Search results for "Mathematical object"

Discussions of Part I Chapters

2016

This chapter is an opportunity for one of the authors of this book to question the other two authors in the light of issues raised in Chaps. 2– 5. It constitutes both a follow-up to discussions between authors which occurred over the writing process, and emergent issues—new discussions once the book was almost complete. Some fundamental issues are addressed, about the birth of mathematics (and its deep links with the birth of writing), the relationships between mathematics and other sciences, the interactions between conjecture and proof, and the role of visualisation and of gestures. The text is kept short in order to provoke the readers to reflect on these issues rather than for the autho…

An interpretative and cognitive semiotic approach to the learning process of mathematical objects

2013

Alcune riflessioni storico-critiche sul cosiddetto “paradosso di Duval”

2013

In 1993 a famous article by Raymond Duval highlighted a simple fact: students confuse the mathematical object O, that they are trying to build cognitively, with one of its semiotic representations R(O); he explained that this confusion was due to a sort of inevitable paradox: only someone who has already built O, can recognize R(O) as a representation of O and not as an object in itself. This idea has been extremely influential for researchers in the following years. However, many scholars of semiotics have emphasized the same phenomenon, even if in not quite the same words; in this paper we are going to mention some of them.

Objects, Structures, and Logics

2022

This book offers Novel In-Depth Discussions of the Relationship Between Logic and Metaphysics Attempts to Develop a New Framework for the Concept of Mathematical Structure Emphasizes the Importance of Mathematical Practice to the Philosophy of Mathematics

Análisis de los antecedentes histórico-filosóficos de la "paradoja cognitiva de Duval"

2015

In a famous article published in 1993, Raymond Duval highlighted a simple fact: the student may confuse the mathematical object O he is trying to build cognitively with one of its semiotic representations R(O). Duval explained that this confusion was due to a sort of inevitable paradox: only someone who has already built O, can recognize R(O) as a representation of O and not as an object in itself. Thereafter, this thought has been extremely influential for researchers. However, even if in different terms, many scholars of semiotics have emphasized the same phenomenon. In this paper we propose to remind some of them. En un famoso artículo publicado en 1993, Raymond Duval evidenciaba el sigu…