Using novel tasks in teaching mathematics: Three tensions affecting the work of the teacher

Novel (as opposed tofadmiliar) tasks can be contextsforstudents ' development of new knowledge. But managing such development is a complex activityfor a teacher. The actions that a teacher took in managing the development of the mathematical concept of area in the context of a task comparing cardstock triangles are examined. The observation is made ihat some of the teacher's actions shaped the mathematics at play in ways that seemed to counter the goals of the task. This article seeks to explain apossible rationality behind those contradictory actions. The hypothesis ispresented that in managing task com-pletion and knowledge development, a teacher has to cope with three subject-specfic tensions related to direction of activity, representation of mathematical objects, and elicitation of students ' conceptual actions