Memoria de la XXV Escuela de Invierno en Matemática Educativa
Tipo de documento
Autores
Lista de autores
Duval, Raymond
Resumen
In order to analyze the processes of comprehension underlying any mathematical activity we must start from the epistemological and cognitive characteristics that are specific to mathematics. The mathematical activity is based on transformation of semiotic representations in other semiotic representations. Solving problem in a mathematical way always requires mobilizing, explicitly or implicitly, two registers of semiotic representation. We can then observe the various kinds of threshold of comprehension that block many students at different levels of the curriculum. Firstly there are two kinds of transformations of semiotic representations that are quite different sources of difficulties. But one ignores or rejects the one that requires shifting the register within a representation is produced for two reasons. Either because only one kind of transformation is important from a mathematical point of view, or because one believes that a multirepresentation, now obvious with computers, removes any difficulty of the representation conversion, as it is the case in other fields of knowledge. Secondly, for understanding when one learns mathematics one needs first to recognize and not to justify. The ability to solve problems, to explore them in a mathematical way, to anticipate possible treatments, to check by oneself the validity of a procedure is basically the ability to recognize the same object in two different representations or different objects in almost similar representations. This ability requires a coordination of various registers separated by cognitive gaps. The conceptualization in mathematics emerges only from this coordination. We take several examples to give an insight both of the specific problems of comprehension in learning mathematics and of the cognitive way of analyzing them. And we highlight the need of an explicit and global cognitive approach in mathematics education so that learning mathematics means for all students to develop their ability...
Fecha
2011
Tipo de fecha
Estado publicación
Términos clave
Comprensión | Desarrollo | Dificultades | Diseño | Epistemología | Semiótica | Tipos de problemas
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Usuario
Título libro actas
Editores (actas)
Lista de editores (actas)
Conferencia Interamericana de educación Matemática
Editorial (actas)
Lugar (actas)
Rango páginas (actas)
01-12
Referencias
Duval, R., (1988). Graphiques et Equations: l'articulation de deux registres. Annales de Didactique et de Sciences Cognitives, 1, 235-255 Duval, R. (1991). Structure du raisonnement déductif et apprentissage de la Démonstration. Educational Studies in Mathematics, 22(3), 233-261. Duval, R. (1995a). Sémiosis et pensée humaine. Berne, Peter Lang Duval, R.(1995b). Geometrical Pictures : kinds of representation and specific processing. In (Ed. R. Suttherland & J. Mason ), Exploiting Mental Imagery with Computers in Mathematics Education (Ed. R. Suttherland & J. Mason ). Springer, Berlin, 142-157 Duval R (2004) Los problemas fundamantales en el Aprendizaje de las Matematicas y las Formas superiores en el Desarrolo cognitivo. Cali : Universidad del Valle. Duval, R.(2005a). Transformations de représentations sémiotiques et démarches de pensée en mathématiques. Actes du XXXIIe colloque COPIRELEM. IREM, Strasbourg, 67-89. Duval, R. (2005b). Les conditions cognitives de l’apprentissage de la géométrie : développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. Annales de Didactique et de Sciences Cognitives, (10), 5-53. Duval, R. (2006) The cognitive analysis of Problems of comprehension in the learning of mathematics. In (A Saenz-Ludlow, and N.Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Sépcial issue, Educational Studies in Mathematics , 61, 103-131 Duval, R. (2007). Cognitive functioning and the understanding of the mathematical processes od proof. In (Ed. P. Boero) Theorems in schools. Rotterdam/Tapei, Sense Publishers, 137-161 Duval, R. (2008). Eight Problems for a Semiotic Approach in Mathematics Education. In (Eds. L. Radford, G. Schubring, F. Seeger) Semiotics in Mathematics Education; Epistemology, History, Classroom and Culture. Sense Publishers, 39-61 Duval, R. (à paraître). Ver E Ensinar a matemática de Outra forma. (I) Entrar no modo matemático de pensar :os registros de repreentações semióticas
Cantidad de páginas
12