Geometric Understanding and Misconceptions among Gifted Fourth-Eighth Graders

The Van Hiele theory asserts that there exist five hierarchical levels of geometric thinking that a successful learner passes through. The purpose of the study described in this paper was to investigate the geometric understanding and misconceptions in students in the fourth through eighth grades who have been identified as gifted. The students were selected based on intelligence quotient or standardized test scores, teacher recommendations, and other instruments chosen by school districts. Group 1 received 20 hours of instruction in geometry using LOGO. Group 2 attended a 1-week summer camp having 7 hours of geometry instruction and activities. The change in the Van Hiele level between pretest and posttest was significant for both groups. Analysis of the protocols from interviews indicates three categories of reasoning, the relationship between reasoning and knowledge of definitions, and reasoning involving parts of figures. Several implications for mathematics instruction are discussed. Seven references are listed. (YP)