In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings…

Design thinking--a human-centered approach to problem solving--is a process by which K-12 teachers engage students in solving relevant issues that occur in their schools. In this article, the authors describe a project in which fourth-graders used design thinking to solve an unexpected issue related to a much-anticipated class project. The project…

We present an algorithm for solving the time-dependent Schrödinger equation that is based on the finite-difference expression of the kinetic energy operator. Students who have some knowledge of linear algebra can understand the theory used to derive the algorithm. This is because the finite-difference kinetic energy matrix and the Hückel matrix…

College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common…

This paper shows how a freely downloadable and powerful software package, "SMath Studio," can be used to model physical systems in physics teaching. The software can form the basis of lecture demonstrations by teachers or can be used individually by students working in an educational environment or on their own home computers.

In this paper it is demonstrated how the free, and easily downloadable, software package called SMath Studio can be used to set up a model of alpha-particle scattering. The basic physics of the motion of an alpha-particle in the nuclear coulomb field is used to produce a simple stepwise computer algorithm which, in conjunction with a novel set of…

This teaching brief describes an engaging, in-class exercise that introduces genetic algorithms as well as advanced Excel functions and capabilities by modeling the familiar Sudoku puzzle. Student groups are first asked to manually solve a given puzzle and then translate that solution methodology to a spreadsheet model. This exercise can be used…

Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

A bridge course intended to ease the transition from Organic Chemistry I to II was designed for a January term that spans 2 weeks and features sharply focused topics courses. In the first week, key topics from Organic Chemistry I are revisited to ensure that students have a firm foundation on which to build. During the second week, a selection of…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

A multiweek laboratory experiment is described, which guides students to use data to make decisions through multiple steps, before reaching a final conclusion. The lab focuses on the comparisons of fluorescence and absorbance spectroscopies to determine the concentration of a desired substance in an unknown sample in consideration of a complex…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…

This article describes a lesson rooted in "tinkering," an approach to learning that encourages the use of authentic, hands-on experience to develop an understanding of content and physical materials. There were several desired outcomes for this lesson. First, the authors felt that tinkering was an appropriate approach to investigating…

The goal of this paper is to illustrate different ways that cardsorting activities (or "card stacks") can be implemented in the introductory physics classroom, along with various tips and resources for getting started. My first attempt at developing a card stack came about from simply wanting to try out a fun way to change student…