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Mathematics education researchers have been investigating for decades – in math contexts – student understanding of the many uses of algebraic variables. Physics, with its alphabet soup of symbolic representations of quantities and constants, takes this variation in variable use to a whole new level. There is a growing body of evidence from physics education researchers suggesting that student difficulty with manipulating variables presents a barrier to succeeding in physics. The context dependence of symbol use in physics is nuanced, and often not part of students’ mathematics preparation. In this talk we present evidence that the presence of a single variable significantly affects the outcome in even simple quantitative questions for students in calculus-based introductory physics. We present a framework, adapted from mathematics education, for thinking about the various roles that algebraic variables play in physics contexts. We present recommendations for instruction to help students conceptualize these uses.


AAPT SM 21

The mixed messaging of algebraic variables in physics

proportion

variable

reasoning

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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technical paper

Visual pop culture has been employed for physics education because novel examples from visual pop culture can capture students’ attention. Although widely enjoyed by people around the world, Japanese animation (Anime) has been used less frequently than other types of visual pop culture. In this presentation about our recent paper published in “The Physics Teachers”, we introduce how Anime examples can be used to teach fluid mechanics concepts including buoyant force, drag, lift, and key dimensionless numbers such as Reynolds number. This approach was employed in an undergraduate-level fluid mechanics class, and many students were positive about using Anime for teaching fluid mechanics because the examples provided a break from the normal methods of teaching and students were more engaged with the content that they learned. Therefore, Anime has the rich potential as a source of instructional examples that illustrate concepts from fluid mechanics and other areas of physics.

Using Japanese Animation (Anime) for Teaching Fluid Mechanics

Surface charges direct the flow of current through conductors. In anthropomorphic terms, they tell the current where to go and where not to go. As acknowledged by Professors Griffiths, Jackson, and Chabay and Sherwood, surface charges have been difficult to calculate. This paper presents a new way to calculate surface charges in which the surface of the conductor is covered with pixels which hold the surface charge. The pixels (referred to as "sensing pixels") sense the electric fields produced by all the other charges in the system and adjust their internal charge until steady state is reached. Importantly, sensing pixels allow students (and researchers) to understand why surface charge distributions, however calculated, look the way they do by asking the simple question: "What would a sensing pixel sense?" As Professor Sherwood kindly wrote to the author, this can make such counterintuitive phenomena as the accumulation of charges at edges, intuitive.

Surface Charges from a Sensing Pixel Perspective

Looking back, it has been a year like no other for The Physics Teacher. I will shine a spotlight on some of our recent content such as the exciting collection of articles on sex, gender and physics teaching, while also reflecting on some of the metrics we use to measure what we produce. In addition I will attempt to convey some glimpses of possible future feature items in TPT.

TPT Highlights from a Challenging Year

In our presentation, we discuss gender inequality in the physics classroom. Diversity strengthens science, but in most physics classrooms female students are disadvantaged both directly and indirectly: extensive research shows that they are undermined, viewed as less capable, and have less successful experiences both in terms of learning and identity formation. In this article and presentation, written in partnership between a male high school physics teacher and a female student from his 2018-2019 12th-grade physics class, we describe a two-week period in which we worked together to try to change the culture of our physics class.

The Elephant in the (Class)Room: Discussing Gender Inequality in Physics

The Physics Teacher focuses on teaching introductory physics at the high school, two- and four-year college, and university levels. Typical topics include innovative physics demonstrations, new ways of doing lab experiments, ideas for presenting difficult concepts more clearly, suggestions for implementing newer technology into teaching, historical insights that enrich the physics course, and suggestions for using results from physics education research, all focused on teachers in the introductory physics classroom. I’ll discuss our newest process for submitting manuscripts and what to expect after you submit your work.


Submitting a manuscript to The Physics Teacher

The biological cell exhibits a fantastic range of behaviors, but ultimately these are governed by a handful of physical and chemical principles. Here we explore simple theory, known for decades and based on the simple thermodynamics of mixtures of ideal gases, which illuminates several key functions performed within the cell. Our focus is the free-energy-driven import and export of molecules, such as nutrients and other vital compounds, via transporter proteins. Complementary to a thermodynamic picture is a description of transporters via "mass-action" chemical kinetics, which lends further insights into biological machinery and free energy use. Both thermodynamic and kinetic descriptions can shed light on the fundamental non-equilibrium aspects of transport. Our biochemical-physics discussion will remain agnostic to chemical details.

Key biology you should have learned in physics class

The conceptual development of student understanding of weight
Xiangqun Zhang and Lei Bao
Existing research has reported persistent difficulties among students at all levels in understanding the concepts involving weight and gravitation. In the literature and textbooks, there are two versions of weight definition in terms of (1) the gravitational force applied on an object and (2) the force applied on the supporting object. The latter is often referred to as the operational definition of weight, which describes the process of weighing an object. Studies have also demonstrated that using the operational definition in teaching can improve student understanding of the concepts involving weight, gravitation, and weighing. However, in the Chinese middle school physics curriculum, the gravitational definition of weight is mandated and universally implemented in instruction. To investigate the impact on student learning from using the gravitational definition of weight, a post-instruction survey is conducted to examine students’ conceptual understandings of weight. The results will be discussed and compared to the literature.


The conceptual development of student understanding of weight

Reasoning about the concept of electric charge, and the meaning of the term "net charge" in particular, presents a greater learning challenge than students and instructors might initially recognize. This may be due in part to subtleties in the use of positive and negative signs to characterize complementary charges, rather than to indicate that the quantities are greater than or less than zero. In this talk, we discuss the nuances of electric charge as a physical quantity and situate it in a body of work by mathematics and physics education researchers to characterize the uses and meanings of signs. We then describe preliminary research that illustrates the effect of wording differences on student reasoning about electric charge as a signed quantity and discuss implications for instruction.

Electric charge as a signed quantity

Reasoning consistently across contexts is a challenge in learning physics. Even students who demonstrate correct conceptual understanding and reasoning on one task often fail to use the same knowledge and skills on related tasks. Observed inconsistencies can be accounted for by dual-process theories, which assert that human cognition involves two thinking processes: the heuristic, which is fast and automatic, and the analytic, which is slow and deliberate. Inconsistent responses arise when the heuristic process produces an intuitively appealing (but incorrect) response that the analytic process fails to reject. We speculated that instruction that makes the dual nature of human cognition explicit and more visible to the students could help them recognize and evaluate intuitive responses more productively. We will present results of a study designed to probe the impact of such instruction on student learning in introductory calculus-based mechanics courses.

Making dual nature of human reasoning more explicit during instruction*

In accounting for the terminal speed behavior of a falling object, it can be challenging for students to coordinate the quadratic drag force model with the Fnet=0 condition. On some questions, students seem to reason in ways inconsistent with force balance ideas they have successfully applied in related contexts. We have used dual process theories of reasoning to interpret such responses, and also to guide design of an intervention. This talk will present the intervention, link elements of the intervention to dual process theory, and share preliminary results.

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The mixed messaging of algebraic variables in physics

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