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Van Hiele model


In mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The theory originated in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele (wife and husband) at Utrecht University, in the Netherlands. The Soviets did research on the theory in the 1960s and integrated their findings into their curricula. American researchers did several large studies on the van Hiele theory in the late 1970s and early 1980s, concluding that students' low van Hiele levels made it difficult to succeed in proof-oriented geometry courses and advising better preparation at earlier grade levels. Pierre van Hiele published Structure and Insight in 1986, further describing his theory. The model has greatly influenced geometry curricula throughout the world through emphasis on analyzing properties and classification of shapes at early grade levels. In the United States, the theory has influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics and the new Common Core Standards.

The student learns by rote to operate with [mathematical] relations that he does not understand, and of which he has not seen the origin…. Therefore the system of relations is an independent construction having no rapport with other experiences of the child. This means that the student knows only what has been taught to him and what has been deduced from it. He has not learned to establish connections between the system and the sensory world. He will not know how to apply what he has learned in a new situation. - Pierre van Hiele, 1959

The best known part of the van Hiele model are the five levels which the van Hieles postulated to describe how children learn to reason in geometry. Students cannot be expected to prove geometric theorems until they have built up an extensive understanding of the systems of relationships between geometric ideas. These systems cannot be learned by rote, but must be developed through familiarity by experiencing numerous examples and counterexamples, the various properties of geometric figures, the relationships between the properties, and how these properties are ordered. The five levels postulated by the van Hieles describe how students advance through this understanding.


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