Secondary students' performance on Piagetian projective and Euclidean spatial tasks

Four tasks involving Piaget's Euclidean and projective space were administered to a total of 99 students in Grades 8, 10, and 12: Task 1, Volumes of Revolution; Task 2, Geometric Sections; Task 3, Folding Patterns; and Task 4, Projection of Shadows. A scalogram analysis indicated that the tasks scaled in increasing order of difficulty in the following order: Task 1, Task 4, Task 2, and Task 3. These results did not support Piaget's position that projective and Euclidean concepts develop concurrently. Also, significant differences between task performance with regard to gender were found for Tasks 3 and 4. Significant differences between task performance and grade level for Tasks 1 and 4 were found. Standardized achievement test performance and task performance relationships were significant in 3 of the 16 analyses.