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)....
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References
Burger WF, Shaughnessy JM (1986) Characterizing the van Hiele levels of development in geometry. J Res Math Educ 17:31–48
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 420–464
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 287 697
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, USA
Hoffer A (1981) Geometry is more than proof. Math Teach 74:11–18
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, Columbus
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 Unpublished doctoral Dissertation, University of Georgia.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)
Pegg J (2002) Learning and teaching geometry. In: Grimison L, Pegg J (eds) Teaching secondary mathematics: theory into practice. Nelson Thomson Publishing, Melbourne, pp 87–103
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Piaget J, Inhelder B, Szeminska A (1960) The child’s conception of geometry. Basic Books, New York
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, Chicago
Van Hiele PM (1986) Structure and insight: a theory of mathematics education. Academic, New York
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Pegg, J. (2020). van Hiele Theory, The. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_183
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