Abstract. From a didactic point of view, the introduction of a deductive approach presents two interwoven aspects to be developed: on the one hand the need of justification and on the other hand the idea of a theoretical system within which that justification may becomes a proof. Proof makes sense in respect to a theory and vice versa; thus, the introduction of a deductive approach presents two problems of sense, which are interrelated: the sense of proof and the sense of theory. Thus, the first difficulty the teacher has to overcome, is related to developing the need of a justification, and this contrasts with the intuitive approach to which pupils are used, the second difficulty is related to the possible cognitive rupture between argumentation, i.e. a set of arguments supporting the acceptance of a statement, and mathematical proof, validating a statement within a theory. After analysing the nature of these difficulties, the author discusses how it is possible to face these crucial educational issues presenting the choice of a specific "field of experience" (Boero et al., 1995): geometrical constructions within a particular Dynamic Geometry Environment (Cabri- géomètre)

Mariotti, M.A. (2007). Geometrical proof: the mediation of a microworld. In Theorems in school: From history epistemology and cognition to classroom practice (pp. 285-304). ROTTERDAM : Sense Publisher.

Geometrical proof: the mediation of a microworld

MARIOTTI, MARIA ALESSANDRA
2007-01-01

Abstract

Abstract. From a didactic point of view, the introduction of a deductive approach presents two interwoven aspects to be developed: on the one hand the need of justification and on the other hand the idea of a theoretical system within which that justification may becomes a proof. Proof makes sense in respect to a theory and vice versa; thus, the introduction of a deductive approach presents two problems of sense, which are interrelated: the sense of proof and the sense of theory. Thus, the first difficulty the teacher has to overcome, is related to developing the need of a justification, and this contrasts with the intuitive approach to which pupils are used, the second difficulty is related to the possible cognitive rupture between argumentation, i.e. a set of arguments supporting the acceptance of a statement, and mathematical proof, validating a statement within a theory. After analysing the nature of these difficulties, the author discusses how it is possible to face these crucial educational issues presenting the choice of a specific "field of experience" (Boero et al., 1995): geometrical constructions within a particular Dynamic Geometry Environment (Cabri- géomètre)
2007
9789077874219
Mariotti, M.A. (2007). Geometrical proof: the mediation of a microworld. In Theorems in school: From history epistemology and cognition to classroom practice (pp. 285-304). ROTTERDAM : Sense Publisher.
File in questo prodotto:
File Dimensione Formato  
Mariotti_sense.pdf

non disponibili

Tipologia: Post-print
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 13.03 MB
Formato Adobe PDF
13.03 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/42360
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo