Related papers: Difficult Problems Having Easy Solutions
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The paper describes methodology of math education for students interested in chemistry. Suppose we have mathematical circle 2 hours per week. What can be done? We can not provide any systematic study, but we can choose one subject and show…
We are investigating cognitive issues in learning quantum mechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics…
In this companion paper, we explore the use of isomorphic problem pairs (IPPs) to assess introductory physics students' ability to solve and successfully transfer problem-solving knowledge from one context to another in mechanics. We call…
Sliding friction is usually introduced in high school, but rarely through activities in laboratory. A qualitative introduction to friction is presented by proposing exploration of different kind of materials in order to suggest which…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
Introductory algebra-based physics courses frequently feature multiple student major populations in the same course section, however, different majors' requirements may impact students' motivations towards different aspects of the course…
In this article, we reflect upon our positive experiences incorporating or working on extra credit projects in algebra-based introductory physics that asked students to connect physics with humanities, social sciences, and everyday life. We…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…
Discrete mathematics and probability theory contain foundational material for computer scientists. Despite their importance, instructors often worry that students will find these courses to be too abstract and seemingly disconnected from…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
Recent investigations have been carried out on critical analyses of beginning physics teachers confronted with questionable explanations. These studies raise the question of the choices made by teachers for their teaching once they have…
Many undergraduate students of engineering and the exact sciences have difficulty with their mathematics courses due to insufficient proficiency in what we in this paper have termed clear thinking. We believe that this lack of proficiency…
This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are…
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to…
Experimental activities are an essential part of physics education. In addition to conveying scientific knowledge, they play a significant role in developing scientific literacy, inquiry skills, and critical thinking. In today's world,…