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Computation has become an integral part of physics research. However, little is known about how students learn to productively use computation as a tool beyond the introductory level, especially as they transition into physics research. In…
This document chronicles this author's attempt to explore how words come to mean what they do, with a particular focus on child language acquisition and what that means for models of language understanding.\footnote{I say \emph{historical}…
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…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Current conceptions of expert problem solving depict physical/conceptual reasoning and formal mathematical reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving…
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…
Though neural networks trained on large datasets have been successfully used to describe and predict many physical phenomena, there is a sense among scientists that, unlike traditional scientific models comprising simple mathematical…
We report on the idea to use colours to distinguish syntax and semantics as an educational tool in logic classes. This distinction gives also reason to reflect on some philosophical issues concerning semantics.
This paper reviews connections between physics and computation, and explores their implications. The main topics are computational "hardness" of physical systems, computational status of fundamental theories, quantum computation, and the…
In recent years, natural language processing (NLP) has become integral to educational data mining, particularly in the analysis of student-generated language products. For research and assessment purposes, so-called embedding models are…
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics,…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Semantic processing is a fundamental research domain in computational linguistics. In the era of powerful pre-trained language models and large language models, the advancement of research in this domain appears to be decelerating. However,…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
One goal of Artificial Intelligence is to learn meaningful representations for natural language expressions, but what this entails is not always clear. A variety of new linguistic behaviours present themselves embodied as computers,…
To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The…
Prior research has demonstrated how the realist perspectives of classical physics students can translate into specific beliefs about quantum phenomena when taking an introductory modern physics course. Student beliefs regarding the…
Scientists who study how the brain solves problems have recently verified that, because of stringent limitations in working memory, where the brain solves problems, students must apply facts and algorithms that have previously been well…