One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics

Abstract

Over the last decade, there has been an increasing, widespread pedagogical interest in developing various types of integrated curricula for science and engineering programs. Over the last three years, a year-long Integrated Math/Physics course has been developed at Union College. This paper will focus on a model for a one-quarter integrated course organized around a traditional set of electricity and magnetism (E&M) physics topics, integrated with appropriate mathematical topics. Traditional, nonintegrated E&M physics students often struggle with challenging vector calculus ideas which may have been forgotten, not yet encountered, or introduced with different notation in different contexts. Likewise, traditional vector calculus mathematics students are often unable to gain intuitive insight, or fail to grasp the physical significance of many of the vector calculus ideas they are learning. Many of these frustrations are due to the fact that at many schools, the physics and calculus teachers teaching separate courses probably have little or no idea what their fellow educators are actually doing in these courses. Substantial differences in context, notation, and philosophy can cause breakdowns in the transfer of knowledge between mathematics and physics courses. We will discuss the methods, philosophy, and implementation of our course, and then go on to present what we feel were the substantial strengths and insights gained from a thoughtful integration of the two subjects. In addition, some problem areas and recommendations for probable student difficulties will be addressed.

Learning Electromagnetism with Visualizations and Active Learning

“…This problem is still under investigation (Hake, 1998;Maloney, O'Kuma, Hieggelke & Van Heuvelen, 2001). Some researchers cite the lack of a common language between mathematicians and physicists as the root of the learning difficulties of students who study physics (Dunn & Barbanel, 2000). Other researchers place the blame on traditional teaching methods that reward memorization over conceptual thinking (Mazur, 1997).…”

Modelling Mathematical Reasoning in Physics Education

“…The lack of a direct correspondence in their performances is aligned with other studies showing that transfer is an extremely difficult process which cannot be expected to happen automatically (Brown et al 1989). An approach to improve transfer skills is provided by fully integrated math-physics courses where mathematics and physics are taught simultaneously (Yeats and Hundhausen 1992;Dunn and Barnabel 2000).…”

College Students’ Transfer from Calculus to Physics

“…(e.g. [6]) Yeatts and Hundhausen [7] used their own experiences in talking about the difficulties -"notation and symbolism," "the distraction factor" and "compartmentalization of knowledge" -that students have when transferring their knowledge between calculus and physics and provide some recommendations. However, unlike the integrated curriculum developed by Dunn, [6] calculus and physics are taught as separate subjects in most universities.…”