In this paper we report on a study about experts’ strategies for producing examples of mathematical objects. Three strategies have been identified: by trial and error, by transformation and by analysis. These strategies and some related cognitive processes are analysed in detail. In particular, some meta-cognitive and meta-cultural remarks by the subject have been identified as fundamental elements for the activation of strategies as well as for transition between them. Finally we discuss the possibility of identifying links between the strategies for producing examples we expose here and processes of production of conjectures, argumentations and proofs.
Graduate students' processes in generating examples of mathematical objects / Antonini Samuele. - In: PROCEEDINGS OF THE PME CONFERENCE. - ISSN 0771-100X. - STAMPA. - 2:(2006), pp. 57-64. ( 30th Conference of the International Group for the Psychology of Mathematics Education Prague, Czech Republic July 16-21, 2006).
Graduate students' processes in generating examples of mathematical objects
Antonini Samuele
2006
Abstract
In this paper we report on a study about experts’ strategies for producing examples of mathematical objects. Three strategies have been identified: by trial and error, by transformation and by analysis. These strategies and some related cognitive processes are analysed in detail. In particular, some meta-cognitive and meta-cultural remarks by the subject have been identified as fundamental elements for the activation of strategies as well as for transition between them. Finally we discuss the possibility of identifying links between the strategies for producing examples we expose here and processes of production of conjectures, argumentations and proofs.
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