Karam, R., & Mäntylä, T. (2015). The influence of mathematical representations on students’ conceptualizations of the electrostatic field. In F. Claudio, & R. M. Sperandeo Mineo (Eds.): Teaching/Learning Physics: Integrating Research into Practice: Proceedings of the GIREP-MPTL 2014 International Conference. Palermo: Dipartimento di Fisica e Chimica, Università degli Studi di Palermo (819-826). http://www1.unipa.it/girep2014/item6.html The influence of mathematical representations on students’ conceptualizations of the electrostatic field Ricardo Karam 1 Terhi Mäntylä 2 1 Department of Science Education, University of Copenhagen, Denmark 2 School of Education, University of Tampere, Finland Abstract The electrostatic field can be conceptualized in different ways and in order to be able to connect them one must understand why vector and calculus formalisms are used to model electromagnetic phenomena. In this work, we categorize the mathematical representations used by physics teacher students to define central concepts of electrostatics and the physical justifications given by them for using certain mathematical formalisms. The results of our analysis show that many of the students were not able to make sense of essential mathematical tools for this theory (vectors and integrals), which prevents most of them from making meaningful connections between the different conceptualizations of the electrostatic field. Keywords Electrostatic field, Concept network, Physics teacher education, Mathematics in physics. Introduction The abstract character of the field concept poses a major challenge for physics education. In fact, a deep understanding of this theoretical construct seems to correlate with the ability to represent it in different ways (e.g. field lines, vectors, functions, differential operators, etc). Considering the electrostatic field, one student of an introductory course at university level will be introduced to (at least) three different ways to conceptualize it 1 : SK1) Coulomb ( ), where the field is defined in terms of the force acting on a test charge located in some point in space; SK2) Potential ( ), which is derived from energy considerations and is enabled by the conservative character of the electrostatic field and SK3) Gauss ( ), where the notion of electric flux is central and symmetry arguments play an essential role. In this sense, understanding the concept of electrostatic field is associated with the ability to recognize these different conceptualizations, to identify their applications as well as their limitations, and also to connect them through reasoning. Focusing on this latter aspect, 1 SK is the abbreviation for Sähkökenttä, which means electric field in Finnish.