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Covariational reasoning--how a change in one quantity is related to a change in another quantity (e.g., a 1/r potential, or the exponential decay with time of a charged capacitor)--is integral to how scientists model the physical world. It is also a skill we expect students to develop as a result of introductory physics instruction. Little research has been done to characterize physics experts&#39; covariational reasoning. Our research suggests that physics experts use a number of strategies--distinct from those of mathematics experts--that optimize thinking about physical quantities and how they relate to each other. We present a framework that describes physics expert covariational reasoning in introductory-level physics contexts as an important first step toward an understanding of students&#39; covariational reasoning, how students&#39; covariational reasoning changes over the course of physics instruction, and how instruction can be designed to help develop this important type of reasoning.

AAPT SM 20

Framework for the Natures of Covariational Reasoning in Introductory Physics

quantification

quantitative reasoning

covariational reasoning

The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. The program featured plenary speakers, sessions, workshops and many special activities.

For more information please visit the 2020 AAPT Virtual Summer Meeting page at: https://www.aapt.org/Conferences/SM2020/index.cfm.


The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. 

Covariational reasoning--how a change in one quantity is related to a change in another quantity (e.g., a 1/r potential, or the exponential decay with time of a charged capacitor)--is integral to how scientists model the physical world. It is also a skill we expect students to develop as a result of introductory physics instruction. Little research has been done to characterize physics experts' covariational reasoning. Our research suggests that physics experts use a number of strategies--distinct from those of mathematics experts--that optimize thinking about physical quantities and how they relate to each other. We present a framework that describes physics expert covariational reasoning in introductory-level physics contexts as an important first step toward an understanding of students' covariational reasoning, how students' covariational reasoning changes over the course of physics instruction, and how instruction can be designed to help develop this important type of reasoning.

technical paper

Adoption of the Next Generation Science Standards (NGSS) encourages teachers to incorporate various new types of instruction into their classrooms. This leaves us questioning the effectiveness of these new methods on students' physics content knowledge, as well as students’ beliefs in their own ability to learn. Students will step into a physics classroom with a predetermined mindset regarding their ability to learn physics. How can we measure the development of their mindset in the context of learning physics? In my freshman physics classes I integrate elements of Standards-Based Grading and the Investigative Science Learning Environment approach. I use a variety of attitudes and beliefs surveys throughout the year to track shifts in students’ mindsets. In this talk I share how my students’ mindsets have changed and identify elements of my teaching practices that have contributed to these changes.

Tracking Student Mindset Shifts in a HS Physics Classroom

The loop and junction laws typically form the foundations of the study of electric circuits in introductory physics. However, these rules can often be difficult for students to reason about conceptually, especially in circuits with multiple loops. We have developed a graphical representation of the loop law that can be used to bolster students’ conceptual understanding of voltage drops and gains in an electric circuit. We discuss the representation itself, possible variants of the representation, and thoughts from using the representation in a large introductory physics course.

Voltage Diagrams: A New Graphical Representation for the Loop Law

We routinely employ diagrams along with self-reflection in introductory physics, as research has shown that performance on tests and overall conceptual understanding improve when students draw diagrams when reflecting on material taught in class. Our earlier study examined performance on tests and found that using diagrams plus self-reflection led to moderate improvement on test scores. In the current study, we examined three areas: scores on tests, improvements in diagram skill, and frequency of drawing unsolicited diagrams. We found that students benefited more from diagram-based reflections, rather than word-based. This session presents the results of this study and implications for student success.

Using diagrams as a reflection tool in introductory physics

I discuss the development of a two semester sequence on math methods for undergraduate physics students at Ryerson University. Effective strategies for incorporating active learning techniques in a highly theoretical course will be presented. The numerical analysis component of the course will be highlighted, and I provide some examples of context-rich computational lab activities which were employed. Student attitudes about the course, as well as general takeaways about how best physics and math courses can support each other will also be discussed.

Creating a Math Methods Course with an Integrated Computational Lab

In the Centering Project, we are studying how whiteness and masculinity show up in the physics classroom, through video of classroom interactions among students and between students and instructors, and in the content and practices of physics, including curriculum. In this talk we present results of this analysis that we think will be relevant for physics educators.

Perceiving whiteness and masculinity in physics teaching and learning

Because a “spins-first” approach is becoming a more common method of teaching quantum mechanics, we want to know how the knowledge of discrete spin systems might help student’s understanding of continuous quantum systems. Leveraging computation, where wavefunctions are necessarily discretized, is a promising strategy of exploring this. During the junior-year of Oregon State University’s physics curriculum, students take a computational lab course in parallel with the “spins-first” lecture course. In this computational lab, students solve quantum problems by pair-programming in Python. We observed three pairs of students in class while they worked on a computational task of taking inner products of wavefunctions and basis states. In this talk, we will discuss the concepts of inner products students transferred from the discrete case used in the lecture course to the continuous case used in the computational lab and how they implemented these mathematical and physical concepts into their code.

Transfer from Discrete to Continuous Inner-Products in a Computational Course

In this talk, I describe the design of a robotic kinematic apparatus and a curriculum designed to make use of its unique features to shape the inquiry process. Students program a robot by drawing kinematic graphs on a computer, and the robot precisely and reliably produces the motion, providing immediate visual feedback. Preliminary results support the hypothesis that a physics apparatus precise and reliable enough to serve as a control of error minimizes the need for teacher intervention and improves student absorption in inquiry as well as learning outcomes. The importance of optimal feedback inertia emerged from the study. The turn-around time of several minutes to analyze a mistake and test a new idea encourages students to learn from their mistakes and really think things through.

Kinematic Robots in the Physics Classroom

Careful examination of my students’ individual gains on the Force Concept Inventory (FCI) led to the realization that student pretest knowledge on certain key questions appeared to be correlated to enhanced gain during the class. Acting under the hypothesis that addressing those key questions early in the course might result in broader, test-wide gains, I developed two class activities to address one of the key questions. One of the activities is a laboratory experiment and one activity utilizes a PhET simulation. I have tested those activities over the course of four semesters and there is evidence that they significantly increased the class-wide normalized gains on the FCI.

Using FCI Data to Develop Impactful Class Activities

Computational thinking has been emphasized as a main science and engineering practice in the Next Generation Science Standards. However, learning objectives outlined by the standards are written in vague terms that complicate the implementation and assessment of this topic in the classroom. This is especially problematic for high school teachers who have limited experience with computation and are looking to integrate computational modeling in their physics or physical science classrooms. In this study, we explore the variation in computational thinking practices that physics students demonstrate when working through in-class coding activities. Video data of multiple student groups were collected in one high school teacher’s physics and physical science classrooms. The data was analyzed to create a codebook that describes the different ways students engage in computational thinking practices. Ultimately, this work will help practitioners better understand how to identify these practices in a high school physics setting.

Video Analysis of Variation in Computational Thinking Practices in Physics

Mechanics provides many opportunities for integrating computation into physics curricula. We have developed different versions of an adjustable physical pendulum that can help students learn and apply rotational motion concepts while achieving many of the learning outcomes described in the AAPT recommendations for the laboratory curriculum and for computational physics. Because these pendula undergo large amplitude oscillations, they are difficult to investigate analytically. Instead, students can computationally model the experimental data they obtain with these pendula using spreadsheets or structured language programs to better understand the underlying mechanics, and determine whether different dissipation mechanisms are active while the pendulum ‘rings down’. We describe the construction and use of these pendula and the results that can be obtained.

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Framework for the Natures of Covariational Reasoning in Introductory Physics

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