Students ' Responses to Content Specific Open-Ended Mathematical Tasks

The results reported here are from one component of a larger project that explores the classroom potential of content specific open-ended tasks. We propose a framework for discussing such tasks / and justify our focus both on open-endedness and on content. In particular / we examine responses of 1200 students to comparable closed and open-ended tasks and explore the effect of using specific contexts for such tasks. We propose a method for comparing the degree of difficulty of open-ended and closed tasks and conclude that both open-ended and closed tasks can contribute to effective classroom programs. Even though effective mathematics learning and teaching requires more than quality tasks, the task may be seen as a critical prompt for mathematical activity. Christiansen and Walther (1986) explained that the task set, and the associated ~ctivity, serve as the interaction between teacher and learner. They argued that non-routine tasks, because of the interplay between different aspects of learning, provide optimal conditions for cognitive development in which new knowledge is constructed relationally and items of earlier knowledge are recognised an