Related papers: Conceptual Mathematics via Literate Programming
While Large Language Models (LLMs) are often used as virtual tutors in computer science (CS) education, this approach can foster passive learning and over-reliance. This paper presents a novel pedagogical paradigm that inverts this model:…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
This study aims to describe the communication of prospective teachers in learning mathematics. The research was conducted in SMAN 1 Madura. The subject of this research is PLP student from Mathematics Education Study Program of Madura…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Computational thinking should be the fourth fundamental skill, along with reading, writing, and arithmetic (3R). To reach the level where computational thinking skills, especially digital problem solving have their own schemata, there is a…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
Large Language Models (LLMs) have emerged as powerful tools for automating code generation, offering immense potential to enhance programmer productivity. However, their non-deterministic nature and reliance on user input necessitate a…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…
Collaborative problem solving (CPS) is essential in mathematics education, fostering deeper learning through the exchange of ideas. Yet, classrooms often lack the resources, time, and peer dynamics needed to sustain productive CPS. Recent…
Computing according to laymens procedures is changed to contain a paradigm of inoptimality in the high level and assembled code. The code is changed to maximize the flow of information contained in the electrons so that they function more…
Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological…
Within the framework of Technological Pedagogical and Content Knowledge, subject integration is one possible solution for the introduction of meaningful digitalization and digitization in schools. This process incorporates that any school…
LaTeX is a free document preparation system that handles the typesetting of mathematical expressions smoothly and elegantly. It has become the standard format for creating and publishing research articles in mathematics and many scientific…
Quantum computing was once regarded as a mere theoretical possibility, but recent advances in engineering and materials science have brought practical quantum computers closer to reality. Currently, representatives from industry, academia,…
In today's world technology comprises a large aspect of our lives so this study aimed to investigate if using computers and digital tools are better than traditional methods like using textbooks and worksheets for learning math. This study…
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…