The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two components of classroom learning: the process of argumentation as the social perspective and the content of arithmetic properties as the psychological perspective. I administered pre- and post-assessment interviews individually to students. I modified eight lessons from the traditional textbook and introduced sociomathematical norms that supported mathematical argumentation into the whole-class teaching experiment.

I identified and analyzed 67 arguments that emerged from the lesson transcripts and used an empirically-modified model adapted from Toulmin's (1958) model of argumentation and Stylianides' (2007) elements of argumentation to characterize the students' arguments.

With regard to the characteristics of the students' arguments, I partitioned all of the arguments into six model templates and all of the claims into two categories. The justifications that students relied on seemed related to many factors, including the origin of the claim, the mathematical context of the claim, and the type of claim. The study suggests that arithmetic properties should be integrated into new and familiar contexts rather than placed in one section of the fourth-grade curriculum and that argumentation is a beneficial process for teaching the properties to children.