Mathematical Modelling

Abstract

Mathematical modelling plays a prominent role in German mathematics education. The significance of modelling problems in school and in teacher education has increased over the last decades, accompanied by various research projects. In addition, there has been a vivid discussion on the implementation of modelling in schools. This chapter gives on overview on the current state of mathematical modelling in German speaking countries. After a short summary of the development of the past years, a widespread conceptualisation of modelling competence as well as its description within the German Educational standards is presented. Ways of implementing mathematical modelling in classrooms as well as in everyday lessons but also via modelling projects are described and an example of one of these problems worked on by students of grade 9 over two years is given. Furthermore, different modelling cycles are shown and their aims and usage in different circumstances are outlined. In addition, research questions currently being discussed are addressed and an example for a quantitative research project is given.

Mathematical Modelling and Didactic Moments

“…Although research on the MM teaching by Borromeo Ferri ( 2006), Blum and Borromeo Ferri (2009), Perrenet and Zwaneveld (2012), Blum (2015), Greefrath and Vorhölter (2016), Vorhölter, Greefrath, Borromeo Ferri, Leiß and Schukajlow (2019), and Barquero and Jessen (2020), among others, highlight almost dominantly the didactic technique of MM cycles to minimise the complexity existing in the MM process, it is necessary to consider that this technique of cycles from the perspective of the anthropological theory of didactics, from now on ATD, is likely to be questioned, as highlighted by García, Gascón, Ruiz Higueras, andBosch (2006), Bosch, García, Gascón, andRuiz Higueras (2006), Sodré and Guerra (2018), Sodré (2019), and Sodré and Oliveira (2021), but instead of criticising it, providing it with solid theoretical frameworks that allow better understanding and, if possible, making it more accessible to the teaching and learning of MM.…”

The role of spatial, verbal, numerical, and general reasoning abilities in complex word problem solving for young female and male adults

“…Due to these characteristics, CWPs usually address cognitive processes that go beyond algorithmical calculation and the application of factual knowledge. For example, mathematical modeling is typically addressed in CWP solving (Leiss et al 2019;Vorhölter et al 2019;Strohmaier 2020), and linguistic factors are of pivotal importance for their solution (Daroczy et al 2015). With this contemporary and functional perspective, CWP solving arguably addresses fundamental aspects of the recent goals of mathematics education (OECD 2005;Strohmaier 2020).…”

Different complex word problems require different combinations of cognitive skills

“…Mathematical word problems are considered mathematical tasks in which relevant information is presented as text rather than in mathematical notation (Boonen et al, 2016;Daroczy et al, 2015;Verschaffel et al, 2020). They exist in various forms, ranging from a simple verbal description of a basic mathematical operation (e.g., de Koning et al, 2017) to advanced modeling problems (e.g., Leiss et al, 2019;Vorhölter et al, 2019). We consider complex word problems to be mathematical word problems that typically (1) present information in a syntax that does not merely mirror the mathematical task, (2) contain information that might be redundant or superficial, (3) contain multiple representations, and (4) revolve around a context that is functional for the problem solution (Strohmaier, 2020).…”