The Convergent–Divergent Model: An opportunity for teacher–learner development through principled task design

摘要

The tasks that mathematics teachers are invited to use in their classrooms have profound effects not just on the learners who do them but also on the teachers themselves. This paper introduces the Convergent–Divergent Model (CDM) for the design of mathematical tasks. The CDM consists of two distinct phases: the first, a convergent problem-solving episode, and the second, a more divergent, open-ended, exploratory part. The two-phase design is built on twin intentions both for the mathematical growth of the learner and for the pedagogical development of the teacher. The principles of design employed in this model are elucidated through descriptions of the construction of several examples of such tasks in published mathematics teacher resource books written by the author.