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Coordinating visualizations of polysemous action: values added for grounding proportion

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Abstract

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 proportional-equivalence 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.

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Notes

  1. Gestures, too, are dynamical manual actions perceived in the visual modality and bearing semiotic content, yet we will be focusing on pragmatic manual actions operating on objects in the environment and affecting their properties.

  2. These particular students are not featured in the three case studies.

  3. Another resource was an interactive ratio table. When it is layered onto the screen, students effect green by typing numerals into the tables’ cells. This resource is not relevant to the article and so will not be treated further.

  4. In Abrahamson et al. (2012), we present an elaborate table of the interviewers’ tutorial tactics that we determined post facto from analyzing the videography. A list of tutorial tactics is different from an interview protocol, because it describes an instructor’s domain-general dialogical mechanics in service of implementing educational interaction.

  5. See http://tinyurl.com/zdm-viz for video clips from the vignettes.

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Authors and Affiliations

  1. University of California at Berkeley, Berkeley, USA

    Dor Abrahamson, Rosa G. Lee, Andrea G. Negrete & José F. Gutiérrez

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  1. Dor Abrahamson
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  2. Rosa G. Lee
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  3. Andrea G. Negrete
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  4. José F. Gutiérrez
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Correspondence to Dor Abrahamson.

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Abrahamson, D., Lee, R.G., Negrete, A.G. et al. Coordinating visualizations of polysemous action: values added for grounding proportion. ZDM Mathematics Education 46, 79–93 (2014). https://doi.org/10.1007/s11858-013-0521-7

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