Recognition and conversion of electric field representations: The case of the algebraic notation

This conceptual understanding article is part of a series where we analyze the recognition and conversion of representations of the electric field concept; in this article, we present the case of algebraic notation. We conducted a study with introductory and upper-division physics students taking electricity and magnetism courses in a large private Mexican university to learn how students recognize the electric field’s main characteristics in the algebraic notation of the field and how they convert to and from different representations. We refer to the theory of registers of semiotic representations as a theoretical framework and use a phenomenographic approach to analyze data. We explored students’ recognition and conversion abilities through interpretation and construction tasks for the electric field’s algebraic notation. We found that the main difficulties of interpreting and constructing the algebraic notation are related to separating the mathematical expression from the situation’s physical meaning. Sometimes, students referred only to the physical meaning without using algebraic notation. In other cases, they construct algebraic notation without explicitly describing the physical meaning. Another source of difficulty is the treatment process because some students make mistakes or misinterpretations that they carry throughout. We recommend that introductory and upper-division electricity and magnetism instructors and physics education researchers in higher education be aware of the difficulties that some interpretation and construction tasks may present to students learning the electric field concept.