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
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Definition

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)....

Keywords

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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References

  1. Burger WF, Shaughnessy JM (1986) Characterizing the van Hiele levels of development in geometry. J Res Math Educ 17:31–48CrossRefGoogle Scholar
  2. Clements D, Battista M (1992) Geometry and spatial reasoning. In: Grouws D (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 420–464Google Scholar
  3. Fuys D, Geddes D, Tischler R (1984) English Translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele. Brooklyn College. (ERIC Document Reproduction Service No. ED 287 697Google Scholar
  4. Fuys D, Geddes D, Tischler R (1988) The van Hiele model of thinking in geometry among adolescents. J Res Math Educ Monogr 3, pp i+1–196 NCTM, Reston, VA, USAGoogle Scholar
  5. Hoffer A (1981) Geometry is more than proof. Math Teach 74:11–18Google Scholar
  6. Lesh R, Mierkiewicz D (1978) Perception, imaging and conception in geometry. In: Lesh R, Mierkiewicz D (eds) Recent research concerning the development of spatial and geometric concepts. ERIC, ColumbusGoogle Scholar
  7. Mayberry J (1981) An Investigation of the van Hiele levels of geometric thought in undergraduate preservice teachers. Unpublished doctoral Dissertation, University of Georgia. (University Microfilms No. DA 8123078)Google Scholar
  8. Pegg J (2002) Learning and teaching geometry. In: Grimison L, Pegg J (eds) Teaching secondary mathematics: theory into practice. Nelson Thomson Publishing, Melbourne, pp 87–103Google Scholar
  9. Pegg J, Davey G (1998) Interpreting student understanding in geometry: a synthesis of two models. In: Lehrer R, Chazan C (eds) Designing learning environments for developing understanding of geometry and space. Lawrence Erlbaum, Mahwah, pp 109–135Google Scholar
  10. Piaget J, Inhelder B, Szeminska A (1960) The child’s conception of geometry. Basic Books, New YorkGoogle Scholar
  11. Usiskin Z (1982) Van Hiele levels and achievement in secondary school geometry (final report of the cognitive development and achievement in secondary school geometry project). University of Chicago/Department of Education, ChicagoGoogle Scholar
  12. Van Hiele PM (1986) Structure and insight: a theory of mathematics education. Academic, New YorkGoogle Scholar

Copyright information

© 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