Reflecting on the Process of Task Adaptation and Extension: The Case of Computational Starters

For several years we have been designing materials to engage prospective elementary teachers in relearning computation with the kind of understanding necessary to support their work with future elementary students. Many of the tasks used for this purpose are extensions of the (numerical) starter problems from the elementary curriculum, Investigations in Number, Data and Space developed by TERC (1998), a non-profit educational organization in Boston. For example, consider the problem of evaluating 102 –46 by using one of the following numerical starters, or first steps: 46 + 50, 102 – 50, and 106 – 50. In this chapter we discuss the issues that arose as we used these tasks with prospective teachers, and the additional adaptations that were developed over time in order to focus on these issues. Although our work focuses on the use of starters in the context of whole number computation, we conclude with a discussion of the more general advantages of such tasks by connecting our goals with the more general notion of mathematical proficiency, as defined by the National Research Council (2001).