As the topic of relativity is developed in a first-year physics class, there seems to be a tendency to move as quickly as possible to the fascinating ideas set forth in Einstein's special theory of relativity. In this paper we linger a little with the Galilean side of relativity and discuss an intriguing problem and its solution to illustrate a…

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…

A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the…

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying…

The author builds on arguments he has made elsewhere that good commercial video games foster deep learning and problem solving and that such games in fact promote mastery as a form of play. Here he maintains that some good video games engage players with an important type of play, namely of play as discovery, of play as surmising new possibilities…

Just as comprehension strategies have helped millions of students learn to read like proficient readers, they can also help students think like effective test-takers. The authors show how students can use background knowledge, mental images, synthesizing, monitoring, inferring, questioning, and determining of importance to understand the genre of…

According to the U.S. Department of Justice (www.usdoj.gov), Community Policing is defined as: "The focus on crime and social disorder through the delivery of police services that includes aspects of traditional law enforcement, as well as prevention, problem-solving, community engagement, and partnerships. The community policing model balances…

The requirement for a method of capturing problem solving on a whiteboard for later replay stems from my teaching load, which includes two classes of first-year university general physics, each with relatively large class sizes of approximately 80-100 students. Most university-level teachers value one-to-one interaction with the students and find…

This note describes an interdisciplinary project designed to enhance students' knowledge of the basic techniques taught in a multivariable calculus course. The note discusses the four main requirements of the project and then the solutions for each requirement. Concepts covered include differentials, gradients, Lagrange multipliers, constrained…

How should men and women be seated around a dinner table to maximize conversation between members of the opposite sex? What can be said about the distribution of points around two concentric circles? How are the white and black keys on the piano keyboard organized? What spin configuration in the Ising model minimizes energy? These four problems…

This paper introduces, via case study example, the benefit of including risk assessment methodology and inherently safer design practices into the curriculum for chemical engineering students. This work illustrates how these tools can be applied during the earliest stages of conceptual process design. The impacts of decisions made during…

This paper concerns the analysis of a didactic engineering, the aim of which is to introduce Calculus, at secondary-school level, through the relationship between global and local points of view. It was designed for a graphic-symbolic calculator environment and structured in accordance with a learning trajectory from identifying the graphical…

This article discusses how teachers can organize and use mathemagic tricks in their curriculum and classroom to enhance conceptual understanding. Four mathemagic tricks are presented and analyzed. (Contains 3 figures and 5 online resources.)

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)