### VAN HIELE THESIS

I have taken a deductive approach in writing my literature review see below diagram as I examined theoretical approaches in order to structure my approach but have implemented an inductive method of data collection as results are collected and then related to practice. Ollerton highlights this as the key distinction between a reflective practitioner and a practitioner researcher, actually doing something specific about the issue. 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. American researchers did several large studies on the van Hiele theory in the late s and early s, concluding that students’ low van Hiele levels made it difficult to succeed in proof-oriented geometry courses and advising better preparation at earlier grade levels. European researchers have found similar results for European students.

Children identify prototypes of basic geometrical figures triangle , circle , square. Upon learning about angles and lines, children may be able to make better links between shapes. Hubbard and Power and Bell argue that developing this thoughtful style may allow me to assess pupils more in-depth in this investigation to facilitate more accurate analysis and demonstrate good practice in conducting my research study. A child must have enough experiences classroom or otherwise with these geometric ideas to move to a higher level of sophistication. Children can discuss the properties of the basic figures and recognize them by these properties, but generally do not allow categories to overlap because they understand each property in isolation from the others.

This is something I would like to create in my study.

The progressive and interrelating nature of Geometry seems to be further represented by the fact that knowledge of Affine Geometry can help with understanding of the beginnings of C o-ordinate Geometry in Secondary School in modules like transformations DfE, d.

The object of thought is deductive geometric systems, for which the learner thesie axiomatic systems. Learners can study non-Euclidean geometries with understanding. Shapes with rounded or incomplete sides may be accepted as “triangles” if they bear a holistic resemblance vvan an equilateral triangle. Publish now – it’s free.

Although there may be some disagreement with the various cognition theories, it could possibly be assumed that only some children can make connections between shape at this stage of learning. This was validated in my own experiences in learning Mathematics at school.

Hubbard tuesis Power and Bell argue that developing this thoughtful style may allow me to assess pupils more in-depth in this investigation to facilitate more accurate analysis and demonstrate good practice in conducting my research study. Van Hiele Levels of Geometric Reasoning 2. Sample The data were collected at a primary and secondary school and a sixth form college in the same hiels all within a two mile radius in the North East of England.

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.

# Van Hiele model – Wikipedia

The fusion of these 2 approaches may be complementary as huele could allow me to gain a deep knowledge of what I have researched and enact what I have learned in my classroom practice Weick, They cannot link or compare shapes.

Raw data from investigation 8. This seems to imply that children will have some knowledge of the common properties of Euclidean Geometry; in a Piagetian sense by linking it back to previous schemata and also by using visual prototypes to identify other shapes in the Van Hiele model such as comparing the number of equal sides. Throughout the research study, an ethical approach was followed at all times See Appendix 5, p. Mitchelmore and Outhredp.

Geometric ideas are still understood as objects in the Thesjs plane. Cuoco, Goldenberg and Mark propose that thinking geometrically seems to provide an alternate perspective on life, investigations and problem-solving. Senechal states that shape is a vital and key component in learning Mathematics and, if properly vann, can aid cross-curricular links to Science and more creative tesis.

A possible criticism of the Piagetian and Van Hiele models is that they are heavily generalised and do not account for variations in ability. Van Hiele termed this level as analysis where pupils could understand the properties of shape but not yet link them. I would especially like to thank my former A Level Mathematics Teacher Elizabeth Best who has been an inspirational mentor, who further sparked my interest in Mathematics and made me decide to go into a career in education.

National Council of Teachers of Mathematics, pp. Draw a right angle 4. These visual prototypes are then used to identify vwn shapes. Properties are in fact related at the Analysis level, but students are not yet explicitly aware of the relationships.

Conversely, Stenhouse is a proponent of the interpretivist approach which he feels has rigour as the power thesks research lies with the teacher. Mathematics – Didactics Improving mathematics instruction for Children are likely to reach this level at the end of secondary school. In learning Geometry, pupils seem to develop from pure and synthetic Geometry Euclidean but need to have an understanding of Algebra to understand more sophisticated levels of analytic Algebraic Geometry.

## Is The Van Hiele Model Useful in Determining How Children Learn Geometry?

They understand the role of undefined terms, definitions, axioms and theorems in Euclidean geometry. Chazan and Lehrer thesls this is particularly evident in an interactive classroom setting.

They usually reason inductively from several examples, but cannot yet reason deductively because they do not understand how the properties of shapes are related.