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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.…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
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This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical…
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Integrating computation into physics teaching is a curricular move that, at present, has been predominately studied for its cognitive impacts. However, if this modality of instruction shifts how students engage with physics, we argue there…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
Machine learning is rapidly making its pathway across all of the natural sciences, including physical sciences. The rate at which ML is impacting non-scientific disciplines is incomparable to that in the physical sciences. This is partly…
Practical research was conducted to cultivate students' mathematical computation ability using literature analysis, theoretical practice, and statistical analysis methods. The research involved 171 ninth-grade students from the author's…
This study explores student attitudes to the use of substantive on-line assessments that require mathematical answers. Our goal is to learn what are the important aspects in a design of more effective e-assessments that support learning of…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
In this paper we provide a good overview of the problems and the background of mathematics education in Syrian schools. We aimed to study the effect of using popular mathematical puzzles on the mathematical thinking of schoolchildren, by…
This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists'…
The aim of this study is to investigate the decisions and reasoning of undergraduate students when choosing simple measurement instruments in an introductory physics laboratory course. For this study, we have developed a questionnaire and…
Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with…
The use of computer-based mathematics tools is widespread in learning. Depending on the way that these tools assess the learner's solution paths, one can distinguish between automatic assessment tools and semi-automatic assessment tools.…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…