Stochastic sense in the primary education curriculum system in Peru
DOI:
https://doi.org/10.5281/zenodo.17316832Keywords:
primary education, mathematical praxeology, stochastic meaning, didactic transpositionAbstract
Stochastic reasoning, defined as the ability to reason in the face of uncertainty and variability, is a key component of current mathematics education, especially in primary education. Its incorporation into the Peruvian curriculum responds to the need to prepare students for decision-making in everyday situations involving uncertainty. This study aimed to analyze the mathematical and didactic organization of stochastic reasoning in fifth- and sixth-grade primary education textbooks, as well as to identify the transformations of stochastic knowledge in didactic transposition. A mixed approach, predominantly qualitative, was employed, using the praxeological model to identify the tasks, techniques, technologies, and theories present in official textbooks. Additionally, a descriptive quantitative analysis was conducted on the distribution and complexity of the tasks. The sample included 28 probability-related tasks, mostly focused on qualitative comparisons and of low cognitive demand. The results showed a fragmentation of the stochastic meaning, with a predominance of structured tasks and little theoretical foundation to support teaching practices. Furthermore, limitations in authenticity, contextual diversity, and conceptual development were evident, as the tasks focused on personal contexts without addressing advanced concepts such as statistical inference or stochastic modeling. In conclusion, the didactic organization of the stochastic meaning is partial and insufficient. Therefore, its revision is recommended to include authentic tasks, a greater diversity of contexts, and theoretical coherence that favor a more comprehensive development of probabilistic thinking in primary education.
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Alsina, A., & Bosch, E. (2023). Estatísticas e probabilidade no ensino pré-primário e primário: dez manipuladores essenciais para desenvolver o sentido estocástico. TANGRAM - Revista de Educação Matemática, 6(3), 23–59. https://doi.org/10.30612/tangram.v6i3.17587
Batanero, C. (2001). Ideas estocásticas fundamentales: ¿Qué contenidos se debe enseñar en la clase de probabilidad? Universidad de Granada. https://www.ugr.es/~batanero/pages/ARTICULOS/didacticaestadistica.pdf
Bayés, A. S., & Vargas, M. L. (2025). El papel del sentido estocástico en la educación en la ciencia de datos. Revista de Educación Estadística, 4, 1-25. https://doi.org/10.29035/redes.4.1.3
Borovcnik, M., & Kapadia, R. (2014). A historical and philosophical perspective on probability. En E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking (pp. 7-34). Springer. https://doi.org/10.1007/978-94-007-7155-0_2
Bosch, M., & Gascón, J. (2009). Aportaciones de la teoría antropológica de lo didáctico a la formación del profesorado de matemáticas de secundaria. En M. J. González & M. T. González (Eds.), Investigación en educación matemática XIII (pp. 89-113). SEIEM. https://funes.uniandes.edu.co/funes-documentos/aportaciones-de-la-teoria-antropologica-de-lo-didactico-a-la-formacion-del-profesorado-de-matematicas-de-secundaria/
Chevallard, Y. (1985). La transposition didactique: Du savoir savant au savoir enseigné. La Pensée Sauvage.
Chevallard, Y. (1998). La transposición didáctica: Del saber sabio al saber enseñado. AIQUE.
Chevallard, Y. (1999). L’écologie des organisations mathématiques: Entre description et conception. Centre de recherche sur l’enseignement des mathématiques.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. American Statistical Association.
Marion Montoya, M. G. (2024). Prácticas evaluativas de los docentes de 5° y 6° de primaria del área de inglés de una institución educativa privada de Lima [Tesis de maestría, Pontificia Universidad Católica del Perú]. Repositorio institucional. http://hdl.handle.net/20.500.12404/28266
Ministerio de Educación. (2016a). Currículo nacional de la educación básica. MINEDU.
Ministerio de Educación. (2016b). Programa curricular de educación primaria. MINEDU.
Organization for Economic Co-operation and Development (OECD). (2018). PISA 2018 assessment and analytical framework. OECD Publishing.
Piaget, J. (1951). Principal factors determining intellectual evolution from childhood to adult life. En Organization and pathology of thought: Selected sources (pp. 154-175). Columbia University Press. https://www.degruyter.com/document/doi/10.7312/rapa92214-009/html
Rico, L., Lupiáñez, J. L., & Molina, M. (2013). Análisis didáctico en educación matemática: Metodología de investigación, formación de profesores e innovación curricular. Comares.
Rico Romero, L., & Moreno Verdejo, A. J. (2016). Elementos de didáctica de la matemática para el profesor de secundaria. Pirámide.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.
Sowder, J. T. (1992). Making sense of numbers in school mathematics. En G. Leinhardt, R. Putman & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 1-51). Lawrence Erlbaum Associates.
Torres-Roberto, M. A. (2024). Evaluación formativa continua en la enseñanza y aprendizaje del cálculo: Mejorando el rendimiento académico en estudiantes de educación profesional. Journal of Economic and Social Science Research, 4(2), 93-113. https://doi.org/10.55813/gaea/jessr/v4/n2/104
Ureña-Villamizar, Y. C., Henao-Gómez, M. A., Vargas-Velásquez, O. A., Ramírez-Ramírez, J. R., & Fernández-Nieto, E. L. (2024). Ma-Tecn: Modelo innovador para fomentar competencias lógico-matemáticas. AiBi Revista de Investigación, Administración e Ingeniería, 12(2), 63-74. https://doi.org/10.15649/2346030X.3781
Wiggins, G. (2012). Creating authentic performance tasks and projects: Tools for meaningful learning and assessment. Pearson.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
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