1.  Van Hiele Levels Math Alliance September 14, 2010 Kevin McLeod Chris Guthrie

2. Van Hiele Levels of Geometric Reasoning  Level 0: Visualization  Level 1: Analysis (Description)  Level 2: Informal Deduction  Level 3: Formal Deduction  Level 4: Rigor

3. 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”.)

4. 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 …”.)

5. 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”.)

6. 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.

7. 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).