A model for developing students' example space: the key role of the teacher.

Autor/inn/en	Arzarello, Ferdinando; Ascari, Marina; Sabena, Cristina
Titel	A model for developing students' example space: the key role of the teacher.
Quelle	In: ZDM : mathematics education, 43 (2011) 2, S. 295-306 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	1863-9690; 1863-9704
DOI	10.1007/s11858-011-0312-y
Schlagwörter	Bildungsforschung; Pädagogische Forschung; Lehrer; Beispiel; Unterricht; Diskussion; Intervention
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 (Mathematics as a constructive activity: learners generating examples, 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". 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.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2012/2