On Conditional Probability Problem Solving Research – Structures and Contexts

Abstract

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