# Statistical modeling to promote students’ aggregate reasoning with sample and sampling

## Abstract

While aggregate reasoning is a core aspect of statistical reasoning, its development is a key challenge in statistics education. In this study we examine how students’ aggregate reasoning with samples and sampling (ARWSS) can emerge in the context of statistical modeling activities of real phenomena. We present a case study on the emergent ARWSS of two pairs of sixth graders (age 11–12) involved in statistical data analysis and informal inference utilizing TinkerPlots. The students’ growing understandings of various statistical concepts is described and five perceptions the students expressed are identified. We discuss the contribution of modeling to these progressions followed by conclusions and limitations of these results. While idiosyncratic, the insights contribute to the understanding of students’ aggregate reasoning with data and models, with regards to samples and sampling.

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## Notes

1. For a detailed description of the 2015 iteration, see the chapter by Aridor and Ben-Zvi (2018).

2. The three schools were the students’ primary school, another primary school from the same area and a middle school which is also the future school of these two primary schools.

3. The sample data in the second and third cycles were collected randomly using a raffle planned by the students. For n = 60, data were collected from 15 grade 2, 4 and 6 students from their school and 15 eighth graders from their future middle school; For n = 105, an additional 15 grade 2, 4 and 6 students from their school were involved.

4. For a detailed description of the 2016 activity sequence, please see the Connections Website: http://connections.edtech.haifa.ac.il/Research/connections2016LT.

5. Data were presented to and analyzed by the Connections research team, consisting of one Professor, one Doctor, two PhD students and three M.A. students. The authors of this paper are part of this team.

6. Each pair sampled from a similar population of strings. However, the strings̓ measurements were different as the strings were easily stretched.

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## Acknowledgements

This research was supported by the University of Haifa and the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation Grant 1716/12. We deeply thank the Connections research team and the anonymous reviewers of earlier versions of this manuscript.

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Correspondence to Keren Aridor.

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Aridor, K., Ben-Zvi, D. Statistical modeling to promote students’ aggregate reasoning with sample and sampling. ZDM Mathematics Education 50, 1165–1181 (2018). https://doi.org/10.1007/s11858-018-0994-5

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• DOI: https://doi.org/10.1007/s11858-018-0994-5

### Keywords

• Exploratory data analysis
• Informal statistical inference
• Aggregate statistical reasoning
• Statistical model and modeling
• Sample and sampling