The Mathematical Proficiency Promoted by Mathematical Modelling

This study aims to investigate the mathematical proficiency promoted by mathematical modelling tasks that require students to get involved in the processes of developing mathematical models, instead of just using known or given models. The research methodology is grounded on design-based research, and the classroom design framework is supported by complexity science underpinnings. The research intervention consists of high-school students, from a grade 11 mathematics course, aiming to solve four different modelling tasks in four distinct moments. Data was collected during the intervention from students’ written mathematical work and audio and video recordings, and from recall interviews after the intervention. Data analysis was conducted based on a model of mathematical proficiency and assisted by interpretive diagrams created for this research purpose. This research study offers insight into mathematics teaching by portraying how mathematical modelling tasks can be integrated into mathematics classes to promote students’ mathematical proficiency. The study discusses observed expressions and behaviours in students’ development of mathematical proficiency and suggests a relationship between mathematical modelling processes and the promotion of mathematical proficiency. The study also reveals that students develop mathematical proficiency, even when they do not come to full resolutions of modelling tasks, which emphasizes the relevance of learning processes, and not only of the products of these processes.