A complex system analysis of practitioners' discourse about research

Focus on Learning Problems in Mathematics, Wntr, 2008 by Randall E. Groth

The ALN conversation described in this report focused upon an article entitled "Mean and median: Are they really so easy?" (Zawojewsky & Shaugnessy, 2000). The article gave examples of tasks used on the National Assessment of Educational Progress (NAEP) to assess students' understanding of measures of central tendency. It also provided details about students' responses to the tasks. Important findings from the NAEP data included the fact that many students did not understand the relative advantages of the mean and median as measures of center. The authors of the article recommended that readers use the NAEP tasks to probe their own students' thinking about the mean and median in order to gather information to design instruction. I encouraged the study participants to point out perceived strengths and weaknesses of the article and to respond to comments made by their colleagues during ALN interaction.

Data Analysis

A total of 50 messages were posted to the online discussion board during the conversation of the article. As the ALN discourse unfolded, I read each one of them. This analysis led to posts designed to extend participants' thinking. The specific nature of my posts is described along with those of the participants in the next section. My ongoing analysis provided context for a retrospective analysis after the ALN interaction had concluded.

Retrospective data analysis began with the construction of thread response trees (Aviv, Erlich, Ravid, & Geva, 2003) to help model the structure of the ALN discourse. A sample thread response tree is given in Figure 1. Each node in the tree represents a message posted to a discussion board. Nodes are labeled with the initials of the individual making the post. Arrows in the tree point from a post toward the message to which the post replied. The numerals on the arrows correspond to the chronological order of each post in the overall discourse for the week in which the thread was constructed. Given these labeling conventions, the first post in a thread is attached to an arrow that does not connect to any other post. Therefore, in Figure 1, the node labeled AB signifies the first post in a thread but the second overall post to the discussion board that week. The node connected to it signifies that CD replied to AB's post with the fourth overall post for the week, and so forth.

[FIGURE 1 OMITTED]

Once response trees had been constructed for each thread of discourse taking place during the study, retrospective analysis continued through the construction of narratives describing the nature of each strand (Glesne, 1999). Narratives are valuable for modeling complex systems because they help tell the story of the system as it evolves in a way that quantitative tools cannot (Kauffman, 2000). In constructing the narratives, chronological order was generally followed to preserve a sense of how each thread unfolded. The thread response trees and their accompanying narratives are presented together in the next section of this report.