ABSTRACT
This chapter summarizes important findings on the learning and teaching of mathematical modelling, with an emphasis on empirical research. Significant barriers are found in the processes involved in dealing with modelling tasks. Mathematical modelling is a cognitively demanding activity since several competencies must be activated along the road and both mathematical and extra-mathematical knowledge is required, as are appropriate beliefs and attitudes. The chapter introduces the non-contradictory distinction between two over-arching purposes of mathematical modelling in mathematics education. Borromeo Ferri describes an evaluated module for implementing mathematical modelling into teacher education, oriented towards the abovementioned competency model. This module starts with solving and developing modelling tasks for school, accompanied by theoretical reflections on modelling. A particularly broad approach to utilising mathematical models and mathematical modelling as a vehicle for students’ own construction and consolidation of mathematical concepts is the so-called Models and Modelling Perspective, first introduced by R. Lesh and H. M. Doerr.
