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Fostering students’ informal quantitative estimations of uncertainty through statistical modeling

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Abstract

Estimating and accounting for statistical uncertainty have become essential in today’s information age, and crucial for cultivating a sound decision making citizenry. Engaging with statistical uncertainty early on can support the gradual development of uncertainty-related considerations that are often challenging to foster at any age. Statistical modeling is a promising introductory practice given the key role played by statistical uncertainty. However, the probabilistic language and tools utilized to formally account for statistical uncertainty are typically seen as insurmountable hurdles to the meaningful engagement of elementary school students. The goal of this article is to demonstrate the pedagogical potential of a particular learning sequence based on an informal adaptation of statistical modeling, integrating student-led real-world investigations and statistical modeling activities. An instrumental case study of a pair of 12-year-old students’ process illustrates how young learners construct informal accounts of statistical uncertainty as they engage in these activities. The discussion centers on the aspects of the learning sequence and guidance that supported their progression.

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Notes

  1. “Trustworthy” was a term students invented to depict a sample they believed to be "similar" to the population they were to formulate inferences about. The researchers utilized the student-invented term when discussing ideas related to sample's representativeness with the students.

  2. The Sampler allows students to design and run probability simulations and visually represent the results of the outcome over many samples.

  3. Pseudonyms.

  4. When executing a complex computation in TinkerPlots, the screen freezes for about a minute.

  5. We utilize square brackets to provide information about the students’ actions, clarifications interpreted based on their gestures (e.g., pointing towards something) or additional evidence from previous segments. All interpretations were triangulated as explained in the Methods Section.

  6. This was the only instance in the 2016 learning sequence in which a center of “18 point something” was found.

  7. By “dragging” a case in TinkerPlots a scatterplot can be turned into a plot with a finite set of bins.

  8. Note that anthropomorphic descriptions such as this express somewhat naïve views of sampling and the role of simulations; However this discussion is beyond the scope of this article.

  9. Erez previously used the term “reasonable” to either differentiate between outliers and reasonable cases, or judge the reasonableness of data according to his contextual knowledge. However, this was the first utilization of the term during the probabilistic inquiry in the second cycle.

  10. As opposed to a formal confidence interval, a range of estimates for an unknown real-world parameter, calculated from a single real-world sample.

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Acknowledgements

This work was supported by the University of Haifa, the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation Grant 1716/12.

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

    Michal Dvir & Dani Ben-Zvi

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  1. Michal Dvir
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  2. Dani Ben-Zvi
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Correspondence to Michal Dvir.

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Dvir, M., Ben-Zvi, D. Fostering students’ informal quantitative estimations of uncertainty through statistical modeling. Instr Sci 51, 423–450 (2023). https://doi.org/10.1007/s11251-023-09622-y

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