In mathematics education, the Van Hiele model is a theory describing how students learn geometry, originating in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele, a wife-and-husband team, at Utrecht University in the Netherlands. Soviet researchers studied the theory in the 1960s and folded their findings into their own curricula, and American researchers ran several large studies on it in the late 1970s and early 1980s, concluding that students at low Van Hiele levels struggled to succeed in proof-oriented geometry courses and recommending better preparation at earlier grade levels. Pierre van Hiele published Structure and Insight in 1986, elaborating the theory further. The model has strongly shaped geometry curricula worldwide by emphasizing the analysis of shape properties and classification at early grade levels, and in the United States it has influenced the geometry strand of the National Council of Teachers of Mathematics standards and the Common Core Standards.
Facts
Core ClaimStudents move through five hierarchical levels of geometric understanding and cannot be expected to prove theorems until the earlier levels have built the relational understanding a proof depends on. 1 Sources
1. Van Hiele model (Wikipedia)
Wikimedia FoundationHistory section, 1957 origin statement
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.
Levels section, rationale for the hierarchy
Students cannot be expected to prove geometric theorems until they have built up an extensive understanding of the systems of relationships between geometric ideas.
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