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Van Hiele LevelsMath Alliance
September 14, 2010
Kevin McLeodChris 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
(“It’s 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
(“It’s 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.
(“It’s 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).