Training study on Bayesian Reasoning in school

Being able to evaluate hypotheses in uncertain situations by using Bayes' formula is an essential part of probabilistic thinking, which should already be promoted in school. Therefore, approaches to understanding Bayesian situations (i.e., situations in which Bayes' formula can be applied) have been discussed in mathematics education for decades. Beyond school, Bayes' formula is central to probability theory and highly relevant in many professions such as medicine or law as well as in everyday life. However, numerous findings of psychologically oriented research, but hardly ever directly related to learning in school, show that laymen as well as experts often fail to apply Bayes' formula adequately. Based on these findings, strategies have been developed in psychology and mathematics education to increase competence in Bayesian situations. These include natural frequencies as a format of statistical information, their visualization, and training courses, although school-based instruction has hardly been studied. In the previous DFG project ( Training Study on Bayesian Reasoning ), the strategies were combined to derive conditions for success in promoting Bayesian reasoning among the professional groups of medicine and law, for which Bayesian situations are highly relevant. The present follow-up application aims at adapting the strategies of a psychologically oriented training developed and systematically combined in the previous DFG project for the learning at school of students of grade 11, taking over the controlled instruction from the previous project and integrating it into the learning at school. As an innovation, the aspects Calculation (calculation of a positive-predictive value), the situation-appropriate Communication as well as the Covariation (effect of parameter changes on the positive-predictive value), which were focused on in the previous DFG project, will be investigated as extended Bayesian thinking for learning in school. In school, Calculation and Covariation relate to functional thinking and Communication to the interpretation and communication of a model. For comparing the different instructional approaches, two optimal training courses with natural frequencies will also be implemented with the in school more commonly used probabilities. Additionally, two other school-specific curricular approaches will be designed. The students are taught in class and assigned to the different conditions, whereby the instructional phases are strongly controlled, but the project as a whole progresses from the strongly controlled experimental design to the weaker controlled, but more ecologically valid learning in school.