Launching mathematical futures: The key role of multiplicative thinking

Access to multiplicative thinking has been identified as the single, most important reason for the eight-year range in mathematics achievement in Years 5 to 9. While elements of multiplicative thinking are variously represented in the Australian Curriculum, the connections between these and how they contribute to the development of multiplicative thinking over time is not entirely clear. Two aspects of Hanna Neumann's internationally respected reputation as a mathematician, teacher, researcher, and mentor will be used to frame this presentation. The first is her commitment to making the abstract accessible. The second is her passionate interest in reforming school mathematics curricula. Examples will be used to demonstrate how the abstract might be rendered accessible in the context of school mathematics and, conversely, how abstracting the everyday can help challenge long-held beliefs about learning mathematics. But the major part of this presentation will be concerned with the critical importance of multiplicative thinking in launching mathematical futures and its representation in the Australian Curriculum.