Related papers: Bridging knowing and proving in mathematics An ess…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
This paper describes some strategies used in a `transition' course. Such courses help undergraduate mathematics majors move from learning procedures to learning to function as critical mathematicians in order to understand and work with…
A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning…
Diproche ("Didactical Proof Checking") is an automatic system for supporting the acquistion of elementary proving skills in the initial phase of university education in mathematics. A key feature of Diproche - which is designed by the…
Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…
Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
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…
In this work we study the knowledge acquisition process in a teaching-learning scenario that takes place within the classroom. We explore two complementary approaches, which include classroom observations and student surveys, and the…
Proof theory began in the 1920's as a part of Hilbert's program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted,…
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
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…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…
Successful teaching entails a complex interaction between a teacher and a learner. The teacher must select and convey information based on what they think the learner perceives and believes. Teaching always involves misaligned beliefs, but…