Abstract
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.
Highlights
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
Mathematics education is a result of different scenarios and demands around the world, teachers need to be cautious not to narrow down students’ learning processes and miss the opportunity to work on what matters
The research questions are: How is mathematical proficiency observed and expressed in the actions and interactions of students when engaged in mathematical modelling approaches? What are the affordances on students' mathematical proficiency through modelling approaches?
Summary
Students develop their sense of what it means to "do mathematics" from their actual experiences with mathematics, and their primary opportunities to experience mathematics as a discipline are seated in the classroom activities in which they engage. (Henningsen & Stein, 1997, p. 525). Allowing for new possibilities in mathematics teaching can be challenging Teachers carry their students’ learning encounters for life. This article portrays a doctoral research that analyzes one of these possibilities (Corrêa, 2019; Dias Corrêa, 2017) It explores a classroom complex environment, in which students’ development of mathematical proficiency is investigated when students engage in mathematical modelling tasks. Mathematical modelling tasks have the features of high-level tasks (Silver et al 2009), that is, cognitively demanding tasks that promote students' mathematical thinking and understanding. Within this scenario, students’ mathematical proficiency is examined based on Kilpatrick, Swafford and Findell’s proficiency model (2001). The research questions are: How is mathematical proficiency observed and expressed in the actions and interactions of students when engaged in mathematical modelling approaches? What are the affordances on students' mathematical proficiency through modelling approaches?
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