Introduction to Section II

Abstract

In the chapters in this section the focus is on the role of models, symbols and tools in instructional design. The chapters reflect the shift in the way models, symbols and tools are viewed in instructional design. Instead of the conventional focus on models that embody the formal mathematics to be taught, the emphasis is on alternative perspectives. Within these perspectives the ways in which symbols are used and the meanings they come to have, are seen to be mutually constitutive. Another common thread is formed by the instructional design theory for realistic mathematics education (RME). The RME theory features as an example of a design theory that takes the aforementioned dialectic relation into account. Key design heuristics of the RME theory are ‘guided reinvention’ (Freudenthal, 1973), ‘didactical phenomenology’ (Freudenthal, 1983), and ‘emergent models’ (Gravemeijer, 1999). It is especially the latter heuristic that is relevant for this book, since the emergent-models heuristic aims at the design of instructional activities that support the evolution of ways of symbolizing as part of a process of fostering the development of mathematical meaning.