Tropes et figures du discours mathématique

Résumé

Cet article est une contribution à l’étude de la mise en signes des conceptualisations mathématiques.

Au niveau descriptif, il établit que le mathématicien utilise la plupart des figures de rhétorique. Depuis la métaphore et la métonymie jusqu’à la parasynonymie et le polysémisme en passant par le polymorphisme.

Les observations et l’analyse de leurs conséquences (par exemple : statut et fonction des figures relevées) sont conduites à partir de contraintes théoriques a priori telles que : définition du signe et du symbole, hétérogénéité des constituants du langage mathématique, hypothèse conceptuelle, etc.

L’auteur soutient qu’il est urgent de développer en didactique des mathématiques une attitude théorique. Une telle attitude permettrait, en effet, de fonder rationnellement une didactique authentiquement expérimentale. De là, il deviendrait possible de comparer et d’articuler les résultats de la didactique descriptive ainsi que les savoir-faire des praticiens.

Abstract

This paper contributes to the study of the signs used in writing down mathematical concepts. At a descriptive level, this paper argues that a mathematician uses almost all classical figures of rhetoric from the metaphor to the metonymy as well as the parasynonymy. He uses words and symbols with a variety of meanings as well as a variety of forms.

Under some theoretical constraints (the definition of signs and symbols, the heterogeneity of the elements of the mathematical language, etc.) the autor observes and analyses some consequences from the use in mathematics of such figures of speech.

The author states that it is urgent to develop a possible theoretical attitude concerning didactic of mathematics. Such an attitude would in fact rationally build an anthentically experimental didactic. It then would be possible to organize results from descriptive didactic as well as the knowhow of pedagogues.

Resumen

This paper contributes to the study of the signs used in writing down mathematical concepts.

At a descriptive level, this paper argues that a mathematician uses almost all classical figures of rhetoric from the metaphor to the metonymy as well as the parasynonymy. He uses words and symbols with a variety of meanings as well as a variety of forms.

Under some theoretical constraints (the definition of signs and symbols, the heterogeneity of the elements of the mathematical language, etc.) the autor observes and analyses some consequences from the use in mathematics of such figures of speech.

The author states that it is urgent to develop a possible theoretical attitude concerning didactic of mathematics. Such an attitude would in fact rationally build an anthentically experimental didactic. It then would be possible to organize results from descriptive didactic as well as the knowhow of pedagogues.