This article helps educators answer questions about geometric thinking and the activities that develop it. It outlines the 3 levels of thinking about shape and space and the 5 phases of activities known as the van Hiele model. The tangram puzzle provides a vehicle for describing these phases and the types of thinking students achieve in each one. The article concludes with a suggestion about followup activity.
Keywords:Grade 2,Visualization,Scale,Make use of structure,NSDL,Grade 4,Grade 3,Critical thinking,Early Elementary,Spatial sense,Kindergarten,Grade 1,Quadrilaterals,Visual representation,Mathematics,oai:nsdl.org:2200/20140728161219476T,Analyze and persevere,Concept formation,Process skills,Inductive reasoning,Mathematical language,Angles,Modeling,Vocational/Professional Development Education,NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-027,Geometry,Reason abstractly,Practice Standards,Elementary School,Representation,Upper Elementary,Communication,Congruence,Plane geometry,Engineering,Problem solving,Education,Reasoning,Triangles