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Innovations Through Institutionalized Infrastructures: The Case of Dimitris, His Students and Constructionist Mathematics

  • Chronis KynigosEmail author
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 9)

Abstract

The paper discusses the case of Dimitris, a secondary mathematics teacher, who selected three micro-experiments from an institutionalized portal, re-mixed them and then gave his version to his students who in turn made their own changes and constructions. The case is discussed in the frame of the potential for institutionalized portals and digital infrastructures to afford pedagogical innovation which in this particular instance was about designing and re-mixing digital artefacts as an activity for educators, designers, teachers and students alike. Innovation is considered simultaneously at diverse levels, the representational affordances of digital artefacts, the potential for experiential mathematics for students, the potential for teacher-designer expressivity and the potential for economy-of-scale interventions. Dimitris’ changes were about the level of abstraction of the available linked representations in a simulation, about restructuration by bringing up front the notion of equivalence in solving equations, about encouraging the use of the negation of a property in a geometrical justification and about laying the ground for students to discover the usefulness of linear functions in working with geometrical properties. The students employed equivalence in a situated context, created an auxiliary point and segment to think around a geometrical property and embedded a linear relationship between segment lengths to create a rectangle which can never be a square. The paper discusses the potential for accredited large-scale institutionalized infrastructures to become the starting point for the generation of personalized living digital artifacts for both teachers and students rather than a showcase of exemplary interactive artifacts.

Keywords

Institutionalized portals Constructionist re-mixes Half-baked Micro-experiments 

Notes

Acknowledgements

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 610467—project “M C Squared”, http://mc2-project.eu. The c-book technology is based on the widely used Freudenthal Institute’s DME portal and is being developed by a consortium of nine partner organisations, led by CTI&Press “Diophantus”.

This work has been supported by the Greek National project “Digital School Platform, Interactive Books, and Learning Object Repository” (Contract Νο 296441/2010-2015) that is co-financed by the European Union (ESF) and National funds in the context of Operational Programme “Education and Lifelong Learning” of the Greek National Strategic Reference Framework (NSRF), and is being implemented by CTI “Diophantus”.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Educational Technology Lab, School of PhilosophyNational Kapodistrian University of Athens and CTI-DiophantusAthensGreece

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