Encyclopedia of Mathematics Education

2020 Edition
| Editors: Stephen Lerman

van Hiele Theory, The

  • John PeggEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-030-15789-0_183


The van Hiele theory offers a framework that describes how students learn geometry.

The van Hiele theory had its beginnings in the 1950s in the companion doctoral work of husband and wife team Pierre van Hiele and Dina van Hiele-Geldof. Dina died in 1958. Pierre continued to develop and refine the theory that is explored thoroughly in his 1986 book, Structure and Insight. Pierre died in 2010 at the age of 101.

Much of the resurgence of interest in the teaching of geometry that began in the 1980s and 1990s can be traced to the ideas developed in the van Hiele theory. Detailed accounts and summaries of this early, but still highly relevant, work can be found in the following, e.g., Burger and Shaughnessy (1986), Clements and Battista (1992), Fuys et al. (1988), Hoffer (1981), Lesh and Mierkiewicz (1978), Mayberry (1981), and Usiskin (1982).

The theory has two main aspects that combine to provide a philosophy of mathematics education (even though the emphasis is on geometry)....


Van Hiele theory Philosophy of mathematics education Geometry Levels of thinking Teaching phases Cognitive growth Role of language Develop student understanding 
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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.SiMERR National Research CentreUniversity of New EnglandArmidaleAustralia

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA