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Recent research in mathematics education points to an "epistemic clash" when programming and computational thinking (CT) are leveraged alongside more established forms of mathematical thinking (MT). The emergence of generative AI emphasises…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Computation is intertwined with essentially all aspects of physics research and is invaluable for physicists' careers. Despite its disciplinary importance, integration of computation into physics education remains a challenge and, moreover,…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
The term visual programming has started to be used in Informatics so far, however, there are different views on its meaning. The separation of visual programming from development tools of interfaces provides not only the certainty for this…
As belief around the potential of computational social science grows, fuelled by recent advances in machine learning, data scientists are ostensibly becoming the new experts in education. Scholars engaged in critical studies of education…
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
How can elementary grade teachers integrate programming and computational thinking with the science curriculum? To answer this question, we present results from a long-term, design-based, microgenetic study where 1) agent-based programming…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…
Undergraduate physics education has greatly benefited from the introduction of computational activities. However, despite the benefits computation has delivered, we still lack a complete understanding of the computationally integrated…
Graphs are essential representations in the professions and education concerning the science, technology, engineering, and mathematics (STEM) disciplines. Beyond their academic relevance, graphs find extensive utility in everyday scenarios,…
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…
Computational thinking in physics has many different forms, definitions, and implementations depending on the level of physics, or the institution it is presented in. In order to better integrate computational thinking in introductory…