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The integration of undergraduate students’ informal and formal inferential reasoning

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Abstract

Since statistical inference is a probabilistic generalization about a population analyzed on the basis of a sample, inferential reasoning demands producing reasons (statistical and contextual) to substantiate and validate generalizations. To convey an understanding of students’ inferential reasoning, we present a proposal—based on Toulmin’s argumentation model—in which the production of statistical and contextual reasons serve as fundamental components of students’ inferential reasoning by providing supporting arguments that can be expressed as a sequence of statements. We analyze the inferential reasoning of university students asked to work in teams on an inferential activity in the context of environmental pollution. Results show that they integrated informal and formal methods to produce statistical reasons, complemented by contextual reasons to support their conclusions. Their reasoning model allowed us to identify (a) a potential transition from informal to formal inferential reasoning; and (b) ambiguity, or an absence of expressions of uncertainty, about generalizations regarding the population, possibly related to their confidence in using formal methods (e.g., hypothesis testing). We conclude that our proposal helps encourage and analyze students’ inferential reasoning. Future research will require clearer definitions of the characteristics of the argumentation model in the field of statistical inferential reasoning because arguments depend on their disciplinary context.

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Data availability

The authors declare that the data supporting the findings of this study are available within the article and its supplementary information provided in Tobías Lara’s (2019) reference.

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Acknowledgements

The authors acknowledge the translation support of the Writing Lab, Institute for the Future of Education, Monterrey Technology, Mexico.

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  1. Instituto Politécnico Nacional, CICATA-Legaria, Ciudad de México, México

    Ana Luisa Gómez-Blancarte

  2. Departamento de Ciencias, Tecnológico de Monterrey, Monterrey, Nuevo León, México

    María Guadalupe Tobías-Lara

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  1. Ana Luisa Gómez-Blancarte
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Correspondence to Ana Luisa Gómez-Blancarte.

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Gómez-Blancarte, A.L., Tobías-Lara, M.G. The integration of undergraduate students’ informal and formal inferential reasoning. Educ Stud Math 113, 251–269 (2023). https://doi.org/10.1007/s10649-022-10205-w

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