Developing second level students' understanding of the inverse square law and electric fields

There are specific mathematical tools involved in building an accurate model of introductory electric field theory. Algebra operations, vectors, field lines, proportional reasoning and the inverse square law are all integral parts of gaining a complete understanding of an electric field. In this paper we present a small body of research, taken from a case study with a group of 14 upper second level students, in which they developed their understanding of the inverse square law, using a pre-test-tutorial-post-test tutorial lesson model. Students struggle to understand the inverse square law unless they are repeatedly exposed to it. Using the context of intensity, our students develop their understanding of the inverse square law using a variety of representational forms, such as diagrammatic, tabular / graphical and calculations using formulae. Using our pre-test and post-test results, our students showed gains in their reasoning used to explain the variation of intensity when an object is moved various distances from a source, which we attribute to their reasoning developed in the tutorial lessons. Additionally, students completed quantitative problems involving the inverse square law in the context of Newton's gravitational law. Six weeks after the completion of the inverse square tutorial, our students completed a tutorial lesson, in which they applied their understanding of the inverse square law to Coulomb's law and the electric field. Our results show that our students could apply the inverse square law to these contexts when guided, but some difficulties still remained, such as proportional reduction / increase based on variation of the distance, and transfer between representations, such as algebraic to graphical.