# Charting the microworld territory over time: design and construction in mathematics education

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## Abstract

The study discusses the development of theoretical ideas and constructs related to digital microworlds within the mathematics education community and their implications for interpretations of mathematics learning. Starting from Papert’s introduction of the concept during ICME 2 in 1972, we trace the evolution of theoretical approaches concerning the essence of the idea in an attempt to situate the notion of constructionism in the light of contemporary frameworks. We argue that microworlds, and the search for a learnable mathematics, have a continued relevance to mathematics education, but that the lens research attention has shifted over time, with the current foci on communal design, situated and embodied approaches and artefacts whose use crosses boundaries between different practices. To illustrate these shifts and the challenges that still remain, we present examples from our current work involving the use of microworlds for learning and teaching through communication, design and construction.

### Keywords

Microworlds Communal design Body and ego synonicity Boundary objects## Notes

### Acknowledgments and projects

We would like to thank Guilherme Rodrigues Margalhães, Maisa Aparecida Sigueira Rodrigues, Elen Graciele Martins, Franklin Rodrigues de Souza and Amarilis Reto Ferreira for their ongoing contributions to the design of the musi*CAL*colorida microworld and FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for their financial support in this endeavour (grant nos. 2004/15109-9 and 2005/60655-4). Our thanks are also due to Costis Kontogiannis, Vassilis Tsitsos, Stassini Frangou, Nikoleta Yiannoutsou and the Psychico College students for their engagement with the Juggler microworld. We acknowledge too the support received in relation to the research projects reported in the paper, ‘ReMath’—Representing Mathematics with Digital Media FP6, IST-4, STREP 026751 (2005–2008) and “SEED”: “Seeding cultural change in the school system through the generation of communities engaged in integrated educational and technological innovation”, European Community, IST, School of Tomorrow, IST-2000-25214. (2001–2004).

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