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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…
Developing and making sense of quantitative models is a core practice of physics. Covariational reasoning -- considering how the changes in one quantity affect changes in another, related quantity -- is an essential part of modeling…
Covariational reasoning -- how one thinks about the way changes in one quantity affect another quantity -- is essential to calculus and physics instruction alike. As physics is often centered on understanding and predicting changes in…
We examine the process through which computational thinking develops in a perspectival fashion as two middle school students collaborate with each other in order to develop computational models of two graphs of motion. We present an…
Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational…
Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…
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…
Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory…
In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…
A classroom activity for high school physics students is presented to explore the distinction between correlation and causation. Using data linking ice cream sales to drowning deaths, presented within a fictional news article, students…
The resources framework emphasizes the potential productivity of student intuitions for constructing a canonical understanding of physics. It models learning as the progressive coordination and refinement of these resources. Yet, there is a…
Research in student knowledge and learning of science has typically focused on explaining conceptual change. Recent research, however, documents the great degree to which student thinking is dynamic and context-sensitive, implicitly calling…
We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical…
Mastering problem solving requires students to not only understand and apply physics concepts but also employ mathematics and mathematical representations (sketches, diagrams, graphs, gestures, equations and spoken language) skillfully. As…
Utilizing covariate information has been a powerful approach to improve the efficiency and accuracy for causal inference, which support massive amount of randomized experiments run on data-driven enterprises. However, state-of-art…
We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we…
Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…