Argumentation, Justification, and Proof in Middle Grades: A Rose by Any Other Name

In this chapter, we consider the teaching and learning possibilities associated with the Number Trick task featured across the middle school chapters, a task designed to engage students in proving-related activity. We also discuss the consequences associated with analyzing classroom data of the task’s implementation from the three different perspectives of argumentation, justification, and proof. In the former case, we discuss the possibilities afforded by the task itself, the potential instructional goals associated with the task, and the opportunities, both taken and missed, by the teacher to meaningfully engage his students in proving-related activity. In the latter case, we discuss how the three different perspectives and, importantly, the different analytic lens each set of chapter authors used to guide their data analyses, influenced not only the outcome of the analyses but also the insights each analysis offered with regard to the teacher’s efforts to meaningfully engage his students in proving-related activity.