Students’ mathematical modelling behaviors: Strategies and competencies

Mathematical modelling has recently taken the spotlight in mathematics education as a means to prepare students for the challenges they face in the modern world, and there have been numerous proposals on the modelling cycles describing students’ approaches to solve modelling tasks. Within these proposed modelling cycles, researchers emphasize the importance of building a real model to describe the real situation and the application of extra-mathematical knowledge to highlight the relationship between reality and mathematics. However, the concept of extra-mathematical knowledge and the process to establish a real model have only been described in broad strokes and these descriptions lack details. This thesis aims to add to the descriptions of extra-mathematical knowledge and the process to develop a real model based on empirical data by closely examining students’ mathematical Modelling behaviors. To achieve these goals, I administered two rudimentary mathematics complex tasks, a special type of tasks that present a complex situation but allow the audience to apply their well-worn tools in mathematics to establish a solution, to two groups of junior secondary school students. These tasks allow me to tip the balance of between reality and mathematics in mathematical modelling in order to focus on students’ modelling behaviors. With regard to the process leading to a real model, my analysis indicates that students hold different intentions in building a real model and these intentions affect the strategies they use and therefore their modelling process and the quality of their solutions deeply. In the analysis of these strategies, I also apply flow theory to understand these intentions. As for extra-mathematical knowledge, my analysis demonstrates that extra-mathematical knowledge is a multi-faceted, complex construct composed of various competencies, that contains different characteristics and can deeply affect students’ engagement with the tasks.