A Comparison of U.S. and Chinese Geometry Standards through the Lens of van Hiele Levels

Abstract

The present study aims to compare the geometry standards in U.S. Common Core State Standards of Mathematics (CCSSM) and Chinese Compulsory Education Mathematics Curriculum Standards (CMCS) through the lens of van Hiele levels. The study considered a standard unit as one or multiple learning expectation(s) and placed each learning expectation into van Hiele levels. By examining the van Hiele level distributions of the learning expectations and major topics, this study investigated how CCSSM and CMCS propose the students' development of geometric thoughts. The findings reveal different emphases in geometry learning expectations of CCSSM and CMCS. Specifically, (a) Geometry standards in CCSSM are more general, whereas geometry standards in CMCS are more specific; (b) CMCS shows a more consistent progression through grade bands than CCSSM; (c) CCSSM makes more connections between various aspects within a topic and across multiple topics than CMCS; (d) CCSSM highlights Dynamic Geometry Environments (DGEs), whereas CMCS underscores abstract and rigor at the upper level. Implications of this study and suggestions for future revisions for both standards are discussed.