This paper deals with an important item in Mathematics Education: mathematical definitions. In particular it focuses on the definition of a triangle, an only seemingly “simple” mathematical object. In order to do this, we discuss the main following points: 1) the distinction between the formal mathematical concept of definition and the use of this word in classroom practice; 2) some specific problems concerning geometry, along with a comparison of many different definitions of a triangle and of different curricular choices; 3) a possible impact of modern technologies on the definition of triangle. Finally, we emphasize the necessity for a teacher to employ a balanced mix of intuition and formalism both in compulsory and in upper school.
Can any definition of triangle be considered the best one? / E., Castagnola; Tortora, Roberto. - STAMPA. - 2:(2009), pp. 219-232. (Intervento presentato al convegno 5th International Colloquium on the Didactics of Mathematics tenutosi a Rethymnon, Creta, Grecia nel aprile 2008).
Can any definition of triangle be considered the best one?
TORTORA, ROBERTO
2009
Abstract
This paper deals with an important item in Mathematics Education: mathematical definitions. In particular it focuses on the definition of a triangle, an only seemingly “simple” mathematical object. In order to do this, we discuss the main following points: 1) the distinction between the formal mathematical concept of definition and the use of this word in classroom practice; 2) some specific problems concerning geometry, along with a comparison of many different definitions of a triangle and of different curricular choices; 3) a possible impact of modern technologies on the definition of triangle. Finally, we emphasize the necessity for a teacher to employ a balanced mix of intuition and formalism both in compulsory and in upper school.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.