The Van Hiele Theory: Levels of Geometric Thinking
Keywords:
understanding, reasoning, geometry, learning, van Hiele levels
Abstract
In this article we describe the key elements of the van Hiele theory, which is useful for analyzing the process of students' cognitive growth. Particularly we expose the characteristics of each one of five levels of thinking that students grow through in acquiring competence and understanding of geometrical ideas, and the teaching phases that assist students to move through the levels. The van Hiele theory is useful to explain why students show several difficulties to understand geometry, and provides useful suggestions to design learning scenarios that can favor development of high-level cognitive processes.
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References
Burger, W. F. & Shaughnessy, J. M. (1986). Characterizing the van Hiele Levels of Development in Geometry. Journal for Research in Mathematics Education, 17(1), 31-48.
Crowley, M.L. (1987). The van Hiele model of the development of geometric thought. En M. M. Lindquist (Ed.), Learning and teaching geometry, K-12 (pp. 1-16). Reston, VA: National Council of Teachers of Mathematics.
Fuys, D., Geddes, D. &Tischler, R. (1988).The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph Number 3. Reston, VA: National Council of Teachers of Mathematics.
Guillén-Soler, G. (2004). El modelo de van Hiele aplicado a la geometría de los sólidos: describir, clasificar, definir y demostrar como componentes de la actividad matemática. Educación Matemática, 16(3), 103-125.
Gutiérrez, A. & Jaime, A. (1988). On the assessment of the van Hiele levels of reasoning. Focus on Learning Problems in Mathematics, 20(2, 3), 27-46.
Peg, J. (2014). The van Hiele theory. En S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 613-615). Dordrecht: Springer.
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). Chicago, IL: University of Chicago, Department of Education.
van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 6, 310-316.
Zambrano, M. A. (2006). El razonamiento geométrico y la teoría de van Hiele. Kaleidoscopio, 3(5), 28-33.
Crowley, M.L. (1987). The van Hiele model of the development of geometric thought. En M. M. Lindquist (Ed.), Learning and teaching geometry, K-12 (pp. 1-16). Reston, VA: National Council of Teachers of Mathematics.
Fuys, D., Geddes, D. &Tischler, R. (1988).The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph Number 3. Reston, VA: National Council of Teachers of Mathematics.
Guillén-Soler, G. (2004). El modelo de van Hiele aplicado a la geometría de los sólidos: describir, clasificar, definir y demostrar como componentes de la actividad matemática. Educación Matemática, 16(3), 103-125.
Gutiérrez, A. & Jaime, A. (1988). On the assessment of the van Hiele levels of reasoning. Focus on Learning Problems in Mathematics, 20(2, 3), 27-46.
Peg, J. (2014). The van Hiele theory. En S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 613-615). Dordrecht: Springer.
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). Chicago, IL: University of Chicago, Department of Education.
van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 6, 310-316.
Zambrano, M. A. (2006). El razonamiento geométrico y la teoría de van Hiele. Kaleidoscopio, 3(5), 28-33.
Published
2015-07-05
How to Cite
Barrera Mora, F., & Reyes Rodríguez, A. (2015). The Van Hiele Theory: Levels of Geometric Thinking. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 3(5). https://doi.org/10.29057/icbi.v3i5.554
Section
Research papers
