Using Novel Tasks in Teaching Mathematics: Three Tensions Affecting the Work of the Teacher

Abstract

Novel (as opposed to familiar) tasks can be contexts for students’ development of new knowledge. But managing such development is a complex activity for 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 that 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 a possible rationality behind those contradictory actions. The hypothesis is presented that in managing task completion and knowledge development, a teacher has to cope with three subject-specific tensions related to direction of activity, representation of mathematical objects, and elicitation of students’ conceptual actions.