Geometry Trajectory It All Together –Putting Each concept builds on the previous idea and students should explore and construct concepts in such a sequence Level 0 *Kindergarten Level Level 1 Analysis Level 2 Information Level 3 Deduction Level 4 Rigor Deduction Visualization The object of thought is The objects of The objects of classes of shapes. thought are the thought are the The objects of thought are The object of thought (focus) is relationships deductive the properties. Students consider all shapes the properties. axiomatic systems. individual shapes. – in a class instead of an Students understand that – individual example. The products of The products of Students are operating on – properties are related. thought are the thought are specific examples of the shapes What makes a shape – “a deductive comparisons and they see. One set of properties – WALLE shape”? may relate to another axiomatic systems. contrasts among DE Orientation may even change – different axiomatic property. DE The outcome is discovering what a student observes. systems of VAN properties of shapes. Students can understand – geometry. VAN The goal is to see likenesses – logical reasoning about the Focus on properties. – and differences. properties. Apply ideas to entire classes – of figures. The outcomes are relationships properties. Adapted from the and taken from van de Walle & Lovin van Hiele Levels of Geometric Thought Teaching Student-entered Mathematics (k-3) The Big Picture in Kindergarten
Geometry Trajectory –Putting It All Together Each concept builds on the previous idea and students should explore and construct concepts in such a sequence VAN DE WALLE VAN DE Level 0 *Kindergarten Level Visualization The object of thought (focus) is individual shapes. – Students are operating on specific examples of the shapes they see. – Orientation may even change what a student observes. – The goal is to see likenesses and differences. Level 1 Analysis The object of thought is classes of shapes. – Students consider all shapes in a class instead of an individual example. – What makes a shape “a shape”? The outcome is discovering properties of shapes. – Focus on properties. – Apply ideas to entire classes of figures. Level 2 Information Deduction The objects of thought are the properties. – Students understand that properties are related. – One set of properties may relate to another property. – Students can understand logical reasoning about the properties. The outcomes are relationships properties. Level 3 Deduction The objects of thought are the relationships the properties. The products of thought are the deductive axiomatic systems. Level 4 Rigor The objects of thought are the deductive axiomatic systems. The products of thought are comparisons and contrasts among different axiomatic systems of geometry. Adapted from the van Hiele Levels of Geometric Thought and taken from van de Walle & Lovin Teaching Student-entered Mathematics (k-3) The Big Picture in Kindergarten
CCGPS_Math_K_Unit1Framework.docx