In this paper, selected lessons from the pre-service course illustrate aspects of the taskbased
lesson design, while examples of student solutions for particular tasks illuminate how the
specified classroom activity promotes engagement with targeted mathematical constructs.
Elements of the lesson design that are discussed include;
1. decomposition of the mathematical topic under study, in terms of its underlying
structure and relationship to other constructs, and its position within a carefully
articulated mathematical learning trajectory;
2. identification of a context that “begs to be organized” by the construct under study;
3. creation of an open-process task that permits entry and active engagement from a
range of skill and conceptual levels; and
4. orchestration of the classroom processing of selected students’ solutions that exhibit
aspects of the underlying mathematical structure