Learning to reason about distribution

TLDR: The development of reasoning about distribution in seventh-grade classes is described in three stages as students reason about different representations, and it is shown how specially designed software tools, students’ created graphs, and prediction tasks supported the learning of different aspects of distribution.

Abstract: The purpose of this chapter is to explore how informal reasoning about distribution can be developed in a technological learning environment. The development of reasoning about distribution in seventh-grade classes is described in three stages as students reason about different representations. It is shown how specially designed software tools, students’ created graphs, and prediction tasks supported the learning of different aspects of distribution. In this process, several students came to reason about the shape of a distribution using the term bump along with statistical notions such as outliers and sample size. This type of research, referred to as “design research,” was inspired by that of Cobb, Gravemeijer, McClain, and colleagues (see Chapter 16). After exploratory interviews and a small field test, we conducted teaching experiments of 12 to 15 lessons in 4 seventh-grade classes in the Netherlands. The design research cycles consisted of three main phases: design of instructional materials, classroom-based teaching experiments, and retrospective analyses. For the retrospective analysis of the data, we used a constant comparative method similar to the methods of Glaser and Strauss (Strauss & Corbin, 1998) and Cobb and Whitenack (1996) to continually generate and test conjectures about students’ learning processes.