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Understanding student errors in comparing data sets with boxplots.

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Title: Understanding student errors in comparing data sets with boxplots.
Authors: Abt, Martin1 (AUTHOR) martin.abt@ph-freiburg.de, Loibl, Katharina2,3 (AUTHOR) katharina.loibl@ph-freiburg.de, Leuders, Timo1 (AUTHOR) leuders@ph-freiburg.de, Van Dooren, Wim4 (AUTHOR) wim.vandooren@kuleuven.be, Reinhold, Frank1,3 (AUTHOR) frank.reinhold@ph-freiburg.de
Source: Educational Studies in Mathematics. Sep2025, Vol. 120 Issue 1, p169-193. 25p.
Subject Terms: *Error analysis in education, *Individualized instruction, *Data analysis, *Cognitive development, Box plots (Graphs), Empirical research, Data visualization
Abstract: In the boxplot, the box always represents – regardless of its area – the middle half of the data and thus a measure of variability (interquartile range). However, when students first learn about boxplots, they are usual already familiar with other forms of statistical representations (e.g., bar or circle graphs) in which a larger area represents a higher frequency of observations. If students erroneously apply this well-established area-represents-frequency schema to boxplots, it results in a systematic error which we describe as the consequence of an incomplete conceptual change. We empirically validated difficulty-generating characteristics that allow the differentiation between item types with varying complexity (item level) and aimed to identify profiles (person level) that differ depending on which schema was used in which item type. For this purpose, we conducted two cross-sectional studies with N = 100 university students (study 1) and N = 297 participants who finished secondary school or higher (study 2) and used generalized linear mixed models (item level) and k-means clustering with predefined cluster centers (person level) to test our hypotheses. We could replicate the systematic error that was described in previous research and found new difficulty-generating characteristics in boxplot items. Our results support the notion of different profiles potentially emerging based on varying degrees of conceptual change. From an instructional perspective, information about individual progress in conceptual change could be considered for tailoring individualized interventions. [ABSTRACT FROM AUTHOR]
Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Educational+Studies+in+Mathematics%22">Educational Studies in Mathematics</searchLink>. Sep2025, Vol. 120 Issue 1, p169-193. 25p.
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  Data: In the boxplot, the box always represents – regardless of its area – the middle half of the data and thus a measure of variability (interquartile range). However, when students first learn about boxplots, they are usual already familiar with other forms of statistical representations (e.g., bar or circle graphs) in which a larger area represents a higher frequency of observations. If students erroneously apply this well-established area-represents-frequency schema to boxplots, it results in a systematic error which we describe as the consequence of an incomplete conceptual change. We empirically validated difficulty-generating characteristics that allow the differentiation between item types with varying complexity (item level) and aimed to identify profiles (person level) that differ depending on which schema was used in which item type. For this purpose, we conducted two cross-sectional studies with N = 100 university students (study 1) and N = 297 participants who finished secondary school or higher (study 2) and used generalized linear mixed models (item level) and k-means clustering with predefined cluster centers (person level) to test our hypotheses. We could replicate the systematic error that was described in previous research and found new difficulty-generating characteristics in boxplot items. Our results support the notion of different profiles potentially emerging based on varying degrees of conceptual change. From an instructional perspective, information about individual progress in conceptual change could be considered for tailoring individualized interventions. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Sep2025
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