The Effects of a Piagetian Geometry Model on Beginning School Children

According to Piaget, intuitive ideas of topology develop in the child before Euclidean and projective geometry. The emphasis in this study was to provide an in-depth investigation of a young child's understanding of selected geometric ideas through a descriptive, subjective evaluation. Specifically, the objective was to determine if a group of five year- old and eight-year-old students' understanding of selected geometric ideas paralleled Piaget's topological, projective and Euclidean thesis; to investigate which geometric ideas the group learned easiest as a result of intervening and teaching certain concepts; and to examine the relationship of geometry understanding to the factors of age, ability and approaches.

The sample in this study consisted of 24 beginning school children, 12 five-year olds and 12 eight-year olds, enrolled in a private school in Charlottesville, Virginia. The group was categorized according to high mathematical ability or low mathematical ability as determined by standardized tests.

To achieve the objective of this study, a test instrument, a pretest and posttest composed of three topological, three projective and three Euclidean ideas was abstracted from Piaget's research and developed by the investigator. These ideas were considered compatible for the age group studied.

Results of the descriptive, subjective evaluation that were confirmed by a statistical analysis indicate a topological, projective and Euclidean progression advanced by Piaget. Recommendations are offered for incorporating selected geometric ideas into the elementary school program, and for providing additional valuable developmental research in mathematics education.