ABSTRACT
This chapter describes the Dutch approach to geometry education, an approach that builds on students’ informal knowledge about geometric aspects of everyday life situations. Most students have a great deal of informal geometrical knowledge at their disposal, and even young children can model situations with gestures and imagine events and objects from different perspectives. In this chapter, we argue that this informal knowledge can be explicated and built on in geometry education within the framework of the domain-specific instruction theory of Realistic Mathematics Education (RME), an approach developed in the Netherlands. The key characteristics—reinvention through progressive mathematization, didactical phenomenological analysis, and use of emergent models—function as the scaffolding for an RME curriculum. Such an approach enables students to construct their own mathematical knowledge, fosters a reflective attitude toward the world, and fits in with the overall philosophy that views mathematics as a human activity. As such, this approach also accommodates the critique by Ehrenfest-Afanassjewa (1931), van Hiele-Geldof (1957), Freudenthal (1971), and van Hiele (1973) of traditional instruction of Euclidean geometry in the Netherlands.
