A modelling approach to probability – analysing students’ conceptual structures
This research study investigates how middle school students use probability to model random behaviour in real-world contexts and how they articulated fundamental prob- abilistic concepts to show aspects of the mental models that they generated. This article is concerned with the conceptual structures that the students develop when exploring computer-based simulations. The results suggest that the students relied on their experience to provide a context reality from which to construct their mental model of the situation, from which they then defined the probability model. While the students attempted to build mental models, they checked the adequacy of the mapping between their probability models and reality by interrogating the context of their personal experiences. The results also suggest that the way students express this relationship between signal and noise seems to have a particular importance in building comprehensive models that link observed data to modelling distributions.
Dr Theodosia Prodromou is a mathematician, statistician and educator. She lectures mathematics education at the University of New England (UNE) in New South Wales, Australia. Her research interests are focused on exploring the relationship between technology and mathematical thinking – especially statistical thinking and probabilistic thinking. She is very interested in statistics education.