Versprachlichung von Anteilen und natürlichen Häufigkeiten anhand von Baum- und Netzdiagrammen
摘要
Risk literacy includes the ability to accurately verbalize statistic information, such as proportions and probabilities. Research on conditional probabilities and Bayesian tasks has shown that using visualizations and so-called “natural frequencies” (e.g., “80 out of 100 people”) instead of probabilities (expressed as percentages) can reduce errors in determining probabilities. However, little is known about the reverse process—the verbalization of information presented in visualizations—although these verbalizations are also considered essential for the development of conceptual knowledge. Therefore, this study investigated how well students succeed in verbalizing proportions and natural frequencies presented in visualizations. A paper-and-pencil test was conducted with 138 secondary school students (grade 9), in which participants were asked to describe the meaning of the statistic information presented in probabilistic visualizations as detailed as possible. The study focuses on the influence of the visualization (tree diagram vs. net diagram) and the information format of the visualization (proportion in percentages vs. natural frequencies) on the accurate verbalization of different types of relationships (joint information vs. conditional information). The results show, among other things, that information expressed in natural frequencies is verbalized significantly better compared to proportions in percentages, and that joint information expressed in percentages is better verbalized using net diagrams than using tree diagrams. Furthermore, the findings provide insights into typical (incorrect) verbalizations by students and could serve as a basis for developing language-sensitive instruction on proportions and probabilities in school-level stochastics classes.