RELATIONSHIPS BETWEEN STAGE OF COGNITIVE DEVELOPMENT AND VAN HIELE LEVEL OF GEOMETRIC THOUGHT AMONG PUERTO RICAN ADOLESCENTS

LIVIA P DENIS, Fordham University

Abstract

The purpose of this descriptive study was to explore the relationship between Piagetian stage of cognitive development and van Hiele level of geometric thought among Puerto Rican adolescents.^ Subjects who had already taken the high school Euclidean geometry course and were enrolled in a special experimental/demonstration school were identified. From this accessible population, 156 participated in the final study.^ Subjects were classified as being in concrete-operational or formal-operational stages of development. Only 36% of the subjects were found to be in the formal-operational stage of development. Twenty from each group were randomly selected, and their van Hiele level of geometric thought development was determined.^ Guttman Scalogram, Consensus, and Chi-square analyses were made to test the hypotheses of the study. The results were: (a) the van Hiele levels are hierarchical among subjects in the formal-operational stage, concrete-operational stage, and across their Piagetian stage of development; (b) no consensus across concepts under study was found in van Hiele level of subjects; (c) there was a significant difference between means highest van Hiele level reached by subjects at the two Piagetian developmental stages.^ More than 74% of the high school geometry students were found to be not capable for dealing with the demands of traditional high school Euclidean geometry course.^ Some implications of the study are: (a) the geometry curriculum needs to be revised to provide experiences for developing subjects van Hiele levels of geometric thought by concept; (b) provisions should be made to determine periodically students' Piagetian stage of development.^ Although a subject at a formal-operational stage of development may move faster through the van Hiele levels, it is necessary to use questions and answers in class to determine the actual van Hiele level by concept, to provide experiences corresponding with actual van Hiele level, and to facilitate movement through the van Hiele levels.^ It was predicted that movement to higher van Hiele levels would be reflected in the subjects' change in the Piagetian stage of cognitive development. ^

Subject Area

Mathematics education

Recommended Citation

DENIS, LIVIA P, "RELATIONSHIPS BETWEEN STAGE OF COGNITIVE DEVELOPMENT AND VAN HIELE LEVEL OF GEOMETRIC THOUGHT AMONG PUERTO RICAN ADOLESCENTS" (1987). ETD Collection for Fordham University. AAI8715795.
http://fordham.bepress.com/dissertations/AAI8715795

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