相关论文: Mathematical Education
Research on reasoning in language models (LMs) predominantly focuses on improving the correctness of their outputs. But some important applications require modeling reasoning patterns that are incorrect. For example, automated systems that…
The amount of published research in Physics Education Research (PER) shows, on one hand, an increasing interest in the design and development of high performance physics teaching strategies, and, on the other hand, it tries to understand…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
The problem of class imbalance is extensive for focusing on numerous applications in the real world. In such a situation, nearly all of the examples are labeled as one class called majority class, while far fewer examples are labeled as the…
The aim of this work is to show that contemporary mathematics, including Peano arithmetic, is inconsistent, to construct firm foundations for mathematics, and to begin building on these foundations.
Popularity of the use of free software in the IT industry is much higher than its popular use in educational activities. Disadvantages of free software and problems of its implementation in the educational process is a limiting factor for…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by…
Credit allocation in the mainstream bibliometrics is fundamentally flawed and the popular indicators have been misleading science for decades. Originally a simple technical mistake has become an integral part of our culture and is very…
The topics of Artificial intelligence (AI) and especially Machine Learning (ML) are increasingly making their way into educational curricula. To facilitate the access for students, a variety of platforms, visual tools, and digital games are…
Recent studies have shown that not only primary school students but also their future teachers reach science courses with pre-constructed and consistent models of the world surrounding them. These ideas include many misconceptions which…
Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in this. Our actions affect what others, in particular our…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
The growing need for trustworthy machine learning has led to the blossom of interpretability research. Numerous explanation methods have been developed to serve this purpose. However, these methods are deficiently and inappropriately…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
The debate over whether "thinking machines" could replace human intellectual labor has existed in both public and expert discussions since the mid-twentieth century, when the concept and terminology of Artificial Intelligence (AI) first…
The challenges of solving complex university-level mathematics problems, particularly those from MIT, and Columbia University courses, and selected tasks from the MATH dataset, remain a significant obstacle in the field of artificial…
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts,…