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…

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…

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…

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…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

"Problem-Based Learning in the Physical Science Classroom, K-12" will help your students truly understand concepts such as motion, energy, and magnetism in true-to-life contexts. The book offers a comprehensive description of why, how, and when to implement problem-based learning (PBL) in your curriculum. Its 14 developmentally…

In recent years, the integration of science and mathematics has become popular among educators because of its potential benefits for student learning. The purpose of this study is to introduce a two-day interdisciplinary lesson that brings science and mathematics concepts together, actively engaging students in working with percentages of the…

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…

The exact expressions for the drain time and the height, velocity and acceleration of the free surface are found for the draining reservoir problem of the incompressible and non-viscous liquid. Contrary to the conventional approximate results, they correctly describe the initial time dependence of the liquid velocity and acceleration. Torricelli's…

In preparing to teach the advanced physics course at my high school, I found it useful to work through the end of chapter problems in the book used by the advanced class. A problem on motion in one dimension involved a stunt woman in free fall from a tree limb onto a horse running beneath her. The problem presents a connected learning opportunity…

Creative movement is an ideal way to help young children develop critical-thinking and problem-solving skills. Most young children are, by nature, extremely physical. They delight in exploring the world with their bodies and expressing their ideas and feelings through movement. During creative movement experiences, children learn to think before…

The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical mechanics, the solution of this problem is the primary example of the power of variational calculus. Here, we…