The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…

This final report describes activities of the 3-year Generalized InService Training (GIST) Project to develop and field test an inservice training model for educators serving children with moderate, severe, and profound handicaps. Critical elements of the approach are identified, including: (1) training of educators and supervisors to work…