The task of designing tasks for teacher education and development

Posing, adapting, and creating worthwhile tasks that support student learning are significant pedagogical practices of teachers. However in mathematics education, task design and curriculum development are not often the responsibility of practicing teachers. Textbooks can become the main source of mathematics problems and teachers often follow the text and its sequence of problems. Although mathematics teachers can benefit from access to research-based curriculum resources, limited opportunities to adapt and design tasks can make it challenging to meet the diverse needs and interests of their students. More opportunities for learning to create problems are needed for both practicing and beginning mathematics teachers. What then is involved in learning to pose, adapt and create worthwhile mathematics tasks? More specifically, how can teacher educators design tasks that support teacher candidates in learning to create mathematical tasks? As teacher educators we have, over the past few years, used our own courses as sites in Australia and Canada for investigating various contexts to support preservice teachers in their learning to adapt and create mathematical tasks. Our research includes both large scale and small qualitative studies to explore the perspectives of teacher candidates on learning to create and pose mathematical problems, the kinds of problems they pose, and the opportunities and challenges this offers us as teacher educators. Our work is inspired by Variation Theory that focuses on learning as the act of awareness and discernment of variation. We are exploring both how variation theory can be useful for preservice teachers in their designing, posing and adapting of mathematical tasks and for teacher educators in their design of such pedagogical tasks. The results of our work support the argument that tasks to design, adapt and pose mathematical problems enhance their pedagogical understanding and should be a feature of teacher education courses. This is a new area for research and practice; further exploration of the suitability of particular tasks in elementary mathematics teacher education is recommended.<br />