Five tenets of RME
On the basis of earlier projects in mathematics education, in particular the Wiskobas project, Treffers (1987) in Bakker (2004) has defined five tenets for Realistic Mathematics Education:
1 Phenomenological exploration. A rich and meaningful context or phenomenon, concrete or abstract, should be explored to develop intuitive notions that can be the basis for concept formation.
2 Using models and symbols for progressive mathematization. The development from intuitive, informal, context-bound notions towards more formal mathematical concepts is a gradual process of progressive mathematization. A variety of models, schemes, diagrams, and symbols can support this process, provided these instruments are meaningful for the students and have the potential for generalization and abstraction.
3 Using students’ own constructions and productions. It is assumed that what students make on their own is meaningful for them. Hence, using students’ constructions and productions is promoted as an essential part of instruction.
4 Interactivity. Students’ own contributions can then be used to compare and reflect on the merits of the different models or symbols. Students can learn from each other in small groups or in whole-class discussions.
5 Intertwinement. It is important to consider an instructional sequence in its relation to other domains. When doing statistics, what is the algebraic or scientific knowledge that students need? And within one domain, if we aim at understanding of distribution, which other statistical concepts are intertwined with it? Mathematics education should lead to useful integrated knowledge. This means, for instance, that theory and applications are not taught separately, but that theory is developed from solving problems. In addition to these tenets, RME also offers heuristics or principles for design in mathematics education: guided reinvention, didactical phenomenology, and emergent models (Gravemeijer, 1994) in Bakker (2004). We describe these in the following sections.
Bakker, Arthur. 2004. Design research in statistics education: On symbolizing and computer tools. Utrecht: CD-β Press