Mitchelmore and Outhred , p. The theory originated in in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele wife and husband at Utrecht University , in the Netherlands. Draw a right angle 4. Johnston-Wilder and Mason suggest that Geometry is given less teaching time in the classroom than other disciplines. Learners can construct geometric proofs at a secondary school level and understand their meaning. I have used a mixed methods paradigm in my collection of data. Without such experiences, many adults including teachers remain in Level 1 all their lives, even if they take a formal geometry course in secondary school.

Throughout the research study, an ethical approach was followed at all times See Appendix 5, p. People can understand the discipline of geometry and how it differs philosophically from non-mathematical studies. Geometric ideas are still understood as objects in the Euclidean plane. Students can reason with simple arguments about geometric figures. By using this site, you agree to the Terms of Use and Privacy Policy. The study also draws on theoretical frameworks from eminent researchers like Vygotsky, Piaget and Bruner as well as engaging fully with current educational literature and research. For Dina van Hiele-Geldof’s doctoral dissertation, she conducted a teaching experiment with year-olds in a Montessori secondary school in the Netherlands.

Van Hiele model – Wikipedia

This is exemplified by the duality of my approach in analysing task 4 where participants are asked to draw a rectangle that looks visually appealing. I have few recollections of studying shape topics; many of my lessons were orientated on Number and Algebra. A person at this level might say, “A square has 4 equal sides and 4 equal angles.

There may be a finite thseis of geometrical reasoning that a student can reach and that their understanding of Geometry will eventually plateau. It was found that geometrical ability increases with age although young children can display sophisticated knowledge of shape and that students mainly drew shapes of a non-prototypical orientation.

My model of research is not essentially interactive as it is being individually conducted by me. The best known part of the van Hiele model are the five levels which the van Hieles postulated to describe how children learn to reason in geometry.


If a shape does not sufficiently resemble its prototype, the child may reject the classification. She reported that by using this method she was able to raise students’ levels from Level 0 to 1 in 20 lessons and from Level 1 to 2 in 50 lessons. A student at this level might say, ” Isosceles triangles are symmetric, so their base angles must be equal.

Retrieved from ” https: The object of thought is deductive reasoning simple proofswhich the student learns to combine to form a system of formal proofs Euclidean geometry. Senechal states that shape is a vital and key component in learning Mathematics and, if properly developed, can aid cross-curricular links to Science and more creative subjects. A child must have enough experiences classroom or otherwise with these geometric ideas to move to a higher level of sophistication.

This was validated in my own experiences in learning Mathematics at school. Thesie Read Edit View history. There does seem to be evidence that children are influenced by can teaching, particularly in their approach to prototypical images.

They may therefore reason at one level for certain shapes, but at another biele for other shapes.

van hiele thesis

Although the analysis is partially positivist in conducting a statistical test non-parametric one sample t-test hielle using known theoretical research about the golden ratioit is also interpretivist as the test used is inferential so a supposition about the data can be assumed.

Researchers found that the van Hiele levels of American students are low. However, Haggerty asserts not all geometrical learning is linear and discrete; it can be discontinuous as pupils develop at different rates.

van hiele thesis

However, DfE a state that children are taught to make connections between shapes from KS1. DfE d highlight that a knowledge of Euclidean Geometry and a developing knowledge of spatial awareness vzn studying topics like tessellations is conducive to understanding Affine Geometrythe study of parallel lines which is introduced in Mathematics at KS3 Level.


The student understands that properties are related and one set of properties may imply another property. Students at this level understand the meaning of deduction.

van hiele thesis

I am using a positivist paradigm in my approach to this research study. Chazan and Lehrer suggest this is particularly evident in an interactive classroom setting. Van Hiele termed this level as analysis where pupils could understand the properties of shape but not yet link them.

Van Hiele model

Draw a rectangle that looks nice Van Hiele Level: On the other hand, Haeussler, Paul and Wood advocate the advantages of a small sample size being expedient and necessary as it allows data to be collected and analysed efficiently although they recognise the potential limitations in accuracy a small sample size could have.

Pierre van Hiele noticed that his students tended to “plateau” at certain points in their understanding of geometry and he identified these plateau points as levels. A supposition could be presumed that all students need a good comprehension of Algebra to comprehend more sophisticated Geometry topics.

Methodology Throughout my teaching practice and career I have always tried to be a reflective practitioner and recognise what needs to be changed about my own and possibly whole school practice. Roughly when a child starts secondary school, they enter the Van Hiele abstraction stage where they can compare shapes and make connections between them such as in the diagram below: If a figure is sketched on the blackboard and the teacher claims it is intended to have congruent sides and angles, the students accept that vam is a square, even if it is poorly drawn.

Without such experiences, many adults including teachers remain in Level 1 all their lives, even if they take a formal hirle course in secondary school. Research carried out by Senkp.