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Generating examples: focus on processes

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Abstract

Constructing an example can be a rich and complex activity, interesting to investigate mathematical thinking and with many potentialities in mathematics education. In this article, I analyse processes involved in example generation, with particular emphasis on production and transformation of signs representing mathematical objects and on generation of inferences. The richness and complexity of these processes will also be shown through the notions of prototypes, concept image and concept definition. This investigation reveals aspects that are significant both in education and for the reflection on cognitive and cultural aspects of mathematical thinking.

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Acknowledgments

I would like to thank Anna Baccaglini-Frank (University of Siena, Italy, and Institute of Education, University of London, UK) for polishing the English of the present paper.

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  1. Dipartimento di Matematica, Università di Pavia, via Ferrata, 1, 27100, Pavia, Italy

    Samuele Antonini

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  1. Samuele Antonini
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Correspondence to Samuele Antonini.

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This article is dedicated to the memory of Giorgio Tomaso Bagni (1958–2009), researcher, teacher, and friend.

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Antonini, S. Generating examples: focus on processes. ZDM Mathematics Education 43, 205–217 (2011). https://doi.org/10.1007/s11858-011-0317-6

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