We contribute to research on visualization as an epistemic learning tool by inquiring into the didactical potential of having students visualize one phenomenon in accord with two different partial meanings of the same concept. 22 Grade 4-6 students participated in a design study that investigated the emergence of proportionalequivalence notions from mediated perceptuomotor schemas. Working as individuals or pairs in tutorial clinical interviews, students solved non-symbolic interaction problems that utilized remote-sensing technology. Next, they used symbolic artifacts interpolated into the problem space as semiotic means to objectify in mathematical register a variety of both additive and multiplicative solution strategies. Finally, they reflected on tensions between these competing visualizations of the space. Micro-ethnographic analyses of episodes from three paradigmatic case studies suggest that students reconciled semiotic conflicts by generating heuristic logico-mathematical inferences that integrated competing meanings into cohesive conceptual networks. These inferences hinged on revisualizing additive elements multiplicatively. Implications are drawn for rethinking didactical design for proportions. I didn't pay enough attention to change of perspective. …. The subject deserves a more systematic treatment, which I do not dare undertake. …. Learning processes are marked by a succession of changes in perspective which should be provoked and reinforced by those who are expected to guide them. (Freudenthal, 1991, as cited in Streefland, 1993 This article builds on a paper presented to the Special Interest Group on Research in Mathematics Education (SIG RME) at the 2012 annual meeting of the American Educational Research Association (AERA).
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