This investigation is part of a combined research/curriculum development project in which children's learning is being examined in the context of developing and testing instructional units on 3-D geometry in grades 3, 4, and 5. There are two components to the article. First, the strategies and cognitive constructions that students utilize to conceptualize and enumerate the cubes in 3-D arrays are described. Second, the change in thinking of students as they are involved in instructional tasks that help them develop more sophisticated thinking about enumerating cubes in 3-D arrays are examined. (Author/MKR)