Advanced algebraic thinking processes in students’ modelling activities

Abstract

Abstract This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as follows: how are students’ advanced algebraic thinking processes expressed (or not) in modelling activities that involve differential equations? Additionally, we presented the concept of advanced algebraic thinking as an extension of the (elementary) algebraic thinking notion and as a relevant part of advanced mathematical thinking. We included written records of two models that were produced and used in two classes and concluded that practically all groups showed processes of symbolic representation and representation translation. We also observed that around half of the groups presented suitable algebraic synthetization and development processes to solve the model equation. Another finding was that none of the groups applied generalization processes. Therefore, not all processes involved in advanced algebraic thinking were developed.