This paper explores student interactions from the Virtual Math Teams-With-GeoGebra Project, a computer-supported collaborative learning environment that allows individuals to interact, collaborate, and discuss user-created dynamic mathematics objects. Previous studies of virtual math teams have focused on the coconstruction of a joint problem space and the ways collaborative meaning making can be accomplished in the online environment. Instead, this study explored the development of the students’ argumentation practices. The researchers used Toulman’s (1969) model to analyze and explain the structure of the online interactions and the argumentative practices that become normative among students. In particular, the researchers found that the students made increasingly detailed and mathematical descriptions of the data, developed more abstract warrants, and increasingly acted as if giving reasons was normative in the discussion.
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A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to pass seamlessly among verbal, geometric, symbolic, and numerical representations of the same mathematical object. The preservice teachers in this study attended a seminar where they were introduced to the underlying concepts and the pedagogical advantages of multirepresentational fluency. For select topics, this idea was reinforced with interactive GeoGebra applets that allowed preservice teachers to alter a parameter and simultaneously view how it changes all four associated representations simultaneously. A qualitative study found that this approach appeared to (a) promote the use of multirepresentational fluency in problem solving approaches used among preservice teachers, (b) change preservice teachers’ perceptions of what it means for a student to understand a concept, and (c) change the nature of evaluations that preservice teachers felt were appropriate for high school students.