Reconsidering the Roles and Characteristics of Models in Mathematics Education

Abstract

A model is generally assumed to be built by translating a real world problem into a mathematical representation. We attempt to re-construct this interpretation and point to at least two distinct meanings: (Role 1) models as hypothetical working spaces, and (Role 2) models as physical/mental entities for comparing and contrasting. This leads us to draw attention to four different perspectives of modelling: (a) where modelling is interpreted as interactive translations among plural worlds not between two fixed worlds; (b) where models have the potential to incorporate scenarios beyond the initial problem situation; (c) where the mathematical world is used as a source of mental entities for comparing and contrasting; (d) where modelling competency means knowing how to balance between these different roles. Perspectives (a) and (d) are concerned with Role 1 and (b), (c) and (d) are concerned with Role 2.