Epistemic Configurations and Holistic Meaning of Binomial Distribution

Nicolás Alonso Fernández Coronado, Jaime I. García-García, Elizabeth H. Arredondo and Ismael Andrés Araya Naveas
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Nicolás Alonso Fernández Coronado: Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno 5290000, Chile
Jaime I. García-García: Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno 5290000, Chile
Elizabeth H. Arredondo: Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno 5290000, Chile
Ismael Andrés Araya Naveas: Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno 5290000, Chile

Mathematics, 2022, vol. 10, issue 10, 1-23

Abstract: The competencies that today’s citizen must possess have led to a transformation of the teaching of probability, which has been repositioned on the school curriculum from an algorithmic view to a practical one based on the understanding of the concepts and their application in daily life. In this task, the understanding of the binomial distribution is essential as it allows the analysis of discrete data, the modeling of random situations, and the learning of other notions. However, weaknesses are identified in teachers and students with respect to the binomial distribution attributed to the lack of knowledge of its origin and meaning throughout history. For this reason, our work consists of the identification of its partial meanings and essential components as well as its relationships from a historical epistemological study and its analysis, based on the notions of the Ontosemiotic Approach (OSA) to Mathematical Knowledge and Instruction and the specialized literature on statistics and probability. As a result of our work, we present a reconstruction of the holistic meaning of the binomial distribution from the elements that compose it, which are essential for didactic purposes such as the identification and resolution of learning conflicts, the design or evaluation criteria, and teacher education.

Keywords: binomial distribution; primary objects; probabilistic culture; partial meanings; holistic meaning; epistemology; configurations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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