The interconnective relationship of students’ visualization and argumentation in geometry

In my work, I investigate the role of visualization in students’ argumentations while they work on geometric tasks, whose specific design aims to promote students’ visualization. The data presented here are from the implementation of my study in a 9th grade school class in Germany. Two theories underlie this work: Toulmin’s (1958) theory on argumentation and his functional model of argumentation, and Duval’s (1999/2002) cognitive approach to visualization. These theories help me to describe the meaning of the argumentation and visualization processes in students’ work. In order to observe these phenomena, I use two argumentation analysis methods to analyze my data and reconstruct students’ argumentations. The two methods are Reid’s (2002b) method of “patterns of reasoning” and Knipping’s (2003, 2008) method of “argumentation structures”. The two methods combined unwind the argumentation processes that take place while students work on given geometric tasks. Employing Duval’s (1999/2002) visualization theory in the reconstructed argumentations reveals the roles of visualization in students’ argumentations and, as a consequence, visualization’s contribution in their learning of geometry.

The data analysis reveals five roles that visualization plays in students’ argumentation (e.g. supporting the creation of a hypothesis) and also three functions that the students attribute to them in their arguments (e.g. as warrants). In the results, I also explain how visualization can be indicated in argumentation both through students’ verbal descriptions (including metaphors) as well as their actions (e.g. gestures, use of drawings). Furthermore, I discuss how the task design as well as the organization of the learning social settings – students working in pairs and participating in classroom discussions – influence students’ work and contribute to their learning in different ways.

This work concludes with a discussion in which all the important results are brought together and are also linked to the already existing literature. The contributions of my work are discussed and implications for the teaching of geometry and for further research are proposed.