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Primary school children’s strategies in solving contingency table problems: the role of intuition and inhibition

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Abstract

Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school children’s strategy use, and to explore the extent to which psychological theories of intuition and inhibition help better understand the cognitive mechanisms underlying these strategies. In an initial study, we investigated 231 second-graders’ performance on various types of contingency table problems in a paper-and-pencil test. In a second study, we asked 45 second- and fourth-graders to give reasons for their decisions on contingency table problems in an interview situation. Results of both studies suggest that ignoring relevant information and referring to additive rather than multiplicative relationships between cell frequencies were among the children’s primary strategies. These strategies can be explained by intuition, which the children were often not able to inhibit. We discuss the implications of this interpretation from a mathematics education perspective.

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Notes

  1. An alternative measure is the \(\chi^{2}\)-test, which cannot be used, however, for small sample sizes.

  2. There are several other normative measures of the association of two binary variables, such as the odds ratio OR, or the contingency coefficient C.

  3. Non-parametric tests were used because the data did not follow a normal distribution.

  4. The transcripts were translated from the German original by the authors.

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Authors and Affiliations

  1. Heinz Nixdorf-Stiftungslehrstuhl für Didaktik der Mathematik, TUM School of Education, Technische Universität München, Munich, Germany

    Andreas Obersteiner, Matthias Bernhard & Kristina Reiss

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  1. Andreas Obersteiner
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  2. Matthias Bernhard
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  3. Kristina Reiss
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Correspondence to Andreas Obersteiner.

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Obersteiner, A., Bernhard, M. & Reiss, K. Primary school children’s strategies in solving contingency table problems: the role of intuition and inhibition. ZDM Mathematics Education 47, 825–836 (2015). https://doi.org/10.1007/s11858-015-0681-8

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