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La transferencia de aprendizaje algorítmico y el origen de los errores en la sustración

  • Autores: Ana Belén Sánchez García Árbol académico, Ricardo López Fernández Árbol académico
  • Localización: Revista de educación, ISSN 0034-8082, Nº 354, 2011 (Ejemplar dedicado a: La formación práctica de estudiantes universitarios: repensando el Practicum), págs. 429-445
  • Idioma: español
  • DOI: 10.4438/1988-592X-RE-2011-354-006
  • Títulos paralelos:
    • The transfer of algorithmic learning and the origin of errors in subtraction
  • Enlaces
  • Resumen
    • español

      Los resultados de la investigación que presentamos demuestran que la influencia del conocimiento formal, intuitivo y procedimental en el proceso de aprendizaje algorítmico; el contexto pedagógico del aula y el proceso de transferencia del conocimiento matemático son decisivos en la generación del error que se nutre de mecanismos de transferencia analógica. Específicamente, hemos estudiado este hecho en el algoritmo de la sustracción. En este artículo analizamos las respuestas emitidas por nueve niños/as de edades comprendidas entre siete y diez años, en una prueba compuesta por 20 sustracciones. En total, fueron grabados los procesos ejecutados por los nueve niños/as en 180 restas. Los datos obtenidos a través de protocolos en voz alta, fueron analizados con ayuda del programa estadístico Nud*ist 4.0. El estudio que presentamos, se inscribe en una investigación en la que hemos analizado una base de datos de 7.140 restas realizadas por 357 niños/as de edades comprendidas entre siete y trece años, al objeto de determinar si producían errores sistemáticos y conocer su tipología. En este artículo, evidenciamos como los errores, se focalizan en torno a determinados factores de la tarea relacionados con la comprensión de conceptos esenciales para el aprendizaje significativo de la habilidad. Lo último, opinamos es esencial para ayudar a los profesores en la programación didáctica de la enseñanza del algoritmo de la sustracción y en la práctica metodológica específica a aplicar en el aula; pues contribuyen a clarificar la naturaleza de los procesos algorítmicos y la generación del error en la sustracción. Finalmente, demostramos la importancia de los factores contextuales, como el lenguaje utilizado en el proceso de enseñanza. Lo anterior, es debido a que los niños/as al iniciar el aprendizaje construyen algunas interpretaciones sobre el procedimiento, en base a una serie de conceptos o vocabulario específico organizado dentro del campo conceptual de la sustracción.

    • English

      The results of the study presented in this paper demonstrate that the influence of formal, intuitive and procedural knowledge in the process of algorithmic learning, the pedagogical context of the classroom and the process of transferring mathematical knowledge are decisive in error generation through mechanisms of analogical transfer. The paper reports this fact in the subtraction algorithm. The answers given by nine children of ages between seven and ten years in a test made up of 20 subtraction problems were analysed. Altogether, the processes executed by the nine children were recorded in 180 subtraction operations. The volume of data obtained via talk-aloud protocols was analysed with the help of the Nud*ist 4.0 statistical program. The study falls within the context of a larger study where the authors analysed a database of 7,140 subtraction operations performed by 357 children between the ages of seven and thirteen years, with the aim of determining whether systematic errors occurred and typing any systematic errors found. The article shows how the errors most commonly found cluster around certain factors of the task. These factors are related to the understanding of essential concepts for the meaningful learning of the ability. In the authors' opinion, it is essential to help teachers plan how to teach the subtraction algorithm and provide teachers with a specific methodological practice to apply in the classroom; these things would help make the nature of algorithmic processes clearer and reduce error generation in subtraction. Lastly, the paper demonstrates the importance of contextual factors, such as the language used in the teaching process. When children begin learning, they build interpretations of the procedure, based on a series of concepts or specific vocabulary organised within the conceptual field of subtraction.

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