Authors

Mary Bridget Kustusch, Kyle Benjamin, and Grace Heath

When you are working on a problem and get stuck, how do you get “un-stuck”? Many of us have developed a myriad of tools, some explicit and some implicit, for helping us move past those sticky places in our work, but how did we develop these tools? How do we help our students develop these tools?

As a part of a larger collaboration, we are working to better understand the role of epistemological, or epistemic, framing in problem-solving in upper-division physics. Epistemic framing refers to how a task is perceived, particularly with regard to what knowledge and tools are necessary for completing the task. The particular theoretical framework that we are using considers framing along two dimensions: from conceptual to algorithmic and from math to physics. By putting these dimensions along two axes, we can map how an individual or group moves through this framing space (see Figure). For example, if one is discussing the properties of the physics quantities related to the problem at hand, they are framing this as more conceptual than algorithmic and more as physics than math. Thus, they would be somewhere in the upper right quadrant of this space.

Previous research has shown that students’ epistemic framing has a significant impact on student learning during problem solving and in upper-division physics, productive problem solving involves shifting between frames, particularly with regard to the use of math in physics. We are exploring how instructors can help students shift into more productive frames during problem solving. In doing so, we hope this larger project will lead to a theory based, research validated set of tools which teachers can use in the classroom.

Within this project, two of our undergraduate researchers were concurrently taking the class (upper-division Electricity and Magnetism) that was the context for the study. Kyle took it in Autumn Quarter 2019 just after he started working on the project and Grace took it in Spring Semester 2020 after working on the project for almost a year. Thus, they were in a unique position to reflect on how their increasing understanding of framing and the research that they were doing was impacting their own problem solving. They embarked on a collaborative autoethnography to explore this question.

In collaborative autoethnography, the research involves an on-going dialogue between one’s role as researcher and participant, a dialogue which is facilitated by interactions with one’s collaborators. During their individual courses, Kyle and Grace each maintained a journal in which they reflected on their problem-solving processes. Together, they analyzed these reflections to look for patterns in their problem solving and how these patterns might be connected to framing. Unfortunately, due to COVID, they were not able to complete their analysis, but here we highlight one of the primary insights that was starting to emerge from their work.

One of the major patterns that they honed in on was their tendency to intentionally switch frames: when they were stuck; when a problem seemed to be too difficult or complex; and/or when they felt that they didn’t really understand what they were doing or why.

Before taking the class, Grace had been steeped in our research which emphasizes that all frames are useful and often necessary for problem solving. As a result, she found that when she got stuck or felt that she didn’t understand, she would often explicitly evaluate her own framing. Then, she would intentionally ask a question that would help her to switch into a new frame. For example, when solving problems involving surface integrals, she realized that although she could solve the given problem algorithmically, she didn’t understand what da (the infinitesimal area) was. So, she asked her professor to help her draw it, in order to switch to a more conceptual frame.

For both Grace and Kyle, the need to shift frames often involved moving from a more algorithmic to a more conceptual framing. However, while the trigger to switch frames was often explicit and intentional for Grace, it was often more implicit for Kyle. This was likely due to the fact that Kyle was just beginning his work on framing while taking the class. When he felt that he was just “plugging and chugging”, it would cause him to ask what those numbers/symbols were telling him, shifting him to a more conceptual framing which would often help him solve the problem. For both of them, this push from more algorithmic to more conceptual framing in a given problem seems to be connected to a broader desire/need to understand the why of certain algorithmic moves: both in solving the problem and in making a conscious effort to learn. However, for Grace at least, this push was also connected to the understanding that she developed through the research of the value of all of the different frames and of the importance of moving between frames.

Kyle also noted that it was often the difficulty of a problem that prompted him to consider shifting frames. For example, when a problem was particularly difficult, it would trigger the idea that there had to be an easier way to solve it. At times, pushing forward through the difficulty would lead to the correct solution. At other times, scrapping the current approach and finding a different solution path was a better option. Thus, as the difficulty and/or complexity would mount, he would often go back and reread the problem statement to see if he missed anything and consider whether other approaches (e.g., representations, coordinate systems, etc.) would be more appropriate. While not necessarily directly connected to the theoretical framework that we were using, he felt that his understanding of framing implicitly helped him to consider looking at the problem from different perspectives.

While this work is still very preliminary, Kyle’s and Grace’s work has provided insight into how a student’s understanding of framing, reflecting on their own framing, and considering alternative framing could be productive for problem-solving and learning. Consistent with work on metacognition, this suggests that helping students reflect on and evaluate their own framing and consider appropriate frame shifts may provide tools that are valuable beyond addressing specific misconceptions about a particular topic.

Acknowledgments

Undergraduate researchers on this project were partially funded by the National Science Foundation REU Program and a DePaul Scholarship of Teaching and Learning Grant. Much of this work was conducted as a part of the Professional development for Emerging Education Researchers (PEER) program.

Bios

Mary Bridget Kustusch is an Associate Professor in the Department of Physics and Astrophysics at DePaul University and specializes in Physics Education Research. She has conducted qualitative and mixed methods research on topics such as the intersection between mathematics and physics, the development of student agency in the classroom, and equity in small group interactions. As a co-director of the Professional development for Emerging Education Research (PEER) program, she has developed and conducted numerous field schools on education research.

Kyle Benjamin is a recent graduate of DePaul University. He received a BS in Physics doing research under the guidance of Dr. Kustusch.

Grace Heath is a senior Physics major at Loyola University New Orleans. She has done research involving epistemic framing with RIT, DePaul, and KSU. Recently, she has been working on gender equity in physics labs at Cornell.