Abstract:
In the field of probability education, probabilistic thinking research has mainly focused on two aspects. The first is students’ conceptual reasoning within situations of inherent uncertainty, and the second is the nature of the ideas encompassing probabilistic thinking. With new learning technologies probability modelling has the potential to become commonplace amongst students learning about probability. Hence there is a need to understand and explicate the key ideas underpinning probability thinking and modelling in order to provide a base for the setting of new goals for probability education. To determine these key ideas, interviews with seven practitioners who worked with and developed probability models were analysed. The interviews covered the practitioners’ perspectives on and field experiences of probability thinking and modelling and their opinions on the essential concepts underpinning probability. The practitioners came from a variety of backgrounds ranging from theoretical probability to commercial statistics. A thematic analysis approach was conducted on the interview data. The software package NVivo 10 was used in conjunction with the thematic analysis method to produce four thematic frameworks for (1) probability, (2) probabilistic thinking, (3) probability modelling, and (4) essential concepts of probability thinking and modelling. The main findings were that Quantifying Uncertainty, Seeing Structure, and Applying Structure were central themes within the probability, probabilistic thinking, and probability modelling frameworks, respectively. Randomness, Distribution, Conditioning, and Mathematics were identified as essential foundational concepts for probability thinking and modelling. The four frameworks explicate how these key probability themes provide a unique way of engaging with, thinking about, and interacting with a diverse range of real world situations where randomness and uncertainty are omnipresent. When compared with the probability education literature, the findings suggested that the frameworks might be useful starting points for setting new goals in education and research.