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).