Related papers: Mathematical Education
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
We provide an historical overview of how advances in technology influenced high school and university mathematical competitions in the United States and at the International Mathematical Olympiad. While students are not allowed the usage of…
In Grammatical Error Correction, systems are evaluated by the number of errors they correct. However, no one has assessed whether all error types are equally important. We provide and apply a method to quantify the importance of different…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
In this article, we present our findings from ten years of research on intelligent educational games. We discuss the architecture of our training environments for learning spelling and mathematics, and specifically focus on the…
Embedded computing systems are pervasive in our everyday lives, imparting digital intelligence to a variety of electronic platforms used in our vehicles, smart appliances, wearables, mobile devices, and computers. The need to train the next…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
Underlying complex systems, there is a rich web of interconnected components that determine the relational properties of the system. Yet, traditional methods used in education sciences often disregard the underlying complexity of the…
Machine learning (ML) is increasingly deployed in real world contexts, supplying actionable insights and forming the basis of automated decision-making systems. While issues resulting from biases pre-existing in training data have been at…
This paper examines the integration of STEAM (Science, Technology, Engineering, Arts, and Mathematics) into education, emphasizing the inclusion of the Arts to foster creativity alongside traditional STEM skills. STEAM encourages…
This report aims to evaluate the performance of large language models (LLMs) in solving high school science questions and to explore their potential applications in the educational field. With the rapid development of LLMs in the field of…
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
Statistical models have seen a significant rise in popularity in recent years. Despite their undeniable success in various industry use cases such as sabermetrics, investment portfolio management, and artificial intelligence, there has been…
Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis…
In this paper we will discuss problems and techniques related to underactuated systems. We give a mathematical formulation of several problems arising from applications, review some standard and new techniques, and pose some interesting and…
Both the basic educational contents for students and study programs for science teachers include several topics in physics and astronomy, from the simplest ones to others as advanced as nuclear fusion to explain stellar evolution and…
Computer programs do not always work as expected. In fact, ominous warnings about the desperate state of the software industry continue to be released with almost ritualistic regularity. In this paper, we look at the 60 years history of…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
In this paper, we describe the possibilities of using a rapid mental computation system in elementary education. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…