Developing a Modelling Approach to Probability Using Computer-Based Simulations

Abstract

The introduction of digital technology into secondary schools is ideally suited for supporting students as they manipulate and portray data in a range of different representations to draw inferences from it without relying on a classical understanding of probability theory. As a result, probability is overlooked from school curricula and is gradually becoming almost a non-existent topic. The aim of recent curricula (e.g. ACARA 2010) to support the parallel development of statistics and probability and then progressively build the links between them seems utopic since statistics prevails over probability in mathematics curricula. In this chapter, it is argued that it is worthwhile to consider an alternative approach for teaching probability - presenting probability as a modelling tool, which reflects the mindset of an expert when using probability to model random behaviour in real-world contexts. This chapter discusses results from two recent research studies (Prodromou 2008, 2012) that investigated middle school students' understanding of probability as a modelling tool. Within this chapter, the students' reasoning will be considered from different perspectives: 1. How students articulated fundamental probabilistic concepts associated with the construction of univariate probability models when using probability to model random behaviour. 2. Students' discussion as they engaged in exploring recently developed computer-based simulations which treat probability as a modelling tool.