The Role Played by Extra-mathematical Connections in the Modelling Process

Literature review in Mathematics Education on connections makes evident the necessity of delving into extra-mathematical connections. In this line, we answer the question: What types of mathematical connections are required to develop the modelling process? To this end, we consider three theoretical references: Onto-Semiotic Approach, Extended Theory of Connections, and Mathematical Modelling Cycle from a Cognitive Perspective, following a methodology used in two theoretical articulations previously developed by the authors between these frameworks, based on the use of models for the analysis of mathematical activity proposed by the Onto-Semiotic Approach for connections and the modelling process. The results of this analysis consist of, on one hand, the evidence of the types of intra- and extra-mathematical connections intervening in the different phases of the modelling cycle and, on the other hand, the proposal of a more detailed classification of mathematical connections.