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Exploración del uso de los lenguajes natural y simbólico en la enseñanza de Matemática superior

ABSTRACT Introducción Los estudiantes, mayoritariamente, consideran que los conceptos y propiedades trabajadas en un curso son parte de una verdad matemática que deben aprender por medio del docente, a quien conciben como el poseedor de esta verdad y el encargado de transmitírsela utilizando lenguaje natural y simbólico. El primero generalmente se usa en el medio oral, siendo pocas las veces que el docente lo utiliza por escrito en el pizarrón, opuesto a lo que ocurre con el lenguaje simbólico. En un proyecto de investigación en curso 2 nos propusimos explorar el uso -del docente-de los lenguajes natural y simbólico en sus medios oral y escrito al enseñar un recorte de la verdad matemática. El recorte incluye conceptos y propiedades de límite, continuidad y derivabilidad pues demandan esfuerzo para su comprensión y conllevan notación simbólica compleja. Para recolectar datos a partir de los cuales se pudiera obtener información de los lenguajes natural y simbólico en ambos medios (oral y escrito en el pizarrón), el instrumento elegido fue la observación no participante de clases de Análisis Matemático del primer año del nivel superior. Con el fin de captar la simultaneidad entre lo oral y escrito, se filmaron con audio dichas clases. Presentamos en este trabajo los primeros avances realizados en esta línea, limitando nuestros ejemplos –por cuestión de espacio-a conceptos vinculados con la noción de límite, previos a su enseñanza, que extrajimos de una de las clases observadas. Marco teórico El marco teórico utilizado toma centralmente a) elementos de las Teorías de la Verdad en Matemática y en la clase de Matemática ([7], [1], [12]); b) lenguajes y registros, y c) 1 Parte de este trabajo cuenta con financiamiento de la Universidad Abierta Interamericana. 2 Proyecto de tesis doctoral en curso "Un estudio sobre el uso del lenguaje natural y simbólico en la enseñanza y el aprendizaje de Matemática superior". Cristina Camós es alumna del Doctorado en Ciencias, Mención: Didáctica de las Ciencias Formales -Matemática-de la Universidad Nacional de Catamarca, Argentina.

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