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Previous research has found that introductory physics students perform far better on numeric problems than on otherwise equivalent symbolic problems. This paper describes a framework to explain these differences developed by analyzing…
Misconception is the difference between a student's idea and his scientific concept. Physics learning needs to be designed by teachers to minimize misconceptions. Different diagnostic tools have been developed and used by researchers to…
Most introductory quantum physics instructors would agree that transitioning students from classical to quantum thinking is an important learning goal, but may disagree on whether or how this can be accomplished. Although (and perhaps…
Physics education researchers have argued that authentic physics education includes computation as part of a physics student's training, and many parties have made efforts towards this goal. However, most research on this teaching modality…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
In mathematical reasoning tasks, the advancement of Large Language Models (LLMs) relies heavily on high-quality training data with clearly defined and well-graded difficulty levels. However, existing data synthesis methods often suffer from…
We introduce Matched Machine Learning, a framework that combines the flexibility of machine learning black boxes with the interpretability of matching, a longstanding tool in observational causal inference. Interpretability is paramount in…
One of the objectives of the undergraduate physics curriculum is for students to become aware of the connections between the fundamental principles of classical physics and their personal experience. Nonetheless, numerous studies have shown…
The large number of published articles in physics journals under the title "Comments on ..." and "Reply to ..." is indicative that the conceptual understanding of physical phenomena is very elusive and hard to grasp even to experts, but it…
Very little is known about how the nature of expertise in introductory and advanced courses compares in knowledge-rich domains such as physics. We develop a framework to compare the similarities and differences between learning and patterns…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this…
Computational Thinking (CT) is still a relatively new term in the lexicon of learning objectives and science standards. There is not yet widespread agreement on the precise definition or implementation of CT, and efforts to assess CT are…
Despite significant progress, multimodal large language models continue to struggle with visual mathematical problem solving. Some recent works recognize that visual perception is a bottleneck in visual mathematical reasoning, but their…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
The introduction of computing education into curricula worldwide requires multi-year assessments to evaluate the long-term impact on learning. However, no single Computational Thinking (CT) assessment spans primary school, and no group of…
In this paper, we present a new way of matching in observational studies that overcomes three limitations of existing matching approaches. First, it directly balances covariates with multi-valued treatments without requiring the generalized…
The objective of physics laboratory training is to develop, in students, a variety of important cognitive and psycho-motor abilities related to experimental physics. These include conceptual understanding, procedural understanding,…
Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces…
We introduce \textsc{MathSticks}, a benchmark for Visual Symbolic Compositional Reasoning (VSCR), which unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation that…
The Energy and Momentum Conceptual Survey (EMCS) is a multiple-choice survey that contains conceptual problems involving a variety of energy and momentum concepts covered in a typical introductory physics course for science and engineering…