Pierre van Hiele and Dieke van Hiele-Geldof, mathematics teachers from the Netherlands, observed their geometry students in the 1950's. They describe five levels of geometrical reasoning, which are sequential and hierarchical. Progress from one level to the next is more dependent on mathematical experiences than chronological age.

DESCRIPTION

Recognize basic shapes by appearance without attention to parts, attributes, or propertiesRefer to visual prototypes such as doors, balls, and signs

• Examine examples and non-examples
• Find "hidden" figures
• Rearranging into other shapes
• Tangrams
• Mosaic puzzle