The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

The International Technology and Engineering Educators Association (ITEEA) defines STEM as a new transdisciplinary subject in schools that integrates the disciplines of science, technology, engineering, and mathematics into a single course of study. There are three major problems with this definition: There is no consensus in support of the ITEEA…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

By describing the motion of a charged particle in the well-known nonuniform field of a current-carrying long straight wire, a variety of teaching/learning opportunities are described: 1) Brief review of a standard problem; 2) Vector analysis; 3) Dimensionless variables; 4) Coupled differential equations; 5) Numerical solutions.

This case explores Crabapple Middle, a struggling urban school in the midst of a transition that seeks new leadership that can overcome the challenges of two sub-cultures that divide the school and community. In an effort to address issues of low academic performance and negative community perception, an International Baccalaureate magnet program…

We describe a range of practical activities that allows students to investigate the properties and applications of magnets. The activities can be used in isolation or used together to build a rounded understanding of the subject area. The activities include simple demonstrations using common or inexpensive equipment, hands-on experiments for small…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

This little problem arose because I was frustrated with the standard electromagnetism texts, which show the magnetic field due to a current-bearing wire outside the wire [proportional to] 1/r and inside [proportional to] r. However, they never point out that the moving electrons must be influenced by the magnetic field created by the other moving…

The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.

We solve exactly the problem of calculating the electromagnetic fields produced by a finite wire with a constant current, by using two methods: retarded potentials and Jefimenko's formalism. One result in this particular case is that the usual Biot-Savart law of magnetostatics gives the correct magnetic field of the problem. We also show…

The John Ball Zoo School, an alternative program for highly motivated sixth graders, prepares independent learners to tackle the problems of life in the 21st century. (Author/WD)

Presents two geography problem-solving scenarios for use with elementary and middle school children or preservice teachers in social studies methods courses. Provides problems about the magnetic poles and the presence of ice in desert conditions. Calls upon teachers to encourage students to use their thinking skills to solve the problems. (SG)

Describes interdisciplinary activities with real-world applications ranging from science to mathematics to technology. Cites the study and construction of model bridges as a way for students to learn about engineering concepts and some of their relationships. States that the exercise enhanced teacher cooperation between the different fields. (RT)

Describes a study of three parts: (1) the application of a statistical technique for predicting performance; (2) a computer program for teaching basic problem-solving skills; and (3) evidence for the value of teaching with complex homework problems in an introductory physics course required for engineering majors. (Contains 42 references.)…

How do meetings in elementary classrooms influence student attitudes and behaviors, both individually and collectively? Can regular opportunities to participate in collective problem solving educate students for peacemaking and alter the social dynamic of the classroom? As an experienced teacher who previously studied class meetings in a private…