相关论文: The teaching of proof
This article explores the parallels between improvisational theater (Improv) and teaching in an Active Learning environment. It presents the notions of Active Teaching as a natural complement to Active Learning, and discusses how unexpected…
The article deals with the problems of information and communication technologies (ICT) development in teaching mathematics of engineering specialities students in the United States. In the article the nature of trends of convergence of…
The purpose of this paper is to emphasize the role of language in the process of teaching and learning mathematics. We will begin with the definition of mathematics given by Cassiodorus (in its essential features repeated in Kolmogorov's…
The book was written on the basis of materials that we presented at several faculties, either as lectures or as part of auditory exercises. Aware that there are more books and textbooks in the area in which the topics covered by this book…
How does the mathematical community accept that a given proof is correct? Is objective verification based on explicit axioms feasible, or must the reviewer's experiences and prejudices necessarily come into play? Can automated provers avoid…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
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…
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…
The field of ethnomathematics holds significance in the pursuit of comprehending how students can grasp, express, manipulate, and ultimately apply mathematical concepts. However, ethnomathematics is also considered a complex concept in…
In the past two decades, teaching and outreach have come to hold an expected place in more missions of mathematics departments and organizations. Still, there is more to do as a mathematical sciences community for mathematics education and…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
In accordance with Bloom's taxonomy, a four-level evaluation abstraction was generated with the objective of structuring and hierarchizing curricula knowledge, allowing students to dominate a subject and progressively reach the top of…
Assessments such as standardized tests and teacher evaluations of students' classroom participation are central elements of most educational systems. Assessments inform the student, parent, teacher, and school about the student learning…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations…
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these questions.
Reinforcement learning (RL) can elicit strong reasoning in large language models (LLMs), yet most open efforts focus on math and code. We propose Reasoning Curriculum, a simple two-stage curriculum that first elicits reasoning skills in…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Starting from the Italian unification in 1861, we describe the role of mathematics teaching in the Italian system of education giving an account of the main features of Italian mathematics education, and referring to the official syllabi,…