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Project
The fluent and flexible use of external representations in statistics: empirical studies on representation use in distributional problem solving.
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 eachrepresentation elicited misinterpretations. This was especially the case for box plots and histograms.
The second research question was: Which reasoning mechanismsunderlie 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 elicitedby 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.
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 eachrepresentation elicited misinterpretations. This was especially the case for box plots and histograms.
The second research question was: Which reasoning mechanismsunderlie 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 elicitedby 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.
Date:1 Sep 2009 → 30 Sep 2014
Keywords:Flexibility, Routine expertise, Adaptive expertise, Distribution, External representations, Statistics education
Disciplines:Instructional sciences, Education curriculum, Education systems, General pedagogical and educational sciences, Specialist studies in education, Other pedagogical and educational sciences
Project type:PhD project