The present article shows a historical-epistemological study on the Chi-square statistic. In which theoretical-methodological notions from the Onto-Semiotic Approach (OSA) of mathematical cognition and instruction were used to identify four problems that have been key to the evolution of the Chi-square statistic: the Goodness-of-fit-test, the test of independence, the test of homogeneity and distribution. Furthermore, various meanings of the Chi-square statistic were recognized in the mathematical-statistical practices that are used to solve each of those problems. These meanings could help to establish epistemic criteria that allow, on the one hand, to propose progressive levels of inferential reasoning for the statistic (from informal to formal); and on the other hand, to design tasks oriented to promote the understanding of the diverse meanings of the Chi-square.

Resumen En este artículo presentamos una propuesta de niveles progresivos, de lo informal a lo formal, de razonamiento inferencial para el estadístico t-Student, a partir de criterios epistémicos identificados con un estudio de tipo histórico-epistemológico sobre este estadístico y de la investigación desarrollada sobre razonamiento inferencial. Para ello, utilizamos algunas nociones teórico-metodológicas introducidas por el Enfoque Onto-Semiótico del conocimiento y la instrucción matemáticos (EOS), las cuales permitieron tanto identificar y caracterizar diversos significados conferidos al estadístico t-Student, a lo largo de su evolución y desarrollo, como presentar una perspectiva integral de lo que se considera razonamiento inferencial. Los atributos matemáticos de los diversos significados del estadístico t-Student se encuentran fuertemente vinculados a los indicadores de los distintos niveles de razonamiento aquí expuestos. Además, cada nivel se encuentra asociado a un razonamiento inferencial informal, pre-formal o formal. La propuesta de niveles de Razonamiento Inferencial para el estadístico t-Student y sus indicadores, se prevén útiles para el diseño de actividades que promuevan, gradualmente, un razonamiento inferencial formal sobre la base del razonamiento inferencial informal, sobre este estadístico.

The pandemic and its disruption of social dynamics, including school dynamics, necessitates a review of both the proposals for education in situations of confinement and the research that must be carried out to account for exceptional educational situations. It is likely that this pandemic is only the first circumstance that has highlighted the need to investigate more decisively areas that have not been previously considered or have been put aside. This document presents the case of three Latin American countries, Mexico, Colombia, and Chile, in relation to educational difficulties generated by the pandemic, with respect to regional actions on the educational problems that have been revealed, and proposes regional research agendas for the Mathematics Education research community.

The COVID-19 pandemic generated a new scenario in education, where technological resources mediate teaching and learning processes. This paper presents the development of a virtual teacher training experience aimed at promoting inferential reasoning in practicing and prospective mathematics teachers using inference problems on the Chi-square statistic. The objective of this article is to assess the implemented or intended institutional meanings and the degree of availability and adequacy of the material and temporal resources necessary for the development of the training experience. For this purpose, we use theoretical and methodological notions introduced by the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), among which are the notions of practice and suitability criteria. The participants of this experience were divided into three groups; one of them was comprised of practicing teachers and the other two of prospective teachers. The intervention used different virtual modalities that enabled the development of the participants’ inferential reasoning in a similar way.

Working with statistical data from real contexts has become fundamental in school-level statistics, because it enables the development of statistical reasoning. In this regard, the notion of the random variable is fundamental to statistical data analysis. Thus, the aim of this research was to characterise the meanings of the concept of the random variable that are promoted in the Chilean mathematics curriculum for secondary education. To achieve this, we examined the representativeness of the meanings of the random variable intended by the curriculum in relation to the meanings of reference for this concept, using theoretical and methodological notions from the onto-semiotic approach. The findings show that the meanings of reference were not fully represented in the textbooks and the national curriculum, and that the most promoted meaning was that of the random variable as a variable of interest. Regarding the types of representation, it was observed that the graphical and tabular representations were neglected. Lastly, it was noticed that definitions of the concept of variable, its classifications, and differences were omitted almost entirely from the textbooks.