Visualising chance: Learning probability through Modelling

Project Description

The project was a two year exploratory study involving a collaboration between two researchers, two conceptual software developers/interactive graphics experts, three university lecturers/practitioners, four teacher observers and one quality assurance advisor. The project team designed innovative software tools and associated tasks aimed to expose undergraduate introductory probability students to a modelling approach to probability and sought to discover what conceptual understanding of probability and what probabilistic reasoning could be promoted from such an approach.

Aims

The aim of the project was to consolidate and build on knowledge about a modelling approach to probability and learning strategies that involved the development of static and dynamic visual imagery and language for promoting student conceptual growth. Specifically, we aimed to address the gap in the existing knowledge base which is the extent to which learning probability from a theoretical and modelling perspective will allow students to have access to the essential conceptual ideas underpinning probabilistic reasoning. We aimed to discover: what conceptual understanding of probability and what probabilistic reasoning is promoted when introductory university students are exposed to a modelling approach to probability and to learning strategies focused on dynamic and static visual imagery?

Why is this research important?

Probabilistic reasoning is needed to help us operate sensibly and optimally in the face of uncertainty due to randomness in processes that affect us at all levels of society. However, current teaching of probability has largely been grounded in a mathematical approach, paying insufficient attention to modelling and simulating realistic problems. The modelling approach, incorporating static and dynamic visualisations, shows promise in making transparent concepts such as the nature and effects of randomness, often inaccessible within the formal framework of mathematical probability. This research provides insights into student learning and reasoning capabilities and will inform current and future practice at the undergraduate and Year 13 levels.

What did we do?

The project involved action research methodology comprising five phases. In the first phase, through collaborative meetings, interviews with professionals who make use of probability modelling in their work, and reviewing the probability education literature, the project team conducted a conceptual analysis in order to identify some of the essential conceptual ideas underpinning probabilistic reasoning. The second phase involved a qualitative thematic analysis of the interviews, project team deliberations, and literature review, to identify the main problem areas and conceptual ideas that needed addressing. In the third phase, the project team identified four significant areas for development of probabilistic reasoning for which tasks and software tools could be developed. For each area, a conceptual analysis of the underpinning concepts and possible conceptual pathways was undertaken. The fourth phase involved trialling each of the software tools and associated tasks with three pairs of students who had already completed an introductory probability course. In the fifth phase, a retrospective analysis was carried out, followed by modifications to the tools and tasks.

Data

In the first phase of this project we collected interview data from professionals who use probability modelling in their work. While trialling the tools and tasks in the fourth phase, we collected data in the form of pre-tests, task interviews and reflection interviews with all of the participating students. We also recorded audio data from the project team meetings.

Analysis

The data were analysed qualitatively using thematic analysis and constant comparative methods. A combination of theoretical and inductive thematic analyses were used. The theoretical analysis was informed about what is already known about common probability misconceptions and conceptual development. The inductive analyses were grounded in the student data to allow for a richer description of the data.

Contact details

Dr Stephanie Budgett
Department of Statistics
The University of Auckland
Private Bag 92019
Auckland 1142
s.budgett@auckland.ac.nz
Phone: 64 9 923 2346