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…

Defines spatial structuring as the mental operation of constructing an organization or form for an object/set of objects. Examines in detail students' structuring and enumeration of two-dimensional rectangular arrays of squares. Concludes that many students do not see row-by-column structure. Describes various levels of sophistication in students'…

Describes how to deal with students' structuring of rectangular arrays of squares and other two-dimensional regions. Presents activities that connect spatial structuring to the development of multiplicative thinking. (ASK)

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

Utilizes the psychological and sociocultural components of a constructivist paradigm to provide a detailed analysis of how the cognitive constructions students make as they enumerate 3D arrays of cubes develop and change in an inquiry-based, problem-centered mathematics classroom. Describes the classroom work of three pairs of 5th-grade students…

Investigates gender differences and the role of spatial visualization in problem solving in high school geometry. Reports that, whereas males and females differed in spatial visualization and in their performance, they did not differ in logical reasoning ability or in their use of geometric problem-solving strategies. (Author)