Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives

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.

Literature review on networking of theories developed in mathematics education context

“…The main conclusion that we want to highlight from this literature review is the evolution that goes from networking between general theories towards networking between general theories and more specific theories (Ledezma et al, 2022;Vergel et al, 2021). In the next section we will delve into this type of networking, describing the articulation between the ETC and the OSA, taking as a context of reflection the establishment of connections in the study of the derivative.…”

“…This study (Thanheiser et al, 2021) is a powerful and important case of networking because its content looks in detail at how researchers made high-level efforts to connect five theoretical approaches. This could mean that multi-theoretical analyzes are relevant (Bikner-Ahsbahs & Vohns, 2019), but also one or more theories could help refine or improve conceptual and methodological tools of other theories (e.g., Bikner-Ahsbahs & Prediger, 2014; Kidron & Bikner-Ahsbahs, 2015;Ledezma et al, 2022;Rodríguez-Nieto et al, 2021a).…”

“…Currently, the theoretical articulation between the ETC and the OSA has been proposed (Rodríguez-Nieto et al, 2021a) with emphasis on the derivative, because despite the fact that in some investigations they articulated theories using the derivative as a reflection context (Borji et al, 2018;Pino-Fan et al, 2017), in their results they strongly state that students and some inservice teachers have difficulty understanding the derivative because they do not connect meanings or definitions and several representations of the derivative concept. Ledezma et al (2022) can be identified the network between OSA and the modeling cycle from a cognitive perspective. The first gives tools for mathematical activity analysis and the second gives an appreciation of the mathematical activity of modeling.…”

“…However, no relationship was identified with the networking of theories, which is an important line of research that has given good results for the analysis of mathematical activity (Bikner-Ahsbahs, 2022;Font et al, 2016;Rodríguez-Nieto et al, 2021a). In fact, various authors (Bikner-Ahsbahs, 2022;Bikner-Ahsbahs & Prediger, 2010Boero et al, 2002;Ledezma et al, 2022;Radford, 2008;Rodríguez-Nieto et al, 2021a;Tabach et al, 2020;Thanheiser et al, 2021) have investigated networking of theories, but not to report a detailed study that demonstrates the current state of research on this topic. Therefore, this research becomes relevant.…”

Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories

“…One of the topics of great interest in research in mathematics education has been the development of theoretical approaches or theories specially to analyze mathematical activity. These types of research topics were classified into two groups (Ledezma et al, 2022):…”