# Students’ Aggregate Reasoning with Covariation

## Abstract

Helping students interpret and evaluate the relations between two variables is challenging. This chapter examines how students’ aggregate reasoning with covariation (ARwC) emerged while they modeled a real phenomenon and drew informal statistical inferences in an inquiry-based learning environment using TinkerPlots^{TM}. We focus in this illustrative case study on the emergent ARwC of two fifth-graders (aged 11) involved in statistical data analysis and modelling activities and in growing samples investigations. We elucidate four aspects of the students’ articulations of ARwC as they explored the relations between two variables in a small real sample and constructed and improved a model of the predicted relations in the population. We finally discuss implications and limitations of the results. This article contributes to the study of young students’ aggregate reasoning and the role of models in developing such reasoning.

## Keywords

Aggregate reasoning Exploratory data analysis Growing samples Informal statistical inference Reasoning with covariation Statistical modelling## Notes

### 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 Cool-Connections research group who participated in the Connections project 2015, and in data analysis sessions of this research.

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