Models and Modelling for the Future
Lyn D. English, Richard Lesh, Kit Ee Dawn Ng & Gloria StillmanThe terms, models and modelling, have been used variously in the literature, including in reference to solving word problems, conducting mathematical simulations, creating representations of problem situations (e.g., constructing explanations of natural phenomena), and creating internal, psychological representations while solving a particular problem. This proposed roundtable session will focus on the models and modelling perspective first initiated by Richard Lesh. From this perspective, models may be viewed as conceptual systems or tools comprising operations, rules and relationships that can describe, explain, construct, or modify an experience or a complex series of experiences. Modelling involves the crossing of disciplinary boundaries, with an emphasis on the structure of ideas, connected forms of knowledge, and the adaptation of complex ideas to new contexts (English, in press; Hamilton, Lesh, Lester, & Brilleslyper, 2008). The roundtable will begin with a review of the models and modelling perspective and will then be open to discussion on issues including (but not confined to): 1. Models and modelling in different nations, including sharing and collaboration; 2. The role of task context (including interdisciplinary themes) and task design; 3. The nature of the mathematical ideas and processes embedded in modelling problems; 4. Transfer of learning (e.g., from model-eliciting activities to model exploration and model adaptation activities); 5. Models and modelling with young children; 6. Across-grade sharing of modelling products (e.g., grades 2 and 7 students sharing their solutions to a given modelling problem); 7. Towards the future: advancing models and modelling.