Douglas McLean Clarke

Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching

As part of a research and professional development project that focused on the opportunities and constraints provided by different kinds of mathematical tasks, a group of 67 primary and 40 secondary practising teachers of mathematics were asked to complete a survey focusing on their use of tasks. In this article, we discuss responses to one particular item which sought teachers’ ideas on taking a fraction comparison task (which is larger: 2/3 or 201/301?) and converting it into a mathematics lesson in the middle years of schooling. Drawing upon a number of components of ‘mathematical knowledge for teaching’ as a framework, we attempt to examine those aspects of mathematical knowledge which are involved in making such a conversion. Our recommendation following this analysis is that greater emphasis is necessary in professional development settings on taking a potentially useful task and converting it into a worthwhile mathematics learning experience for students. Knowing the relevant mathematics also seems necessary even if not sufficient to make this conversion.

Researching the creation of a national curriculum from systems to classrooms

Under the auspices of its ‘Education Revolution’, the Federal Labor Government is currently implementing a national curriculum for schools. Representing an important intervention into educational practice and governance, the Australian Curriculum offers a unique research opportunity, providing substantial scope for the examination of the changing systems and school-level practices entailed in large-scale curriculum reform. Research into the Australian Curriculum also presents a valuable opportunity to develop educational research methodologies that attend to the complex and multifaceted processes of curriculum reform, from systems to classrooms. Taking two of the disciplinary towers of modern curricula (English and mathematics) and Australia’s two largest jurisdictions (New South Wales and Victoria) as the focus, this article draws on a three-year Australian Research Council Linkage Project to outline an approach to researching major curriculum reform.