Designing for creative mathematical reasoning

With Dr. Steve Thornton

Students’ experience of mathematics is shaped by the tasks they undertake. Tasks shape the understanding of the nature of mathematical activity; they provide opportunities for developing problem-solving and reasoning, fluency and conceptual understanding; they provide opportunities for students to develop productive dispositions to mathematics. Just as the text in all its many forms is the focal point of literature, tasks in all their many forms are the focal point of mathematics.

Tasks might focus on developing fluency and understanding. In this case, the aim is to enable students to become proficient at using mathematics for purposes that are likely to be clearly defined and address key content as described in the Australian Curriculum. Good tasks that develop fluency and understanding require careful design, taking into account principles such as Variation Theory, conceptual change or the development of hypothetical learning trajectories.

Other tasks might focus primarily on problem solving and reasoning. While they do not ignore curriculum content, such tasks provide opportunities for students to connect mathematical concepts and think beyond the boundaries of specified content. Good tasks that develop creative mathematical reasoning also require careful design, taking into account aspects such as the conceptual challenge, the justification challenge and the creative challenge.

The proposed professional learning and research program Designing for creative mathematical reasoning will use theoretical perspectives such as the Anthropologic Theory of Didactics, The Knowledge Quartet and Learning Dispositions to engage teachers in evaluating, designing, implementing and reflecting on mathematical tasks that focus on problem solving and reasoning. Such tasks are particularly appropriate for students of high mathematical potential.

The program is based on principles from design-based research. Unlike typical educational research that studies educational situations with a view to understanding phenomena or quantifying the effect of particular practices, design-based research takes a research-as-engineering approach. Good engineering implies a focus on design—strategic, structural, and technical—and on systematic development in appropriate contexts.

Ticket price includes: Tea, Coffee, and Morning tea.

About Dr. Steve Thornton:

Dr Steve Thornton is a mathematics education lecturer, consultant and researcher. He has wide experience as a teacher of mathematics and curriculum leader, as a researcher in mathematics education, as leader of national professional development programs for the Australian Mathematics Trust and the Australian Academy of Science, and as a consultant and critical friend to numerous mathematics education projects. Most recently Steve was Executive Director of the highly regarded reSolve: Mathematics by Inquiry project conducted by the Australian Academy of Science in collaboration with the Australian Association of Mathematics Teachers, developing exemplary teaching and professional learning resources and recruiting and training a cohort of more than 300 Champion teachers.

Steve has lectured in mathematics teacher education at the University of Canberra, Charles Darwin University and the University of Oxford.

Steve is a Past President and Life Member of the Australian Association of Mathematics Teachers. He serves on the Problems Committee of the Mathematics Challenge for Young Australians and has been awarded a B.H.Neumann medal for excellence in Australian mathematics education. He is a Fellow of the International Society for Design and Development in Education.

Steve holds B.Sc. (Hons) and Grad. Dip. T. degrees from the University of Adelaide; and a Ph. D. from the Australian National University. His research interests include philosophy of mathematics education, task design and knowledge-building in mathematics education, and empowering teachers through classroom-based observation and research. His PhD thesis “Slow Maths: A metaphor of connectedness in school mathematics” used the metaphor of the slow food movement to map a vision for school mathematics that engages students with the culture of mathematics as an underpinning discipline for STEM and as an enjoyable field of study in its own right.