Geometric Understanding in Gifted Students Prior to a Formal Course in Geometry

This study investigated whether the van Hiele model accurately describes the geometric thinking of gifted students in the 6th through 8th grades prior to a formal course in geometry and made comparisons with what has been found with other populations. The results from 120 students who completed a 25-item multiple choice paper-and-pencil test, developed by the Cognitive Development and Achievement in Secondary School Geometry Project, and 64 students who participated in 30-45 minute individual interviews were analyzed. Although the responses of the students on the multiple-choice test did form a hierarchy overall, 35.8% of the gifted students tested skipped levels in the van Hiele model. Analysis of the clinical interviews confirmed that individuals do not demonstrate the same level of thinking in all areas of geometry. Many of the students lacked correct basic definitions of terms such as congruent and similar, but they attempted to deduce the definitions from contextual clues. Once they established a definition, correct or incorrect, most students reasoned consistently from it. Although reasoning was a strength of most of the subjects, they did not know how to construct an acceptable formal geometric proof. (Author)