, one with 24 convex faces and one with 36 triangular faces, that cannot be unfolded by cutting along edges. We further show that such a polyhedron can indeed be unfolded if cuts are allowed to cross faces. Finally, we prove that ``open'' polyhedra with triangular faces may not be unfoldable no matter how they are cut.

cs.CG↗