Dirk Wessels

Documenting the Development of Modelling Competencies of Grade 7 Mathematics Students

Modelling is a mathematical competence and a means of learning significant mathematics. Preliminary findings on the nature of competence and modelling competencies, as well as the development of mathematical modelling competencies of Grade 7 students are presented in this chapter. Twelve students solved three model-eliciting tasks in groups over a period of 12 weeks. The development of competencies is considered across the group as a whole. Analysis of the data shows that modelling competencies are activated and do develop when students take part in well-orchestrated modelling activities.

Developing Mathematisation Practices in Primary Mathematics Teaching through Didactisation-Based Teacher Development.

This article looks at the development of mathematisation in a primary school mathematics teacher’s classroom. The teacher was a volunteer in a professional development programme that promoted didactisation principles for mathematics teacher development. At the heart of didactisation lies the principle of mathematisation. Mathematisation as a fundamental aspect of teaching and learning in mathematics classrooms led us to seek ways to develop the potential for mathematisation in teachers. This article explores how a grade 5 mathematics teacher improved mathematisation in her classroom while she participated in a didactisation-based professional development intervention. Over a period of a year, four lessons were audio-recorded and transcribed. Design research constituted the framework of the professional development programme, while model-eliciting tasks were used as a vehicle for programme delivery. The Realistic Mathematics Education principles of guided reinvention, mathematisation and contextual exploration provided the theoretical framework for analysis and coding of the data. In addition, Gravemeijer’s framework of emergent modelling and Douady’s conceptualisation of tool and object use in mathematics provided the basis for lesson analysis at micro-level. The results show that this teacher was able to change the quality and level of mathematisation in her classroom through improving student mathematical activity, which led to redefining her role in the classroom. Her guiding of the learning process moved from telling to asking questions and, finally, to facilitating mathematical re-invention.

Six Principles to Assess Modelling Abilities of Students Working in Groups

This chapter sets out how the six instructional design principles for model-eliciting activities (MEAs) can be reworded and may serve as principles for assessing modelling abilities of students working in groups. The chapter explores some modelling assessment ideas and explains how the six principles form a framework for a holistic evaluation of group modelling. A design research study investigated the modelling competencies of grade 7 students working in a group. The assessment unit was that of the group as a whole and not of individual students. It was found that the six principles reworded as an assessment framework enabled the authors to evaluate significant aspects of model-eliciting activities such as model construction, reality integration, quality of documentation, self-evaluation, development of prototypes for thinking and generalisation.

The Hidden Benefits of Mathematical Modelling for Students with Disabilities

The impact of learning via mathematical modelling tasks on students with disabilities in a remote part of Australia was studied to answer the question: Can students with disabilities learn through mathematical modelling tasks? Daily mathematics lessons were substituted with a set of modelling tasks for 1 month. A design-based research methodology with a neo-Vygotskian design philosophy and Feuerstein’s theory of structural cognitive modification was coupled to three intensive case studies to monitor how these students with disabilities responded to modelling tasks. Findings showed evidence of engagement and meaningful mathematical learning. “Hidden benefits” of modelling for students with disabilities were the development of literacy, social skills practice around collaboration and social negotiations, and support for the development of potentially more robust thinking operations.