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The concept of infinity is applied widely in various contexts in physics, particularly while implementing the limits of large quantities, such as distance, time, and mass. We are investigating how students deal with this concept when they solve problems in mathematics and physics. We report results from individual semi-structured interviews with physics students, where they are required to use the concept of infinity to solve the problems. We found that students have several difficulties with the implementation and interpretation of the concept of infinity. These difficulties are due to either insufficient understanding of the underlying mathematical concept, differences in how it is interpreted and implemented in mathematics and physics, or inappropriate implementation to physics. We also found that student difficulties stem from the fact that in mathematics infinity is used as an abstract upper bound, whereas in physics it is used to quantify scales of physical quantities.

PERC SM 21

Student understanding and applications of infinity in physics and mathematics

student-understanding

infinity

mathematics

Join AAPT and Physics Educators worldwide in developing and strengthening your professional connections by attending the 2021 AAPT Virtual Summer Meeting. 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.

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AAPT SM 21

poster

**Making Physics More Inclusive and Eliminating Exclusionary Practices in Physics**

As a gateway discipline to STEM majors and careers, physics plays a central role in deciding who does, and who doesn't, get to discover and pursue scientific careers. Technical and scientific professionals are rewarded with economic privilege and status which affords them both social and cultural power. Therefore, social justice will be realized only when the opportunity, and the choice, to excel in physics is open to all students. The culture and practices of the physics classroom reflect the culture of physics at large, which raises the question of how our professional physics communities can embrace, rather than inadvertently repel, a diverse group of academics that can help improve physics culture.  To this end, the 2021 Physics Education Research Conference will focus on defining inclusive spaces and practices. Additionally, we will explore strategies for eliminating exclusionary practices in our classrooms, research spaces, and professional organizations. We call on the community to propose sessions that will drive conversations related to these initiatives throughout PERC 2021.

Please download the full program [here. ](https://drive.google.com/file/d/1TRMC_SYJ3PUqXyP7sskA7LRSA8ow0eRE/view?usp=sharing)

August 4, 2021 - August 5, 2021 in a Virtual Conference Format

Making Physics More Inclusive and Eliminating Exclusionary Practices in Physics

Nowadays computation is considered to be one of the pillars of modern science. This is reflected in the fact that much scientific research and industry work relies heavily on technology and computation. As university educators we need to equip graduates with the tools to help them succeed in their discipline. The study reported here is part of a larger project which aims to identify computational practices used by faculty from across the College of Science in an R1 Irish university in their disciplines and research, in order to inform the design of a computational science course intended for first-year undergraduate students. This paper reports on findings from one-to-one interviews with fourteen faculty from across six schools in the college. Their understanding of the nature of computational thinking and their views on the role that computation does/can play in the undergraduate science curriculum, and specifically in teaching and learning within their disciplinary program are presented. Concerns and challenges related to the embedding of computation in undergraduate science programs voiced by participants are presented here. Finally, implications of the findings for the design of the first year computational science course are discussed

Computational practices in introductory science courses

National calls to transform laboratory courses by making them more discovery based can be met by engaging students in multi-week final projects. One plausible outcome of this approach is that students may feel ownership of their projects. We define ownership as a dynamic relationship between students and their projects characterized by three student-project interactions that evolve over three project phases. Student-project interactions include students' contributions to, emotional responses to, and new understanding of the project. Phases include choosing the topic and team, carrying out the research, and creating and presenting end-of-project deliverables. Drawing on interviews with students collected as part of a multi-year, multi-institutional study, this paper will elaborate on the evolution of students' own new knowledge about the project across different project phases. Throughout our work, we compare the type of ownership that manifests when students work on projects in a lab course to the type of ownership gardeners feel when tending to plots in a community garden. We end with recommendations for instructors wishing to foster project ownership in their lab courses.

Student ownership and understanding of multi-week final projects

Generating graphical representations is an essential skill for productive student engagement in physics laboratory settings. However, there is a dearth of literature highlighting the strategies students use while working to generate graphs using their own experimental data. More recently, as students more frequently engage in open-ended physics lab courses, they experience additional freedom to decide what data to include in graphs and what types of graph(s) would allow for appropriate sensemaking towards answering experimental questions. This paper presents a case study analysis of a student group’s lab investigation to call attention to how students enact various productive strategies when working towards generating graphical representations in an introductory physics laboratory course. Results of this case study analysis identify three productive strategies students enact when working to generate graphs in lab settings, each of which is related to aspects of representational competency (RC) and are emblematic of experimental scientists’ own strategies: 1) identifying (potential) covarying quantities; 2) choosing representative data subsets suitable for representation; and 3) iteratively reducing data and generating graphs to assess graph’s viability in answering research questions. Our analysis also shows how students frequently refer back to their experimental goals when deciding what strategies to enact to generate graphs. This case study helps shed light on undergraduate students’ productive strategies when generating graphs in inquiry-based laboratory courses and provides preliminary evidence that students’ enacted productive strategies display similarities to those of professional experimental scientists.

Students productive strategies when generating graphical representations: An undergraduate laboratory case study

Experiments are of central importance for the natural sciences in general and in science education in particular, but the learning gains that teachers expect from them often fall short of expectations. This is especially true for student experiments, which are often conducted in dyads or small groups. In such a collaborative form of experimentation, the successful execution of the experiment and thus the achievement of the goals of the learning activity also depends on the cooperation of the students, so that a lack of learning success can also be caused by insufficient collaboration. In this study, mobile eye trackers were used with N=40 students to record gaze behavior during collaborative experimentation in the context of geometrical optics in order to investigate the influence of Joint Visual Attention (JVA) on learning success during experimentation. A significant relationship between JVA and learning gains was found for the setup phase with respect to experiment setup. The results show that especially during the setup of the experiment a successful collaboration of the experiment partners is of high importance for later successful execution of the experiment and thus support measures in this phase, such as the targeted directing of the attention of both experiment partners, could lead to an increase of the learning gain.

Using mobile eye tracking to capture joint visual attention in collaborative experimentation

This work focuses on applications of error propagation in undergraduate laboratory courses. A laboratory activity designed for students to compare measured and calculated ranges for a projectile launched from a reference height are presented here. Students used statistical and error propagation techniques to analytically determine the error bounds associated with measured and calculated projectile ranges as well as t-statistics to determine how well the measured and calculated ranges agreed. For all launch angles used in this work, 90% of students found that there was no statistically significant difference (p<1) between the measured and calculated ranges.

Error propagation employed to establish error bounds in projectile motion lab

Scientists are often encouraged to engage in some form of ethical training. With cases of scientific misconduct being reported, we are looking for ways to improve these training sessions. In this study we investigate how scientists engage in Epistemic Games, and if identifying these games can provide some insight into how scientists engage in ethical discussions. This was done through the lens of a fellowship we formed of fifteen faculty at one university. This fellowship met for numerous sessions in the span of a year to discuss topics in the sciences including reproducibility and integrity in data. These sessions were transcribed and organized into Epistemic Games using three characteristics: the target epistemic form, the entry and exit conditions, and the moves made by the participants. Using these games, we can begin to understand the different factors that influence a group discussion towards a particular goal. With this knowledge, we can then begin to understand if there are situations that prompt someone to invoke more ethical values, and whether this knowledge can be used to improve ethical training.

Identifying epistemic games in faculty discussions about values in science

Significant focus in the PER community has been paid to student reasoning in undergraduate quantum mechanics. However, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses. We conducted 15 exploratory think-aloud interviews with students in an upper-division quantum computing course at a large R1 university cross-listed in the physics and computer science departments. Focusing on responses to one particular problem, we identify two notably consistent problem-solving strategies across students in the context of a particular interview prompt, which we term Naive Measurement Probabilities (NMP) and Virtual Quantum Computer (VQC), respectively. Operating from a resources framework, we interpret these strategies as choices of coherent (and potentially mutually-generative)sets of resources to employ and available actions to perform.

Investigating students’ strategies for interpreting quantum states in an upper-division quantum computing course

With the integration of computation into physics courses becoming more prevalent to adequately prepare our graduates for the workforce, there is a need for instructional and assessment materials for computational practices. In introductory physics courses, computation is typically used to model motion and so while loops are one of the first components of programs that students encounter. Our study examines and compares students' conception of the while loop following the completion of three computational problems and their engagement with the while loop in a new computational problem. We present three student cases who have similar conceptions of the while loop with aspects including its update function and the connection of lines of code in the while loop, specifically in how force, position, and momentum depend on each other. Despite their similar conception of the while loop, there is a variation in the outcomes of their engagement with the while loop in a new computational problem.

Comparing student conceptions and construction of while loops in modeling motion

Students in a spins-first course often have difficulties transitioning from discrete to continuous quantum systems. We believe that computation may naturally support the transition because continuous structures like wavefunctions are necessarily discretized in order to be used in operations like numerical integration. We remotely interviewed six students who were concurrently enrolled in a junior-level introductory spins-first quantum mechanics course and a computational lab course, which were designed to synergize with each other. During the interview, participants organized a set of 20 cards that contained a variety of quantum mechanics concepts and representations, including snippets of Python code. Using a phenomenographic approach, this poster will discuss the various ways that participants made sense of the cards and how they organized the cards into groups such as “discrete” and “continuous”.

How Students Organize Quantum Concepts and Representations: A Card Sorting Task

Inquiry-based physics labs often include a focus on collecting and analyzing scientific data. During the process of making sense of the data, students often engage in data cleaning, even if not explicitly instructed to. Data cleaning is the process of identifying and mitigating instances in the data that are misaligned with expectations or hypotheses of the experiment, often due to equipment or software bugs. Our research analyzes think-aloud interviews from thirteen students and observational data in a first-semester, undergraduate IPLS lab. Qualitative coding focused on students’ decision-making processes while engaging in data cleaning in a think-aloud interview setting and in observation data of students working in the lab. Results show that students typically follow a process of noticing an anomaly, reasoning about its cause, and then either keeping or discarding the anomaly. However, nuances in this pattern differed in the lab environment as teaching and learning assistants had a significant impact on students’ methods of data cleaning. Although determining the source of outliers in data is complicated, unpacking students’ decision-making process is important for lab instructors to better support students in learning how to work with and interpret data.

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Student understanding and applications of infinity in physics and mathematics

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