Van Hiele Levels and Achievement in Writing Geometry Proofs

Abstract

This study investigated relations between van Hiele levels, achievement in writing geometry proofs, and achievement in standard geometry content. Two hundred forty-one secondary school students who were enrolled in full-year geometry classes were tested in the fall for van Hiele level of thinking and entering knowledge of geometry, and in the spring for van Hiele level, standardized geometry achievement, and proof-writing achievement. Proof-writing achievement correlated significantly, .5 with fall van Hiele level, .6 with spring van Hiele level and with entering knowledge of geometry, and .7 with standardized geometry achievement in the spring. Proof-writing achievement also varied significantly with van Hiele level when either entering knowledge of geometry or geometry achievement in the spring was used as a covariate. The predictive validity of the van Hiele model was supported. However, the hypothesis that only students at Levels 4 or 5 can write proofs was not supported.