Epistemic Configurations and Holistic Meaning of Binomial Distribution

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.