The van Hiele Model of Geometric Thinking is a well-known and widely used framework in mathematics education. It was developed by Dina van Hiele-Geldof and Pierre van Hiele in the 1950s and 1960s (Uyen et al., 2021). The model describes the levels of geometric thinking that individuals progress through as they develop their understanding of geometry. According to the van Hiele Model, there are five levels of geometric thinking: Visualization, Analysis, Informal Deduction, Formal Deduction, and Rigor (Uyen et al., 2021).

At the Visualization level, learners are able to recognize and describe geometric shapes and figures based on their appearance and properties. They can identify basic shapes and understand their attributes (Uyen et al., 2021). This level is characterized by visual perception and recognition of shapes. Students at this level may struggle with understanding the relationships between shapes and may have difficulty making connections between different geometric concepts (Wang, 2016).

At the Analysis level, learners begin to explore the properties and relationships of geometric shapes and figures. They can compare and classify shapes based on their properties and identify patterns and relationships between shapes (Uyen et al., 2021). This level involves the ability to analyze and compare geometric properties. Students at this level may still rely heavily on visual cues and may struggle with abstract reasoning (Wang, 2016).

At the Informal Deduction level, learners start to make logical deductions and draw conclusions based on their understanding of geometric properties and relationships. They can use informal reasoning to solve geometric problems and prove simple geometric statements (Uyen et al., 2021). This level involves the ability to make logical deductions and construct informal proofs. Students at this level may still have difficulty with more complex geometric concepts and may struggle with constructing formal proofs (Wang, 2016).

At the Formal Deduction level, learners are able to construct formal proofs and use deductive reasoning to solve geometric problems. They can apply formal logic and axiomatic systems to prove geometric theorems and properties (Uyen et al., 2021). This level involves the ability to construct formal proofs and use deductive reasoning. Students at this level may still struggle with more abstract and advanced geometric concepts (Wang, 2016).

At the Rigor level, learners have a deep and comprehensive understanding of geometry. They can apply advanced mathematical concepts and techniques to solve complex geometric problems and prove advanced theorems (Uyen et al., 2021). This level involves the ability to apply advanced mathematical concepts and techniques. Students at this level have a high level of geometric thinking and can engage in sophisticated geometric reasoning (Wang, 2016).

The van Hiele Model of Geometric Thinking provides a framework for understanding the progression of geometric thinking and can inform instructional design in mathematics education. Research has shown that instruction based on the van Hiele Model can improve students’ geometric thinking levels (Abdullah et al., 2015). For example, a study by Abdullah et al. (2014) found that teaching geometry using the van Hiele phases resulted in improved geometric achievement and attitude towards geometry among students (Abdullah et al., 2014). Another study by (2011) developed instructional modules based on the van Hiele phases and found that they were effective in moving learners from one thinking level to the next (Atebe & Schäfer, 2011).

In addition to instructional design, the van Hiele Model can also be used to investigate teaching strategies and assess students’ geometric thinking levels. For example, Armah & Kissi (2019) used the van Hiele Model to investigate teaching strategies used by geometry tutors in college of education and found that the integration of the van Hiele Model in teaching can enable pre-service teachers to operate at higher levels of geometric conceptualization (Armah & Kissi, 2019). Similarly, a study by Ma et al. (2015) explored gender differences and passing rates of van Hiele’s geometric thinking levels among elementary school students (Ma et al., 2015).

Furthermore, research has shown that the van Hiele Model is not only applicable to traditional classroom settings but can also be used in technology-enhanced learning environments. For instance, Abdullah & Zakaria (2013) used the Geometer’s Sketchpad software to implement the van Hiele phases of learning geometry and found that it had a positive effect on students’ levels of geometric thinking (Abdullah & Zakaria, 2013). Another study by Abu & Ali (2012) used Google SketchUp to assist primary school children in progressing through their van Hiele levels of geometry thinking (Abu & Ali, 2012).

Overall, the van Hiele Model of Geometric Thinking provides a valuable framework for understanding and promoting the development of geometric thinking in learners. It can inform instructional design, teaching strategies, and assessment practices in mathematics education. By considering the different levels of geometric thinking described by the van Hiele Model, educators can design effective learning experiences that support students’ progression through the levels and promote deep understanding of geometry.

References:

  1. Uyen, B. P., Ngan, L. K., Kim, Y. H., & Tong, D. H. (2021). Impulsing the development of students’ competency related to mathematical thinking and reasoning through teaching straight-line equations. International Journal of Learning, Teaching and Educational Research, 20(6), 38-65. https://doi.org/10.26803/ijlter.20.6.3
  2. Wang, S. (2016). Discourse perspective of geometric thoughts.. https://doi.org/10.1007/978-3-658-12805-0
  3. Abdullah, A. H., Surif, J., Tahir, L. M., Ibrahim, N. A., & Zakaria, E. (2015). Enhancing students’ geometrical thinking levels through van hiele’s phase-based geometer’s sketchpad-aided learning. 2015 IEEE 7th International Conference on Engineering Education (ICEED). https://doi.org/10.1109/iceed.2015.7451502
  4. Abdullah, A. H., Ibrahim, N. A., Surif, J., & Zakaria, E. (2014). The effects of van hiele’s phase-based learning on students’ geometric achievement and attitude towards geometry. 2014 International Conference on Teaching and Learning in Computing and Engineering. https://doi.org/10.1109/latice.2014.67
  5. Atebe, H. U. and Schäfer, M. (2011). The nature of geometry instruction and observed learning-outcomes opportunities in nigerian and south african high schools. African Journal of Research in Mathematics, Science and Technology Education, 15(2), 191-204. https://doi.org/10.1080/10288457.2011.10740712
  6. Armah, R. B. and Kissi, P. S. (2019). Use of the van hiele theory in investigating teaching strategies used by college of education geometry tutors. EURASIA Journal of Mathematics, Science and Technology Education, 15(4). https://doi.org/10.29333/ejmste/103562
  7. Ma, H., Lee, D. C., Lin, S., & Wu, D. (2015). A study of van hiele of geometric thinking among 1st through 6th graders. EURASIA Journal of Mathematics, Science and Technology Education, 11(5). https://doi.org/10.12973/eurasia.2015.1412a
  8. Abdullah, A. H. and Zakaria, E. (2013). The effects of van hiele’s phase-based instruction using the geometer’s sketchpad (gsp) on students’ levels of geometric thinking. Research Journal of Applied Sciences, Engineering and Technology, 5(5), 1652-1660. https://doi.org/10.19026/rjaset.5.4919
  9. Abu, M. S. and Ali, M. B. (2012). Assisting primary school children to progress through their van hiele’s levels of geometry thinking using google sketchup. Procedia – Social and Behavioral Sciences, 64, 75-84. https://doi.org/10.1016/j.sbspro.2012.11.010