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Rößner, Michael ; Binder, Karin ; Geier, Corbinian ; Krauss, Stefan

Students' performance and typical errors in filling empty probabilistic visualizations with probabilities or frequencies

Rößner, Michael, Binder, Karin , Geier, Corbinian and Krauss, Stefan (2025) Students' performance and typical errors in filling empty probabilistic visualizations with probabilities or frequencies. Educational Studies in Mathematics 120 (1), pp. 137-167.

Date of publication of this fulltext: 15 Oct 2025 04:17
Article
DOI to cite this document: 10.5283/epub.77970


Abstract

It has been established that, in Bayesian tasks, performance and typical errors in reading information from filled visualizations depend both on the type of the provided visualization and information format. However, apart from reading visualizations, students should also be able to create visualizations on their own and successfully use them as heuristic tools in modeling tasks. In this paper, ...

It has been established that, in Bayesian tasks, performance and typical errors in reading information from filled visualizations depend both on the type of the provided visualization and information format. However, apart from reading visualizations, students should also be able to create visualizations on their own and successfully use them as heuristic tools in modeling tasks. In this paper, we first want to broaden the view on Bayesian reasoning to probabilistic tasks with two binary events in general and embed the whole process of solving these tasks using probabilistic visualizations in a modified modeling framework. Thereby, it becomes apparent that most of the steps remained untouched by existing research. Second, in the present empirical study, we focused on one part of the largely unexplored creation process and examined entering statistical information into empty visualizations as heuristic tools. N = 172 participants had to enter conditional and joint probabilities or the corresponding frequencies into empty visualizations in a paper-and-pencil~test. We analyze (a) students' performance when entering information in visualizations and (b) typical errors, both dependent on the information format (probabilities vs. natural frequencies), which empty visualization structure (2⨯2 table, double~tree, net diagram) was provided, and type of information (conditional vs. joint information). The well-known positive effect of natural frequencies on participants' performance was evident when entering conditional information into 2⨯2 tables and net diagrams. However, with respect to joint information, no superior effect of frequencies was observed. Furthermore, the theoretical implementation of our research in a modeling cycle allows~us to identify desiderata for future research.



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Details

Item typeArticle
Journal or Publication TitleEducational Studies in Mathematics
Publisher:Springer
Open Access Type:CC-License
Volume:120
Number of Issue or Book Chapter:1
Page Range:pp. 137-167
Date6 February 2025
InstitutionsMathematics > Prof. Dr. Stefan Krauss
Identification Number
ValueType
10.1007/s10649-024-10372-yDOI
KeywordsFilling empty visualizations, Net diagram, Double tree, 2⨯2 table, Frequency effect, Typical errors
Dewey Decimal Classification100 Philosophy & psychology > 150 Psychology
300 Social sciences > 370 Education
500 Science > 510 Mathematics
StatusPublished
RefereedYes, this version has been refereed
Created at the University of RegensburgPartially
URN of the UB Regensburgurn:nbn:de:bvb:355-epub-779701
Item ID77970

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