Van Hiele Levels of Geometric Reasoning

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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