This paper examines the mathematical conversations of middle school students as they use computer-mediated graphic representations to construct a shared understanding of the basic concepts of probability under two conditions. The first condition used graphical representations to depict important abstract relationships visually, and the second condition used animation to augment the graphic representations to see if animation helped students grasp abstract relationships. Thirteen pairs of students (11 boys and 15 girls) divided themselves into the two condition groups. The analysis of student think-aloud protocols focused on how the visual and dynamic elements of the computer-based graphical representation influenced students' interpretations of the mathematical concepts. Data suggest that students with access to animated representation had qualitatively different mathematical discussions than those who had only the static representation. The conversations of students who used animated representations used a narrative structure and were richer than those of the students who used static representations. (Contains 3 figures and 37 references.) (SLD)