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Modeling the creative mathematical sensemaking that characterizes expert thinking in physics is typically a struggle for new learners. To help students learn to reason this way, we created a set of supplemental activities called Physics…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research, but is also important for emerging technologies. However, many students regard quantum mechanics as a…
The Mathematization project investigates students' use of mathematical tools across the undergraduate physics curriculum. As a part of this project, we look at intermediate mechanics students' written homework solutions to understand how…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
The role of mathematics in physical sciences is discussed, particularly how higher mathematics found applications in empirical problems. Several examples are given to illustrate this role.
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students…
Teaching assistants (TAs) are often responsible for grading in introductory physics courses at large research universities. Their grading practices can shape students' approaches to problem solving and learning. Physics education research…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural"…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Covariational reasoning--considering how changes in one quantity affect another, related quantity--is a foundation of quantitative modeling in physics. Understanding quantitative models is a learning objective of introductory physics…
Search engines for equations now exist, which return results matching the query's mathematical meaning or structural presentation. Operating over scientific papers, online encyclopedias, and math discussion forums, their content includes…
This work examines student meaning-making in undergraduate physics problem-solving. We use a social semiotic perspective to sketch a theoretical framework. The social semiotic approach focuses on all types of meaning-making practices that…
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…
This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel…
Physics education research has probed for the relevance of physics in students' everyday lives. Attitudinal and epistemological surveys have asked students if they think of or use physics in their daily lives. We have previously documented…