### VAN HIELE THESIS

Furthermore, the results will be related to the literature review and my own observations to see how useful the Van Hiele Model is in assessing how pupils learn Geometry. At this level, the focus of a child’s thinking is on individual shapes, which the child is learning to classify by judging their holistic appearance. Ollerton highlights this as the key distinction between a reflective practitioner and a practitioner researcher, actually doing something specific about the issue. Draw 4 different types of triangle 5. Van Hiele termed this level as analysis where pupils could understand the properties of shape but not yet link them. They understand the role of undefined terms, definitions, axioms and theorems in Euclidean geometry.

The van Hieles believed this property was one of the main reasons for failure in geometry. 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. This perceived underrepresentation does not appear to be amended in proposed curriculum reforms; Geometry forms less than a quarter of the amalgamated attainment descriptors in the draft of the Secondary Mathematics curriculum DfE, d. This seems to be evidenced by the dubiousness of whether the results of this study would be replicated in a larger investigation. Students can reason with simple arguments about geometric figures.

Questionnaire given to teachers 5. Students cannot be expected to prove geometric theorems until they have built up an extensive understanding of the systems of relationships between geometric ideas.

## Van Hiele model

Ollerton highlights this as the key distinction between a reflective practitioner and a practitioner researcher, actually doing something specific about the issue.

The objects of thought are classes of shapes, which the child has learned to analyze as having properties. Children simply say, “That is a circle,” usually without further description. Draw a right angle 4.

Based on research hieoe out on students in their own mathematics classes as part of composing their doctoral dissertations in in Utrecht, Netherlands, husband and wife Pierre and Dina Van Hiele devised a model of geometric levels that children progress through See Appendix 1, p. A child must have enough experiences classroom or otherwise with these geometric ideas to move to a higher level of sophistication.

Therefore the system of relations is thesjs independent construction having no rapport with other experiences of the child. The van Hieles believed this property was one of the main reasons for failure in geometry. The model has greatly influenced geometry curricula throughout the world through emphasis on analyzing properties and classification of shapes at early grade levels. It could be argued that Brunerp. Children begin to notice many properties of shapes, but do not see the relationships between the properties; therefore they cannot reduce the list of properties to a concise definition with necessary and sufficient conditions.

Neither of these is a correct description of the meaning of “square” for someone reasoning at Level 1. The object of thought is deductive geometric systems, for which the learner compares axiomatic systems.

# Van Hiele model – Wikipedia

Estimating the size of an angle 3. There may be a finite level of geometrical reasoning that a student can reach and that their understanding of Geometry will eventually plateau. Upon learning about angles and lines, children may be able to make better links vn shapes.

Estimating length of line 2.

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

Journal for Hlele in Mathematics Education. 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. For Dina van Hiele-Geldof’s doctoral dissertation, she conducted a teaching experiment with year-olds in a Montessori secondary school in the Netherlands.

At this level, the shapes become bearers of their properties. Throughout the research study, an ethical approach was followed at all times See Appendix 5, p. Scientific Study, 98 Pages, Thesi At Level 2 a square is a special type of rectangle. When a teacher speaks of a “square” she or he means a special type of rectangle.

This is in contrast to Piaget ‘s theory of cognitive development, which is age-dependent. The sample size of 10 students may not be entirely statistically reliable. Thseis Mother for fostering my interest in education and always believing in and encouraging me to keep going through adversity and my Father for maturing me.

The student does not understand the teacher, and the teacher does not understand how the student is reasoning, frequently concluding that the student’s answers are simply “wrong”. Johnston-Wilder and Mason suggest that Geometry is given less teaching time in the classroom than other disciplines. In conclusion, the methodology I have used seems sound as it tries to complement a positivist research paradigm with a mixed methods paradigm in data collection.

The student learns by rote to operate with [mathematical] relations that he does not understand, and of which he has not seen the originâ€¦.

Children at this level often believe something is true based on a single example. Firstly, to my lecturers Ian Wood and Fiona Lawton who have provided me with invaluable support in both the formulation and production of my research study.