Edward S. Mooney

A Framework for Characterizing Children's Statistical Thinking.

Based on a review of research and a cognitive development model (Biggs & Collis, 1991), we formulated a framework for characterizing elementary childrens statistical thinking and refined it through a validation process. The 4 constructs in this framework were describing, organizing, representing, and analyzing and interpreting data. For each construct, we hypothesized 4 thinking levels, which represent a continuum from idiosyncratic to analytic reasoning. We developed statistical thinking descriptors for each level and construct and used these to design an interview protocol. We refined and validated the framework using data from protocols of 20 target students in Grades 1 through 5. Results of the study confirm that childrens statistical thinking can be described according to the 4 framework levels and that the framework provides a coherent picture of childrens thinking, in that 80% of them exhibited thinking that was stable on at least 3 constructs. The framework contributes domain-specific theory for characterizing childrens statistical thinking and for planning instruction in data handling.

A Practitional Perspective on Probabilistic Thinking Models and Frameworks

Our goal in this chapter is to showcase the various theories and cognitive models that have been developed by mathematics and statistics educators regarding the development of probabilistic thinking from a “practitional” perspective. This perspective juxtaposes the work of mathematics and statistics educators with research on probability from the field of psychology. Next, we synthesize theories and models that have been developed for specific probability concepts and processes. These models suggest different levels or patterns of growth in probabilistic reasoning. Finally, we examine the role these models have had on instruction and curriculum recommendations.

Children's Representation and Organisation of Data

This study investigated how children organised and represented data and also examined relationships between their organisation and representation of data. Two protocols, one involving categorical data and the other involving numerical data, were used to interview 15 students, 3 from each of Grades 1 through 5. Although there were differences between Grade 1 students and the rest, the study suggested that numerical data was significantly harder for children to organise and represent than categorical data. Children beyond Grade 1 could make connections between organising and representing data for categorical data but their connections for numerical data were more tenuous. The process of reorganising numerical data into frequencies was not intuitive for the children in this study but they showed greater readiness in recognising and interpreting data that had already been reorganised as a frequency representation. Given this latter result, a pedagogical approach that asks students to make links between raw data and a frequency representation of it may prepare students to create and construct their own frequency representations.