TEACHING PROBABILITY: USING LEVELS OF DIALOGUE AND PROPORTIONAL REASONING

Understanding probability and conditional probability are important aspects of a statistical literacy program. Unfortunately many students find these difficult concepts to grasp. Enhancing students ’ understandings of probability is explored from two perspectives. The first is based on the notion that students are better able to construct their understanding of probability when teachers use a hierarchy of dialogue questions from descriptive to the abstract, depending on the students’ understanding and responses. The second approach to enhance students ’ understanding of probability is to extend their understanding of proportional reasoning and their ability to conceptualise how the same numerical value can be expressed in different forms. Probability and conditional probability continue to be identified as “hard ” concepts to teach as part of a statistical literacy program of study in schools and even at the University level (Tarr & Jones, 1997; Watson & Kelly, 2007). It is not, however, the intention in this paper to investigate directly the teaching of probability or conditional probability in a school setting (see Shaughnessy, Chance, & Kranendonk, 2009, for examples of this). Rather the intention in this paper is to investigate why students ’ learning of probability and conditional probability is often a complex procedure for them to grasp. This investigation will focus on the hypothesis that the effectiv