Our research addresses the role of examples to foster the students' development of the mathematical concepts, and of their mathematical ways of thinking. We consider the notion of example space introduced by Watson and Mason (2005), particularly when it is not formed by a simple juxtaposition of examples, rather it is endowed by a certain structure. Such a structure is provided by the semiotic actions and by the theoretic and logical dimensions of the mathematical activities. However, the formation of structured example spaces is far from being an automatic process. In this paper we focus on the genesis of examples and on the role of the teacher in helping the students to structure their examples spaces through the so-called cognitive apprenticeship method. We point out that the genesis of examples is often accomplished within a complex cyclic dynamics, the "cycle of examples production and modification" (CEPM). We illustrate it by means of two emblematic episodes from a classroom discussion. We show that the teacher's intervention can be crucial in helping the students to modify a wrong example, to generate the right one for the task and to start the long term process of building up the structure of their own space of examples.

### A model for developing students’ example space: the key role of the teacher

#### Abstract

Our research addresses the role of examples to foster the students' development of the mathematical concepts, and of their mathematical ways of thinking. We consider the notion of example space introduced by Watson and Mason (2005), particularly when it is not formed by a simple juxtaposition of examples, rather it is endowed by a certain structure. Such a structure is provided by the semiotic actions and by the theoretic and logical dimensions of the mathematical activities. However, the formation of structured example spaces is far from being an automatic process. In this paper we focus on the genesis of examples and on the role of the teacher in helping the students to structure their examples spaces through the so-called cognitive apprenticeship method. We point out that the genesis of examples is often accomplished within a complex cyclic dynamics, the "cycle of examples production and modification" (CEPM). We illustrate it by means of two emblematic episodes from a classroom discussion. We show that the teacher's intervention can be crucial in helping the students to modify a wrong example, to generate the right one for the task and to start the long term process of building up the structure of their own space of examples.
##### Scheda breve Scheda completa Scheda completa (DC)
2011
43 (2)
295
306
Example space; teacher's role; semiotic
F. Arzarello; M. Ascari; C. Sabena
File in questo prodotto:
File
2011_Asc_Arz_Sabena_ZDM.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 427.54 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2318/87573`