Algebra and Proof in High School: The Case of Algebraic Proof as Discovery.

• Autores: Mara V. Martínez
• Localización: REDIMAT, ISSN-e 2014-3621, Vol. 3, Nº. 1, 2014, págs. 30-53
• Idioma: inglés
• Títulos paralelos:
  • Álgebra y Prueba en la Secundaria: el Caso de la Demostración Algebráica como Descubrimiento.
• Enlaces
  • Texto completo (pdf)
• Resumen
  • English

    In the United States, students' learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies addressing how to integrate proof into other mathematical domains within the high school curriculum. In this paper, the author reports results from an interview at the end of a teaching experiment which was designed to integrate algebra and proof into the high school curriculum. Algebraic proof was envisioned as the vehicle that would provide high school students the opportunity to learn about proof in a context other than geometry. Results indicate that most students were able to produce an algebraic proof involving variables and a parameter and its multiples. In doing so, students experienced the discovery function of proof.

  • English

    En USA las experiencias de aprendizaje de los estudiantes sobre demostración se concentran generalmente en el dominio de la geometría de secundaria, con énfasis en su función de verificación. Sin embargo, se les da una concepción limitada de lo que significa. Es más, existe una falta de estudios en USA sobre cómo integrar el uso de las demostraciones en otros dominios de las matemáticas dentro del currículum de secundaria. En este artículo se presentan resultados de una entrevista realizada al final de un experimento de enseñanza que fue diseñado para integrar el álgebra y la demostración en el currículum de secundaria. La demostración algebraica se presenta como un vehículo que puede aportar la oportunidad de aprender sobre la demostración en otros contextos que no sean la geometría. Los resultados indican que la mayoría de los estudiantes son capaces de producir demostraciones algebraicas que involucran variables y parámetros. Haciendo esto, los estudiantes experimentan el descubrimiento de la función de las demostraciones.

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