Let's know more about Van Hiele model and Piaget stages!

 

Hello guys! In this post we will talk about Van Hiele model and Piaget stages regarding geometry. 

Geometry is more than shapes and measurements—it's about developing spatial reasoning and logical thinking. One of the most influential frameworks for teaching geometry is the Van Hiele Model, developed by Dutch educators Pierre and Dina van Hiele. This model outlines how students progress in their understanding of geometric concepts, offering valuable insight into how to design effective instruction, but who was Van Hiele?

The Van Hiele model consists of five levels of geometric thinking. Each level represents a different way students perceive and understand shapes and their properties. The progression is sequential: students must master one level before advancing to the next.

Here you have the explanation of each level: 

1. Level 0 (Visualization): At this stage, students recognize shapes based on how they look, not on their properties. In a classroom we can use drawing, sorting or shape hunts in order to strengthen recognition. 
2. Level 1 (Analysis): At this stage, students start to notice and name properties like number of sides, angles, and lengths. In a classroom, we can encourage the use of tools like rulers and protractors to explore shapes. 
3. Level 2 (Abstraction): At this stage, students begin to understand relationships between properties and between shapes. In a classroom we can encourage comparison between figures, classification and questions to develop critical thinking.
4. Level 3 (Deduction): At this stage, students can understand and work with theorems and logical sequences. In a classroom we can practice with theorems and constructing geometric proofs. 
5. Level 4 (Rigor): This stage is quite advanced, students can reason about multiple systems of geometry and analyze the logic behind them. This level would correspond to university students or beyond. 

How can we identify your students’ Van Hiele Level? 

First of all, you have to take into account the language of the students, I mean, pay attention to the words that the students use when describing shapes. For example, two students are looking at a square, the first student says: “it looks like a square (level 0)” and the second student says: “all squares are rectangles but not all rectangles are squares (level 2)”.

Also, you could try a Van Hiele diagnostic test. This is a simple research-based test designed to identify these levels, one popular version includes multiple choice and one response items based on recognizing and analyzing shapes; understanding relationships between shapes and making logical arguments about them. 

On the other hand, Piaget stages have a different vission about how a human develop their knoelgede about geometry, here you can see the information: 

 

https://www.canva.com/design/DAGnuSH3PUg/9H8CvfzmgjLsHNhkmOUFdA/edit?utm_content=DAGnuSH3PUg&utm_campaign=designshare&utm_medium=link2&utm_source=sharebutton

Here you can find a video about Piaget stages: 

That is all for today's post, I hope you have enjoyed it. I will see you soon!

References: 

Jaime, A., y Gutiérrez, A. (1990). Una propuesta de fundamentación para la enseñanza de la geometría: El modelo de van Hiele. En S. Llinares y M. V. Sánchez (Eds.), Teoría y práctica en educación matemática (pp. 295-384). Sevilla: Alfar. www.uv.es/angel.gutierrez/archivos1/textospdf/JaiGut90.pdf.

Lourenço, O. M. (2016). Developmental stages, Piagetian stages in particular: A critical review. New Ideas in Psychology, 40, 123-137. https://www.researchgate.net/profile/Orlando-Lourenco/publication/283771814_Developmental_stages_Piagetian_stages_in_particular_A_critical_review/links/5a05f7730f7e9b682299017d/Developmental-stages-Piagetian-stages-in-particular-A-critical-review.pdf