相关论文: The teaching of proof

Several thoughts are presented on the long ongoing difficulties both students and academics face related to Calculus 101. Some of these thoughts may have a more general interest.

Computer-based testing is an expanding use of technology offering advantages to teachers and students. We studied Calculus II classes for STEM majors using different testing modes. Three sections with 324 students employed: Paper-and-pencil…

This article reviews the current state of teaching and learning mathematical modeling in the context of sustainable development goals for education at the tertiary level. While ample research on mathematical modeling education and published…

In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…

This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…

One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should…

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…

This paper summarizes the author's insights and experiences of teaching mathematics to incarcerated students within the U.S. prison system.

This article analyzes the emerging ethical turn in mathematics education, arguing that it is a nuanced extension of the sociopolitical turn. While sociopolitical studies of mathematics have highlighted systemic issues and group concerns…

Large language models (LLMs) have become capable mathematical problem-solvers, often producing correct proofs for challenging problems. However, correctness alone is not sufficient: mathematical proofs should also be clear, concise,…

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…

The use of argumentation in education has been shown to improve critical thinking skills for end-users such as students, and computational models for argumentation have been developed to assist in this process. Although these models are…

In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…

Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous…

Evidence-based education has become a central concept in science education, with meta-analyses often regarded as the gold standard for informing practice. This emphasis raises critical questions concerning the applicability,…

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,…

Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…

An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…

There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that…

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…