Abstract
Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.
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Notes
Although symbols can be removed from mathematics tasks, such modifications change the nature and intent of the task. For example, removing symbols often provides the opportunity for open-ended problem solving to take place. In this study, the intent was to ensure modifications did not change the intent of the task and consequently the removal of symbols was avoided.
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Acknowledgments
This research was funded by the Australian Research Council (Grant #DP0453366). We would like to thank Jane Greenlees for her contribution to the data collection and KimWoodland for her critical editing. An earlier version of this paper was presented at the 31st Annual Conference of the Mathematics Education Research Group of Australasia (Logan and Greenlees 2008).
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Appendix: The standard and modified items
Appendix: The standard and modified items
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Lowrie, T., Diezmann, C.M. & Logan, T. A framework for mathematics graphical tasks: the influence of the graphic element on student sense making. Math Ed Res J 24, 169–187 (2012). https://doi.org/10.1007/s13394-012-0036-5
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DOI: https://doi.org/10.1007/s13394-012-0036-5