Abstract

This chapter describes a socio-constructivist elaboration of Realistic Mathematics Education (RME) that emerged from my collaboration with Paul Cobb and Erna Yackel. It is argued that RME and socio-constructivism are compatible and complement each other. Socio-constructivism points to the critical role of the classroom culture, while RME offers a theory on supporting students in (re-)constructing mathematics. Furthermore, the role of symbols and models is discussed, which was considered problematic in constructivist circles, while being central in RME. The emergent modelling design heuristic is presented as a solution to this puzzle. Together, guided reinvention, didactical phenomenology, and emergent modelling, are combined to delineate RME as an instructional design theory. This is complemented by a discussion of pedagogical content tools as counter parts of the emergent modelling and guided reinvention design heuristics at the level of classroom instruction. Finally, research on student learning and enactment of RME in Dutch classrooms is discussed.

Highlights

  • When Freudenthal (1971) coined his adage of mathematics as a human activity, concrete elaborations of what that would mean in practice still had to be worked out

  • We started our discussion of the socio-constructivist elaboration of Realistic Mathematics Education (RME) with the question of the compatibility of RME and socio-constructivism, and we concluded that on a meta level both positions are well compatible

  • We showed that adopting the collectivist perspective that is inherent to socio-constructivism especially has consequences for how we think about enacting RME in the classroom

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Summary

12.1 Introduction

When Freudenthal (1971) coined his adage of mathematics as a human activity, concrete elaborations of what that would mean in practice still had to be worked out. This became one of the main tasks of the IOWO, the predecessor of the current Freudenthal Institute. In the 1980s, Treffers took stock of what had been developed up to and construed the Realistic Mathematics Education (RME) theory by generalising over the characteristics the prototypical instructional sequences and local instruction theories that were available had in common.

Gravemeijer (B)
12.3 A Socio-Constructivist Perspective on Teaching and Learning
12.4 Symbolising and Modelling
12.4.1 Emergent Modelling
12.5 RME in Terms of Instructional Design Heuristics
12.5.1 Emergent Modelling Heuristic
12.5.2 Guided Reinvention Heuristic
12.5.3 Didactical Phenomenology Heuristic
12.6 Pedagogical Content Tools
12.7 RME and Classroom Practice
12.8 Recent Research on Instructional Practice in the Netherlands
12.9 Conclusion
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