ABSTRACT
My purpose in this chapter is to describe an iterative process of task analysis and its role in supporting students’ mathematical development. In doing so, I will present an episode taken from an eighth-grade classroom in which my colleagues and I conducted a 12-week teaching experiment during the fall semester of 1998. 1 During the course of the teaching experiment, the research team took responsibility for all aspects of the class including the teaching. (I assumed primary responsibility for teaching. I am therefore the teacher quoted in the episode.) The goal of the teaching experiment was to support students’ development of ways to reason about bivariate data as they developed statistical understandings related to exploratory data analysis. This teaching experiment was a follow-up to an earlier classroom teaching experiment conducted with some of the same students during the fall semester of the previous year. Over the course of the two teaching experiments our goal was to investigate ways to proactively support middle-school students’ development of statistical reasoning. In particular, the teaching experiment conducted with the students as seventh graders focused on univariate data sets and had as its goal supporting students’ understanding of the notion of distribution (for a detailed analysis see Cobb, 1999; McClain, Cobb, & Gravemeijer, 2000). Our goal for the eighth-grade classroom was to build on this earlier work and extend it to bivariate data sets (for a detailed analysis see Cobb, McClain, & Gravemeijer, 2000).
