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# The role of model comparison in young learners’ reasoning with statistical models and modeling

## Abstract

The goal of this study is to explore the role of model comparison, which is a key activity of young learners’ informal reasoning, with statistical models and modeling in the context of informal statistical inference. We suggest a framework to describe this reasoning (the RISM framework), and offer an illustrative case study of two-sixth graders showcasing its utility. In particular, we illustrate the benefit of untangling the informal modeling process into three separate, though not independent, modeling processes: modeling a conjecture, modeling data, and comparing them by means of a comparison model. This case study shows the possible progression of a comparison model, and its potential role as a catalyst for the development of the other two modeling processes. Finally, an expansion of our initial framework is discussed, highlighting the centrality of model comparisons.

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## Notes

1. A demonstration of the use of our suggested framework can be seen in the Connections Website, providing a brief summary of several different snapshots of the modeling process described in the findings of this paper: http://connections.edtech.haifa.ac.il/Research/michal-dvir-research.

2. The TinkerPlots Sampler allows students to design and run probability simulations, subsequently plotting the results to give a visual representation of the outcome over many samples. The Sampler provides an opportunity to expand the focus on data and statistics and incorporate probability.

3. A detailed description of the 2016 activity sequence can be seen in the Connections Website: http://connections.edtech.haifa.ac.il/Research/connections-2016.

4. The Divider tool divides a fully-separated numeric variable graph into sections. It is easy to change the width of the intervals and add counts or percentages to show the number, or proportion of cases, in each section.

5. This interpretation has been triangulated: Multiple interpretations were considered, as well as the entirety of the data regarding Erez’ typical articulations.

6. The “hide case” function in TinkerPlots allows omitting one or more cases from the data representation.

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## Acknowledgements

We thank the University of Haifa, the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation Grant 1716/12 for supporting this research, as well as the Connections research team.

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Correspondence to Michal Dvir.

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Dvir, M., Ben-Zvi, D. The role of model comparison in young learners’ reasoning with statistical models and modeling. ZDM Mathematics Education 50, 1183–1196 (2018). https://doi.org/10.1007/s11858-018-0987-4

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• DOI: https://doi.org/10.1007/s11858-018-0987-4

### Keywords

• Statistical model
• Statistical modeling
• Model comparison
• Informal statistical inference