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What I see is not quite the way it really is: students’ emergent reasoning about sampling variability

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Abstract

Currently, instruction pays little attention to the development of students’ sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and interview responses from four students to describe their emergent reasoning about sampling variability. Their reasoning is analyzed using our adaptations of a statistical inference framework and a mental processes framework. Our findings suggest that these students are beginning to develop understanding of sampling variability concepts from probabilistic and generalization perspectives and to articulate the evidence used from the data. We conjecture that these students’ understanding of sampling variability is aided by the development in instruction of the three mental processes of visualization, analysis, and verbal description.

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Acknowledgments

This research is supported in part by a grant from the Teaching and Learning Research Initiative (www.tlri.org). We would like to thank the reviewers for their challenging and insightful comments.

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Authors and Affiliations

  1. The University of Auckland, Auckland, New Zealand

    Maxine Pfannkuch, Pip Arnold & Chris J. Wild

  2. Cognition Education Limited, Auckland, New Zealand

    Pip Arnold

Authors
  1. Maxine Pfannkuch
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  2. Pip Arnold
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  3. Chris J. Wild
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Correspondence to Maxine Pfannkuch.

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This paper is submitted for the Special Issue of ESM on “statistical reasoning”

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Pfannkuch, M., Arnold, P. & Wild, C.J. What I see is not quite the way it really is: students’ emergent reasoning about sampling variability. Educ Stud Math 88, 343–360 (2015). https://doi.org/10.1007/s10649-014-9539-1

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