# Van Hiele Levels of Geometric Reasoning

Van Hiele Levels Math Alliance September 14, 2010 Kevin McLeod Chris Guthrie Van Hiele Levels of Geometric Reasoning

Level 0: Visualization Level 1: Analysis (Description) Level 2: Informal Deduction

Level 3: Formal Deduction Level 4: Rigor Van Hiele Levels of Geometric Reasoning Level 0: Visualization

Students see shapes as total entities, but do not recognize properties (Its a rectangle, because it looks like a door.) Van Hiele Levels of Geometric Reasoning Level 1: Analysis Students identify properties of figures, and see figures as a class of shapes (Its a rectangle, because it has one long set of sides and

one short set of sides, and opposite sides are parallel, and .) Van Hiele Levels of Geometric Reasoning Level 2: Informal deduction Students recognize relationships between properties of shapes, and between classes of shapes; they also develop informal explanations using these relationships.

(Its a rectangle, because it is a quadrilateral with four right angles.) Van Hiele Levels of Geometric Reasoning Level 3: Formal Deduction Students understand the significance of deduction as a way of establishing geometric theory within an axiom system; they also see the interrelationship and role of undefined terms, axioms, theorems, and

formal proof. Van Hiele Levels of Geometric Reasoning Level 4: Rigor Students see geometry in the abstract, even without concrete examples; they compare geometric results in different axiom systems (non-Euclidean geometries).

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