What students can learn from Fibonacci´s error in solving “The lion in the pit” problem

Lo que pueden aprender los estudiantes a partir del error de Fibonacci al resolver el problema “El león en el pozo”

O que os alunos podem aprender com o erro de Fibonacci ao resolver o problema “O leão no poco”

Palabras clave: Fibonacci’s error, using history of mathematics in classroom, learning from errors, problem-solving (en_US)
Palabras clave: el error de Fibonacci, uso de la historia de las matemáticas en las aulas, aprendizaje a partir de errores, resolución de problemas (es_ES)
Palabras clave: o erro de Fibonacci, uso da história da matemática em sala de aula, aprendendo com os erros, solução de problemas (pt_BR)

Resumen (en_US)

This initial study presents the results of the classroom implementation of a learning sequence derived from Fibonacci’s error in solving ‘The lion in the pit’ problem. The study was carried out with 35 physics students in a general first-semester course ‘Development of complex-thinking skills’. The learning sequence was implemented as a paper-and-pencil activity in personal and group modes. The most important results are the following: (a) Students were able to provide an acceptable procedure about how Fibonacci might get the wrong answer, (b) students can argue why that answer is wrong, (c) some students’ solutions presented good conceptual and procedural clarity, frequently missed in historic literature, and (d) students grasped the importance of knowing about errors made by famous mathematicians in two connected aspects: mathematics is a human activity prone to errors and, consequently, fear of errors shouldn’t be an obstacle in learning of school mathematics.

Resumen (es_ES)

Este estudio presenta los resultados de la implementación en el aula de una secuencia de aprendizaje derivada del error de Fibonacci al resolver el problema "El león en el pozo". El estudio se realizó con 35 estudiantes de física en un curso general de primer semestre titulado "Desarrollo de habilidades de pensamiento complejo". La secuencia de aprendizaje se implementó como una actividad de lápiz y papel en modos personales y grupales. Los resultados más importantes son los siguientes: (a) Los estudiantes pudieron proporcionar un procedimiento aceptable sobre cómo Fibonacci podría obtener la respuesta incorrecta, (b) los estudiantes pueden argumentar por qué esa respuesta es incorrecta, (c) las soluciones de algunos estudiantes presentaron un buen concepto y claridad del procedimiento, frecuentemente omitida en la literatura histórica, y (d) los estudiantes comprendieron la importancia de conocer los errores cometidos por matemáticos famosos en dos aspectos relacionados: las matemáticas son una actividad humana propensa a errores y, en consecuencia, el miedo a los errores no debe ser un obstáculo para el aprendizaje de las matemáticas escolares.

Resumen (pt_BR)

Este estudo apresenta os resultados da implementação em sala de aula de uma sequência de aprendizado derivada do erro de Fibonacci na resolução do problema "O leão no poço". O estudo foi realizado com 35 estudantes de física numa disciplina geral do primeiro semestre nomeada "Desenvolvimento de habilidades complexas de pensamento". A sequência de aprendizado foi implementada como uma atividade de lápis e papel nos modos pessoal e coletivo. Os resultados mais importantes são os seguintes: (a) Os alunos foram capazes de fornecer um procedimento aceitável sobre como Fibonacci poderia chegar na resposta errada; (b) os alunos podem argumentar por que essa resposta está errada; (c) as soluções de alguns alunos apresentam um bom conceito e clareza do procedimento, freqüentemente omitido na literatura histórica; e (d) os alunos entenderam a importância de conhecer os erros cometidos por matemáticos famosos em dois aspectos relacionados: a matemática é uma atividade humana propensa a erros e, consequentemente, o medo de erros não deve ser um obstáculo para o aprendizado da matemática na escola.


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Biografía del autor/a

Josip Slisko, Benemérita Universidad Autónoma de Puebla, México

Ph.D. in philosophy of physics and is a full professor of the Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, México. He is member of the National System of Researchers (level II). He is interested in students’ construction of explanatory and predictive models of physical phenomena, and their struggles to overcome ‘fast thinking’ in solving mathematical puzzles. Since 1993, he has been organizing the international workshop ‘New Trends in Physics Teaching’.


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Cómo citar
Slisko, J. (2020). Lo que pueden aprender los estudiantes a partir del error de Fibonacci al resolver el problema “El león en el pozo”. Góndola, Enseñanza Y Aprendizaje De Las Ciencias (Bogotá, Colombia), 15(2). https://doi.org/10.14483/23464712.16041