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The interactive Mind Map of the Van Hiele Model of Geometric Thought is an image-centered diagram that represents connections between various topics and concepts related to van Hiele theory, one of the best-known framework presently available for studying teaching-learning process in geometry. Using the van Hiele model as a basis, the users will know how students understand geometric concepts and how to determine the reasoning levels of these students. Although not universally accepted by all North American educators, the van Hiele model is mathematically elegant and worthy of investigation.

Van Hiele levels  are a product of experience rather than age. In other words, a child must have enough experiences (classroom or otherwise) with these geometric ideas to move to a higher level of sophistication.

• Level 0. (Basic Level) Visualization: children identify prototypes of basic geometrical figures (triangle, circle, square). At this age (or stage), children might balk at calling a thin, wedge-shaped triangle (with sides 1, 20, 20 or sides 20, 20, 39) a "triangle", because it's so different in shape from an equilateral triangle.

• Level 1. Analysis: children can discuss the properties of the basic figures and recognize them by these properties, but might still insist that "a square is not a rectangle."

• Level 2. Abstraction: learners recognize relationships between types of shapes. They recognize that all squares are rectangles, but not all rectangles are squares. They can tell whether it is possible or not to have a rectangle that is, for example, also a rhombus. Students need to be comfortably at this level to be well prepared for a high school geometry course (though many students are not). One of our goals in this class will be to consider ways that we can help children progress to a level 2 understanding of some important geometric topics.

• Level 3. Deduction: learners can construct geometric proofs at a high school level. Learners should be exposed to deduction at a pre-high-school level in the context of level 2 discussions (what properties tell us that all squares are also rectangles), but the primary consideration of level 3 work will not be discussed in this course.

• Level 4. Rigor: learners understand how geometry proofs and concepts fit together to create the structure we call geometry. This is the level at which most college geometry courses (for math majors) are designed.

Last updated: April 26, 2010.