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Can I Bring My Calculator to the Exam? Some Reflections on the Abstraction Level of Computer Algebra Systems

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2022-12-21
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The author began working with computer algebra systems (CAS) in the 80s to perform effective computations for his Ph.D Thesis in algebra. He thought at that moment that there would be an explosion in the use of CAS for research and teaching (at all levels of education). Surprisingly, its use in secondary education is still scarce. This article details some personal reflections on elementary mathematics questions (from both the mathematical and the computational points of view) and proposes a classification of such questions, illustrated with several examples. It is focused on some of the present impressive capabilities of CAS, underlining their abstraction levels in some eye-catching examples. The article is mainly aimed at mathematics teachers who are not experts in CA. Nevertheless, it may also be of interest to CAS experts, as it includes reflections on a topic not usually treated: the abstraction level achieved by CAS and its impact in teaching and assessment.
[El autor empezó a trabajar con sistemas de álgebra computacional (CAS) en los años 80 para realizar cálculos eficaces para su tesis doctoral en álgebra. En aquel momento pensó que se produciría una explosión en el uso de los CAS para la investigación y la enseñanza (en todos los niveles educativos). Sorprendentemente, su uso en la enseñanza secundaria sigue siendo escaso. Este artículo detalla algunas reflexiones personales sobre las preguntas matemáticas elementales (tanto desde el punto de vista matemático como computacional) y propone una clasificación de dichas preguntas, ilustrada con varios ejemplos. Se centra en algunas de las impresionantes capacidades actuales de los CAS, subrayando sus niveles de abstracción en algunos ejemplos llamativos. El artículo se dirige principalmente a profesores de matemáticas que no son expertos en AC. No obstante, también puede ser de interés para los expertos en CAS, ya que incluye reflexiones sobre un tema que no suele tratarse: el nivel de abstracción que alcanzan los CAS y su repercusión en la enseñanza y la evaluación].
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CRUE-CSIC (Acuerdos Transformativos 2022)
UCM subjects
Lenguajes de programación , Álgebra , Enseñanza de las Matemáticas
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1203.23 Lenguajes de Programación , 1201 Álgebra
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https://hdl.handle.net/20.500.14352/72832
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