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Problemas de Fermi en educación matemática: conceptualizaciones, caracterizaciones y usos

  • Autores: Carlos Segura
  • Localización: Revista de Educación Matemática (RevEM), ISSN-e 1852-2890, ISSN 0326-8780, Vol. 41, Nº. 1, 2026, págs. 53-82
  • Idioma: español
  • DOI: 10.33044/revem.52596
  • Títulos paralelos:
    • Fermi problems in mathematics education: conceptualisations, characterisations, and uses
  • Enlaces
  • Resumen
    • español

      Este artículo es una extensión de la conferencia plenaria impartida en el III Encuentro Conjunto RSME–UMA sobre problemas de Fermi. Estos problemas plantean situaciones del mundo real sin datos explícitos y exigen estimar una magnitud —a menudo grande— que no puede determinarse directamente, sino mediante suposiciones plausibles y una cadena de estimaciones parciales y cálculos debidamente justificados. Los problemas de Fermi son particularmente relevantes para la educación matemática, pues resultan idóneos para introducir la modelización en aulas de Educación Primaria y Secundaria. En este trabajo se presentan los conceptos nucleares que los sustentan, incluidos los procesos de resolución y los criterios de rendimiento. Asimismo, se caracterizan los problemas de Fermi atendiendo a distintas facetas, como el tipo de conocimiento previo requerido para su solución, sus contextos y su articulación en secuencias de tareas. Por último, se discuten usos didácticos clave —por ejemplo, para fomentar la flexibilidad estratégica— y se explora el papel de diferentes entornos de resolución, como el trabajo en exteriores y la interacción con la inteligencia artificial. En conjunto, el artículo configura un marco que guía investigacionesen cognición, diseño e implementación de problemas de Fermi, y establece las bases para su transferencia al aula.

    • English

      This article is an extension of the plenary lecture delivered at the III Joint RSME–UMA Meeting on Fermi problems. These problems pose real-world situations without explicit data and require estimating a quantity—often a large one—that cannot be determined directly, but rather through plausible assumptions and a chain of partial estimates and well-justified calculations. Fermi problems are particularly relevant to mathematics education, as they are well-suited to introducing modelling in primary and secondary classrooms. This paper presents the core concepts that underpin them, including solution processes and performance criteria. It also characterises Fermi problems along several facets, such as the type of prior knowledge required for their solution, the contexts in which they are posed, and their articulation into sequences of tasks. Finally, it discusses key instructional uses—for example, to foster strategic flexibility—and explores the role of different problem-solving settings, such as outdoor work and interaction with artificial intelligence. Taken together, the article sets out a framework that guides research on cognition, design, and implementation of Fermi problems, and lays the groundwork for their transfer to the classroom.

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