From Human Activity to Conceptual Understanding of the Chain Rule

• Autores: Zingiswa Mybert Monica Jojo, Aneshkumar Maharaj
• Localización: REDIMAT, ISSN-e 2014-3621, Vol. 2, Nº. 1, 2013, págs. 77-99
• Idioma: inglés
• Títulos paralelos:
  • De la actividad humana a la comprensión conceptual de la Regla de la Cadena
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Este artículo presenta un estudio sobre la construcción de la definición del concepto de regla de la cadena en el cálculo diferencial en el marco de estudiantes de primer año de ingeniería, en la Universidad Tecnológica de Sudáfrica. Se utiliza el enfoque APOS (Acción-Proceso-Objeto-Esquema) para explorar la comprensión conceptual que los estudiantes muestran en el aprendizaje de la regla de la cadena en cálculo. Se utilizaron fichas de trabajo estructuradas basadas en una instrucción diseñada para inducir la construcción de la comprensión conceptual de la regla de la cadena. Una parte de los estudiantes usaron utilizaron la técnica "directa" para diferenciar tareas complicadas, mientras que muy pocos de ellos utilizaron o bien el método de la conexión, o bien el enfoque de Leibniz, como técnicas de resolución. De esta manera se logró diferenciar cada una de las funciones simples en las funciones compuestas presentadas. Los estudiantes operaron tanto en las etapas inter, como intra, de la triada. Se encontró que incluso aquellos estudiantes con una comprensión no adecuada de las funciones compuestas, aplicaron la regla de la cadena correctamente.

  • English

    This article reports on a study which investigated first year university engineering students� construction of the definition of the concept of the chain rule in differential calculus at a University of Technology in South Africa. An APOS (Action-Process-Objects-Schema) approach was used to explore conceptual understanding displayed by students in learning the chain rule in calculus. Structured worksheets based on instruction designed to induce construction of conceptual understanding of the chain rule were used. A number of students used the straight form technique in differentiating complicated tasks while very few used either the link and Leibniz form techniques. In this manner differentiation of each function within the composite function was accomplished. Students either operated in the Inter- or Trans stages of the Triad. It was found that even students who had inadequate understanding of composition of functions, performed well in the application of the chain rule.

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