相关论文: The teaching of proof

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…

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…

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…

This paper revisits the foundations of mathematical proof through the lens of Aristotle's threefold conception of truth: sensory evidence, axiomatic definition, and syllogistic deduction. I argue that modern mathematics has too often…

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…

Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are…

Logic is one of the most male-dominated areas within the already hugely male-dominated subject of philosophy. Popular hypotheses for this disparity include a preponderance of confident, mathematically-minded male students in the classroom,…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

There are compelling reasons to shift our pedagogy toward evidence-based active learning methods that substantially improve student success, and now plenty of resources to aid in that shift. These include the recent CBMS Statement on Active…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…

We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…

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,…

This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…

If we want mathematics education to be valuable to everybody, including those who do not pursue mathematics-related careers, we need to use mathematics as a training ground for certain ways of thinking. This dissertation focuses on one…

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…

We show how Cartesian method can be used in the proof of fundamental planimetric topics of the school course, such as introduction of trigonometric functions, equation of a line and similarity of triangles. This work also can be considered…

"Is math useful?" might sound as a trick question. And it is. Of course math is useful, we live in a data-filled world and every aspect of life is totally entwined with math applications, both trivial and subtle applications, of both basic…

The theme of the PME-48 conference, Making sure that mathematics education research reaches the classroom, highlights a key concern: not all mathematics education research informs classroom practice. This raises several fundamental…