Title: Thinking outside the box - The role of external representations in distributional reasoning
Authors: Lem, Stephanie
Issue Date: 12-May-2014
Abstract: In this doctoral project we focused on the role of external representations in distributional reasoning. Although in the mathematics education literature a lot has been written about the importance of representations in problem solving and learning, this is much less the case in the statistics education literature. Especially with respect to distributional reasoning, the role of representations is not valued and studied much. In this doctoral project we tried to fill this gap. A first research question was: “What is the role of external representations in distributional reasoning?”. We studied this role by comparing how students solved the same tasks with different representations (dot plot, descriptive statistics, box plot, and histogram). We found, as expected, that the best achievement differs by representation and task. Accuracy was relatively low in general, and each representation elicited misinterpretations. This was especially the case for box plots and histograms. The second research question was: “Which reasoning mechanisms underlie the (mis)interpretation of external representations for data distributions?”. Because we found interesting misinterpretations of box plots and histograms in the first studies, we chose to answer this research question for two specific misinterpretations of box plots and histograms. Using graph design principles and the dual processing theory of reasoning as a framework we found that both misinterpretations are elicited by specific design features of the box plot and the histogram, and can be characterised as the consequence of the intuitive or heuristic processing of salient graph features. The third research question was: “How can students’ interpretation of external representations for data distributions be improved?”. We focused for this research question on one specific misinterpretation of the box in the box plot. We used both multiple external representations and refutational text to improve students’ interpretation of box plots. Multiple external representations had a positive effect when dot plots and box plots were combined. When histograms and box plots were combined, the effect was less clear. Refutational text improved the reasoning of many students and seems to be a promising way to further improve instruction on distributional reasoning.
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Instructional Psychology and Technology
Methodology of Educational Sciences

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