Abstract
This paper traces the evolution of some research projects that relate to the use of a particular
type of classroom task as the focus of the learners' mathematical activity. The tasks used
are, on one hand, open-ended to allow opportunities for thinking and creativity, and, on the
other hand, content specific to ensure that the focus of pupils ' activity is not just mathematics
generally but the specific content that the classroom program seeks to address. The research
grew out of a particular view of learning and teaching, consideration of the motivation of
the learners, a perspective on mathematics as the content focus of the learning, and a
recognition of constraints operating in classrooms. These perspectives are summarised first,
after which there is a discussion of characteristics of the classroom tasks, and some reports
of research into their use. Some implications for teacher education are suggested.