Abstract
The aim of this article is to carry out a work of networking theories which combines two perspectives on the mathematical activity involved in a modelling process, in order to answer the following question: To what extent does the application of the onto-semiotic tools complement the analysis from a cognitive perspective of a mathematical modelling process? To this end, we considered two theoretical frameworks: on the one hand, the onto-semiotic approach, which provides tools for the analysis of any mathematical activity and which here we applied to the activity of modelling; on the other hand, the modelling cycle from a cognitive perspective, which is a reflection on the specific mathematical activity of modelling. Then, we took a modelling problem that we applied to prospective mathematics teachers (at undergraduate and postgraduate level), and we analysed it from the perspective of both frameworks, in order to identify concordances and complementarities between these two ways of analysing the mathematical activity involved in the modelling process. The main conclusion is that both frameworks complement each other for a more detailed analysis of the mathematical activity that underlies the modelling process. Specifically, the analysis with the tools provided by the onto-semiotic approach reveals the phases or transitions of the modelling cycle as a conglomerate of mathematical practices, processes, and the primary objects activated in these practices.
Highlights
The development of models for analysing mathematical activity has been one of the topics that have produced most interest in Mathematics Education
Some research into networking between a general theoretical framework and a theoretical model focused on the analysis of a specific type of mathematical activity has been carried out, it is interesting to extend the study of how these different types of analysis of mathematical activity may complement each other
The Mathematical Modelling Cycle from a Cognitive Perspective (MMCCP) is situated on cognitive bases and the aim is to study the mental processes that occur in the specific mathematical activity of modelling (Borromeo, 2018)
Summary
There are those who develop theoretical constructs to analyse mathematical activity within the framework of the theories of Mathematics Education (e.g., Brousseau, 2002; Chevallard, 1992; Kuzniak, 2011, among others). Some research into networking between a general theoretical framework and a theoretical model focused on the analysis of a specific type of mathematical activity has been carried out (see Pino-Fan et al, 2017, for the process of representation; Campo-Meneses & García-García, 2021; and Rodríguez-Nieto, 2021, for the process of connection), it is interesting to extend the study of how these different types of analysis of mathematical activity (i.e., general and specific frameworks) may complement each other. A general theoretical framework of mathematical activity and a specific framework for the mathematical modelling process are complemented. This research is relevant to the field and addresses a networking of two theories which, as far as we know, has not previously been proposed with these specific theoretical frameworks
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
