Chi-square Reference Meanings: a Historical-epistemological Overview

Jesus Guadalupe Lugo-Armenta; Luis Roberto Pino-Fan; Blanca Rosa Ruiz Hernandez

doi:10.33532/revemop.e202108

Jesus Guadalupe Lugo-Armenta Universidad de Los Lagos http://orcid.org/0000-0001-6679-5115
Luis Roberto Pino-Fan Universidad de Los Lagos https://orcid.org/0000-0003-4060-7408
Blanca Rosa Ruiz Hernandez Tecnológico de Monterrey http://orcid.org/0000-0003-0157-3866

DOI: https://doi.org/10.33532/revemop.e202108

Keywords: Chi-square, history and epistemology, inferential reasoning, meanings, statistics education

Abstract

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.

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Author Biographies

Jesus Guadalupe Lugo-Armenta, Universidad de Los Lagos

Doutorando em Educación Matemática pela Universidad de Los Lagos, campus Osorno. Osorno, Los Lagos, Chile.

Luis Roberto Pino-Fan, Universidad de Los Lagos

Doutor em Didáctica de la Matemática pela Universidad de Granda. Professor da Universidad de Los Lagos, Osorno, Los Lagos, Chile.

Blanca Rosa Ruiz Hernandez, Tecnológico de Monterrey

Doutora em Didáctica de la Matemática pela Universidad de Granda. Professora do Tecnológico de Monterrey, Monterrey, Nuevo León, México.

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