相关论文: Funny Problems!

The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…

I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…

For centuries, bubbles have fascinated artists, engineers, and scientists alike. In spite of century-long research on them, new and often surprising bubble phenomena, features, and applications keep popping up. In this paper I sketch my…

The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…

In the Italian education system, secondary students (ages 14-19) are confronted with the foundations of quantum physics during the final term of scientific high school (pre-university year). The Italian Ministry of Education, University and…

Aspects of quantum physics are no longer confined to the upper years of a physics degree. Concepts like superposition or entanglement that were once reserved for second- or third-year undergraduate courses now deserve attention earlier in a…

Thought experiments are where logical reasoning meets storytelling, catalysing progress in quantum science and technology. Schr\"odinger's famous cat brought quantum science to the public consciousness, while Deutsch's thought experiment to…

In recent years there has been growing evidence that even after teaching designed to address the learning difficulties dictated by literature, many physics learners fail to create the proper reasoning chains that connect the fundamental…

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

Teaching scientific concepts is essential but challenging, and analogies help students connect new concepts to familiar ideas. Advancements in large language models (LLMs) enable generating analogies, yet their effectiveness in education…

University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…

National studies conducted over many years show that, while most Americans are interested in science and support federal funding of scientific research, the scientific literacy of the public is very low. Why this situation exists and who is…

This paper is the second one in a series of work on the mathematical creativity of LLM. In the first paper, the authors proposed three criteria for evaluating the mathematical creativity of LLM and constructed a benchmark dataset to measure…

Scaling reasoning capabilities beyond traditional domains such as math and coding is hindered by the lack of diverse and high-quality questions. To overcome this limitation, we introduce a scalable approach for generating diverse and…

A brief account of some recent controversies about the teaching and learning of physics is presented. A shorter version of this outcome was accepted by The Physics Teacher, but publication is still pending.

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and…

We discuss the development of interactive video tutorial-based problems to help introductory physics students learn effective problem solving heuristics. The video tutorials present problem solving strategies using concrete examples in an…

This is a broad and in places unconventional overview of the strengths and shortcomings of our standard models of fundamental physics and of cosmology. The emphasis is on ideas that have accessible experimental consequences. It becomes…

In India, as in many countries, the main focus in science classrooms is on exams rather than musing on the fascinating concepts and understanding of the world that science offers. This can mean that students lose interest in studying…