1. Students can identify objects by their overall shape. They need to see many examples and non-examples. Van Hiele Model of Geometric Understanding Level 0: Visualization

2. Level 1: Analysis Students can discuss the parts that make up an object. They need to measure, fold, cut, compare. Van Hiele Model of Geometric Understanding

3. Level 2: Informal Deduction Students can explain how parts relate to each other. They can recognize class inclusion (e.g. All squares are parallelograms.). This is the lowest level at which a definition is meaningful. Van Hiele Model of Geometric Understanding

4. Level 3: Formal Deduction Students can use deductive arguments (proofs) to confirm their conjectures. Van Hiele Model of Geometric Understanding

5. Characteristics of the model The levels are sequential. Students cannot “skip a level.” If the level of teaching and the level of understanding are different, little learning will take place. Van Hiele Model of Geometric Understanding

6. The levels start with an inductive approach and work toward a deductive approach. Students begin with many individual examples of a geometric object. As they progress, they recognize commonalities that allows them to consider classes of objects. Examination of individual examples also allows students to make conjectures. They they must move to a deductive level in order to prove or disprove their conjectures. Van Hiele Model of Geometric Understanding