In this paper we summarize the research we have recently carried out on classifying problems<br>of conditional probability. We investigate a particular world of school word problems we call ternary<br>problems of conditional probability. With the help of a mathematical object, the trinomial graph, and the<br>analysis and synthesis method, we propose a framework for a structural, didactical and phenomenological<br>analysis of the ternary problems of conditional probability. Consequently, we have organized this world into<br>several types of problems. With respect to students' behaviour, we identify four types of thinking processes<br>related to data format and the use of data. We also illustrate our approach by use of the diagnostic test<br>situation, and in the particular context of health.<br>The main purpose of our work is to improve secondary school students' understanding of conditional<br>probability and their probability literacy by proposing a teaching approach based on problem solving within<br>appropriate contexts. We believe that the framework we present in this paper could help teachers and<br>researchers in this purpose.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education