MCSquared (http://mc2-project.eu) is funded by the European Commission under FP7 (Project no. 610467), Strategic Objective ICT-2013.8.1 “Technologies and scientific foundations in the field of creativity”

Mathematical Creativity Squared

I. Papadopoulos1, B. Barquero2, A. Richter2, M. Daskolia3, M. Barajas2, C. Kynigos3

1Aristotle University of Thessaloniki and CTI & Press Diophantus, 2 University of Barcelona, 3 University of Athens and CTI & Press Diophantus

Representations of creative mathematical thinking in collaborative designs of c-book units.

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• Digital tools, applets and authoring systems designed to foster Creative Mathematical Thinking (CMT)

• Their usage in educational practice is rather instrumented towards contexts of traditional lecturing and demonstration of exercise solutions.

• We attempt to contribute to our understanding of teachers designing of affordances of CMT

• We study designers’ representations of CMT as they became operationalized in the collaborative production of materials with an innovative e-book author aiming to afford CMT

A paradox

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• Four designer communities (CoI) ensuring diversity among the members in relation to the disciplinary backgrounds

• Research focus:– (a) illuminate the designers initial representations of CMT in

two of the four communities– (b) illuminate the process of operationalization of these

representations during collaborative designs of such technologies for students

In our study

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• Why two communities?• Use of questionnaires for identifying the members;

initial representations of CMT• Each CoI produced one c-book unit (‘Windmills’ and

‘Viral behavior of the Social Networks’)• Evaluation of the CMT affordances of the c-book units

on the basis of specific criteria previously defined.

Description of the study

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• CMT can be fostered in classroom through appropriate instruction

• Importance of interaction between the learning actors• Connection of creativity with mathematics• Tasks of an exploratory nature• Open problems • Combination of various tools and/or representations• Inter/intra disciplinary tasks

Shared Initial representations of CMT

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Windmills: The Greek c-book unit

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• CMT can tasks

Social Networks: The Spanish c-book unit

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Comparative analysis

A focus on exploring ‘real’ problems and questions

Promote openness, exploration, and diversity on the approach taken

Enable multiplicity of mathematical approaches/representations/techniques/solutions

Promote inter/intra-disciplinarity

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Comparative analysis

Promote a progressive modelling process

Involve a constructionist aspect

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• Large scale use of digital media in educational practice is widely dis-aligned from CMT affordances

• Understanding CMT representations in designer communities:– Suggesting a strategy to spread CMT cultures– Illuminating our own understanding

• Potentiality for the c-book units to foster CMT in students

• Operationalization of representations of CMT linked to a specific context

Conclusions