Usos del error en la enseñanza de las matemáticas

• Autores: María José González López , Pedro Gómez Guzmán , Ángela María Restrepo
• Localización: Revista de educación, ISSN 0034-8082, Nº 370, 2015, págs. 71-95
• Idioma: varios idiomas
• Títulos paralelos:
  • Error uses in teaching mathematics
• Enlaces
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• Dialnet Métricas: 3 Citas
• Resumen
  • español

    Los errores de aprendizaje están presentes en muchas de las decisiones que el docente toma en relación con la enseñanza de las matemáticas. Pero, las investigaciones sobre el uso del error en la formación de profesorado son escasas, aunque algunas de ellas muestran que la formación en este ámbito hace a los estudiantes más conscientes de su aprendizaje y mejora su rendimiento. En este artículo, identificamos y describimos los usos del error que 26 docentes de matemáticas de secundaria (organizados en grupos) manifestaron en el contexto de un programa de formación de profesorado de matemáticas en ejercicio de dos años de duración. Para ello, desarrollamos un marco conceptual sobre procesos de toma de decisiones del profesorado cuando planifica la enseñanza de temas de matemáticas. Este marco conceptual está basado en las nociones de propósito, acción y resultado. Con base en este marco conceptual, establecimos un conjunto inicial de categorías que nos permitió codificar los informes finales de los grupos de docentes. En estos informes, ellos registraron las decisiones que tomaron al elaborar sus unidades didácticas de matemáticas y las justificaciones que les llevaron a tomarlas. Realizamos un proceso cíclico de refinado de las categorías y de nueva codificación de la evidencia con las nuevas categorías para verificar su validez. Este proceso nos permitió establecer una jerarquía entre los propósitos, las acciones y los resultados. Encontramos que los usos del error se organizan según tres propósitos generales: superar el error, evaluar el estado cognitivo de los estudiantes y producir información útil para otros aspectos de la planificación. Caracterizamos cada uno de estos usos mediante los propósitos concretos asociados a los propósitos generales, las acciones asociadas a cada propósito y los resultados vinculados a cada acción. Consideramos que conocer estos usos resulta útil para el diseño y desarrollo de programas de formación de profesores.

  • English

    Learning errors arise when teachers make decisions in their teaching. Nevertheless, research on error use in teacher education is scarce, even if some of that research shows that educating teachers on this topic help their students become more conscious of their learning and improves their performance. In this paper, we identify and describe the uses of error that 26 secondary mathematics teachers (organized in groups) revealed in a two years long teacher education program. For that purpose, we developed a conceptual framework on teachers decision making when they plan lessons on mathematical topics. This framework is based on the ideas of purpose, action and result. We used this framework for constructing an initial set of categories with which we codified the final reports that the groups of teachers produced in the program. We looked for the decisions made by the groups in their lesson planning and the justifications that they gave for those decisions. We refined the categories in a cyclic process of coding and revision of the categories. This process enabled us to establish a hierarchy of purposes, actions and results. We found that the uses of error can be organized according to three general teachers purposes: overcoming the error, assessing students cognitive state, and producing information that can be useful in other aspects of lesson planning. For each of these general purposes, we identified the specific purposes, actions and results that configure each error use that we found in the groups of teachers written productions. We consider that knowledge about these uses is useful for the design and development of teacher education programs.

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