Abstract
Mathematically talented students typically begin the traditional precalculus sequence by completing Algebra I in seventh grade or earlier. Consequently, they enroll in geometry early based on their successful completion of Algebra I. Little or no attention is paid to their readiness for geometry as indicated by such measures as their van Hiele level of geometric understanding. Logical reasoning ability is a characteristic often used to identify mathematically talented students, but how it applies to reasoning about geometry is unknown. This study investigated the geometric understanding and reasoning about geometry of mathematically talented students in the sixth through eighth grades prior to a formal course in geometry. This paper describes and analyzes the responses from 120 students who completed the van Hiele Geometry Test, developed by the Cognitive Development and Achievement in Secondary School Geometry Project (Usiskin, 1982), and 64 students who participated in 30–45 minute individual interviews, using an abbreviated version of Mayberry's van Hiele protocols.
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