Modeling in Education: New Perspectives Opened by the Theory of Mathematical Working Spaces

Abstract

AbstractIn this chapter, the guiding line is the mathematical work that students develop in modeling tasks. We report first on MWS studies adopting the idea of a modeling cycle. In these studies, the MWS framework gives insight into the processes involved in students’ work, and it also sheds light upon the complex relationship between reality and mathematics and the multifaceted relationship between the process of problem solving and the underlying educational goals. We question the consistency of a sharp separation between mathematics and reality, and assuming that mathematical modeling is what mathematicians do when they work on models, we look at this work outside of education. Rather than steps of translation between reality and mathematics, we have to think of modeling as a coupling of reality and mathematics that should allow students to develop insight into, and understanding of, both mathematics and reality. We also look to epistemological studies that distinguish between modeling and mathematization, and characterize modeling by (1) plurality of models (2) operativity (3) subjective and social interpretation. The plurality of models for a given reality has been exploited in research studies to design tasks that put at stake transitions or coordination between specific domains corresponding to different a priori suitable working spaces. In these studies, mathematical work contributes to clarify and operationalize models as well as to give meaning to abstract mathematical notions. A MWS perspective could then break with a conception of modeling as an activity pursued individually and for individual competencies. In addition, considering the three dimensions of a working space should help to avoid a reduction of modeling to a translation and of mathematics to a language.KeywordsMathematical working spacesConnected working spacesModeling in educationPlurality of modelsOperativity of modelsSocial aspects of modeling