Chapter 4
Students’ Aggregate Reasoning
with Covariation
Keren Aridor and Dani Ben-Zvi
Abstract Helping students interpret and evaluate the relations between two vari-
ables 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
4.1 Introduction
The purpose of this chapter is to provide an initial scheme for understanding young
students’ emergent articulations of aggregate reasoning with covariation (ARwC) in
the context of informal statistical inference from growing data samples. Handling data
from an aggregate point of view is a core aspect of statistical reasoning (Hancock et al.
1992). Predicting properties of the aggregate is the essential aspect of data analysis
and statistical inference. To achieve this goal, one should develop a notion of data as
an organizing structure that enables seeing the data as a whole (Bakker and Hoffmann
K. Aridor (B ) · D. Ben-Zvi
Faculty of Education, The University of Haifa, Haifa, Israel
e-mail: kerenaridor@gmail.com
D. Ben-Zvi
e-mail: dbenzvi@univ.haifa.ac.il
© Springer Nature Switzerland AG 2019
G. Burrill and D. Ben-Zvi (eds.), Topics and Trends in Current Statistics Education
Research, ICME-13 Monographs, https://doi.org/10.1007/978-3-030-03472-6_4
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