@article{59438, abstract = {{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, 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.}}, author = {{Rößner, Michael and Binder, Karin and Geier, Corbinian and Krauss, Stefan}}, issn = {{0013-1954}}, journal = {{Educational Studies in Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Students’ performance and typical errors in filling empty probabilistic visualizations with probabilities or frequencies}}}, doi = {{10.1007/s10649-024-10372-y}}, year = {{2025}}, } @article{60602, abstract = {{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, 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.}}, author = {{Rößner, Michael and Binder, Karin and Geier, Corbinian and Krauss, Stefan}}, issn = {{0013-1954}}, journal = {{Educational Studies in Mathematics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Students’ performance and typical errors in filling empty probabilistic visualizations with probabilities or frequencies}}}, doi = {{10.1007/s10649-024-10372-y}}, year = {{2025}}, } @article{59435, abstract = {{AbstractPrevious studies on Bayesian situations, in which probabilistic information is used to update the probability of a hypothesis, have often focused on the calculation of a posterior probability. We argue that for an in-depth understanding of Bayesian situations, it is (apart from mere calculation) also necessary to be able to evaluate the effect of changes of parameters in the Bayesian situation and the consequences, e.g., for the posterior probability. Thus, by understanding Bayes’ formula as a function, the concept of covariation is introduced as an extension of conventional Bayesian reasoning, and covariational reasoning in Bayesian situations is studied. Prospective teachers (N=173) for primary (N=112) and secondary (N=61) school from two German universities participated in the study and reasoned about covariation in Bayesian situations. In a mixed-methods approach, firstly, the elaborateness of prospective teachers’ covariational reasoning is assessed by analysing the arguments qualitatively, using an adaption of the Structure of Observed Learning Outcome (SOLO) taxonomy. Secondly, the influence of possibly supportive variables on covariational reasoning is analysed quantitatively by checking whether (i) the changed parameter in the Bayesian situation (false-positive rate, true-positive rate or base rate), (ii) the visualisation depicting the Bayesian situation (double-tree vs. unit square) or (iii) the calculation (correct or incorrect) influences the SOLO level. The results show that among these three variables, only the changed parameter seems to influence the covariational reasoning. Implications are discussed.}}, author = {{Büchter, Theresa and Eichler, Andreas and Böcherer-Linder, Katharina and Vogel, Markus and Binder, Karin and Krauss, Stefan and Steib, Nicole}}, issn = {{0013-1954}}, journal = {{Educational Studies in Mathematics}}, number = {{3}}, pages = {{481--505}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Covariational reasoning in Bayesian situations}}}, doi = {{10.1007/s10649-023-10274-5}}, volume = {{115}}, year = {{2024}}, } @article{57558, abstract = {{AbstractMathematical modelling emphasizes the connection between mathematics and reality — still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It is the aim of the study to analyze how far the mathematical modelling steps of students solving the tasks differ in comparison to the settings and representations. In a qualitative study, 19 lower secondary school students worked on tasks of all three settings in a Latin square design. Their working processes in the settings are compared with a special focus on the modelling steps Simplifying and Structuring, as well as Mathematizing. The analysis by means of activity diagrams and a qualitative content analysis shows that both steps are particularly relevant when students work with real objects — independent from the three settings. Still, differences in the actual activities could be observed in the students’ discussion on the appropriateness of a model and in dealing with inaccuracies at the real object. In addition, the process of data collection shows different procedures depending on the setting which presents each of them as an enrichment for the acquisition of modelling skills.}}, author = {{Jablonski, Simone}}, issn = {{0013-1954}}, journal = {{Educational Studies in Mathematics}}, number = {{2}}, pages = {{307--330}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation}}}, doi = {{10.1007/s10649-023-10215-2}}, volume = {{113}}, year = {{2023}}, } @article{57556, abstract = {{AbstractMathematical modelling emphasizes the connection between mathematics and reality — still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It is the aim of the study to analyze how far the mathematical modelling steps of students solving the tasks differ in comparison to the settings and representations. In a qualitative study, 19 lower secondary school students worked on tasks of all three settings in a Latin square design. Their working processes in the settings are compared with a special focus on the modelling steps Simplifying and Structuring, as well as Mathematizing. The analysis by means of activity diagrams and a qualitative content analysis shows that both steps are particularly relevant when students work with real objects — independent from the three settings. Still, differences in the actual activities could be observed in the students’ discussion on the appropriateness of a model and in dealing with inaccuracies at the real object. In addition, the process of data collection shows different procedures depending on the setting which presents each of them as an enrichment for the acquisition of modelling skills.}}, author = {{Jablonski, Simone}}, issn = {{0013-1954}}, journal = {{Educational Studies in Mathematics}}, number = {{2}}, pages = {{307--330}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Is it all about the setting? — A comparison of mathematical modelling with real objects and their representation}}}, doi = {{10.1007/s10649-023-10215-2}}, volume = {{113}}, year = {{2023}}, }