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International Handbook of Research in Statistics Education pp 139–192Cite as

Reasoning About Data

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Part of the book series: Springer International Handbooks of Education ((SIHE))

Abstract

Many decisions in politics, economics, and society are based on data and statistics. In order to participate as a responsible citizen, it is essential to have a solid grounding in reasoning about data. Reasoning about data is a fundamental human activity; its components can be found in nearly every profession and in most school curricula in the world. This chapter reviews past and recent research on reasoning about data across all ages of learners from primary school to adults. Specifically in this chapter, the term reasoning about data is defined, the implementation of reasoning about data in the curricula of different countries is investigated, and research studies of learner reasoning about distribution, variation, comparing groups, and association, which are fundamental concepts when reasoning about data, are reviewed. The research review presented includes references to existing frameworks and taxonomies that can assess learner reasoning in regard to these concepts and discusses the influence of digital tools to enhance learner statistical reasoning. Finally, some insights for future directions in research about reasoning about data are provided.

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Notes

  1. 1.

    There is also a GAISE report for the statistical education of college students.

  2. 2.

    Mean absolute deviation, or MAD, is the (sum of the distances of all values from the mean )÷ (number of values). In analysis and measure theory, it is the L1 norm.

  3. 3.

    For a more comprehensive categorization of statistical questions, see Biehler (2001, p. 98) and also Arnold (2013).

  4. 4.

    Summary statistics refer to measures of central tendency in this case.

  5. 5.

    The development and the implementation of these minitools were the starting point to develop the educational software TinkerPlots , which includes the features of the minitools.

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Authors and Affiliations

  1. Institute of Mathematics, University of Paderborn, Paderborn, Germany

    Rolf Biehler & Daniel Frischemeier

  2. SiMERR National Research Centre, University of New England, Armidale, NSW, Australia

    Chris Reading

  3. The Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, USA

    J. Michael Shaughnessy

Authors
  1. Rolf Biehler
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  2. Daniel Frischemeier
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  3. Chris Reading
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  4. J. Michael Shaughnessy
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Correspondence to Rolf Biehler .

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Editors and Affiliations

  1. Faculty of Education, The University of Haifa, Haifa, Israel

    Dani Ben-Zvi

  2. School of Education, University of Queensland, St Lucia, Queensland, Australia

    Katie Makar

  3. Department of Educational Psychology, The University of Minnesota, Minneapolis, Minnesota, USA

    Joan Garfield

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Biehler, R., Frischemeier, D., Reading, C., Shaughnessy, J.M. (2018). Reasoning About Data. In: Ben-Zvi, D., Makar, K., Garfield, J. (eds) International Handbook of Research in Statistics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-319-66195-7_5

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