Through rich experiences, children can reach Level 2 in elementary school. Thus, children at this stage might balk at calling a thin, wedge-shaped triangle with sides 1, 20, 20 or sides 20, 20, 39 a “triangle”, because it’s so different in shape from an equilateral triangle , which is the usual prototype for “triangle”. However, McNiff and Whitehead highlight that there may only be limitations to what I can change, something which indicates I may need to keep improving and refining my practice. This seems to be evidenced by the dubiousness of whether the results of this study would be replicated in a larger investigation. For example, they will still insist that “a square is not a rectangle. Tests See Appendix 3, p.

In mathematics education , the Van Hiele model is a theory that describes how students learn geometry. A student at Level 0 or 1 will not have the same understanding of this term. However, students at this level believe that axioms and definitions are fixed, rather than arbitrary, so they cannot yet conceive of non-Euclidean geometry. The van Hieles believed this property was one of the main reasons for failure in geometry. Draw a rectangle that looks nice.

Both numbering systems are still in use.

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

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. A supposition could be presumed that all students need a good comprehension of Algebra to comprehend more sophisticated Geometry topics. The sample hirle of 10 students may not be entirely statistically reliable. However, I will have to work hard to ensure this thesls given that the research is being conducted in my former educational establishments, which may induce understandable emotional attachments.

Neither of these is a correct description of the meaning of “square” for someone reasoning at Level 1. They have been great friends and have always been there for me. The cognitive differences in the age of the thesie involved in the study seem to validate this: DfE identify hieke social learning is particularly prevalent when a child starts formal education and learns from teacher exposition and interactions with their peers.

Vygotsky argues this modality of inquiry may deprive me of the possible collaborative benefits of a social fan model of research. Based on research carried 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. They usually reason inductively from several examples, but cannot yet reason deductively because they do not understand how the properties of shapes are related.

Howson and Urbach advocate the credentials thssis logical empiricism, something which I have used as tasks 4 and 5 rely on the scientific verification of prototypical images which seems a reliable framework on which to base my conclusions on.

Piaget suggests this development seems to be formulated during the latter vam stages tertiary, circular reactions, curiously and novelty of the formative sensorimotor stage when a child interacts with the world around them and begins to explore the properties of new objects.

Ideally, the teacher and students need shared experiences behind their language. Students understand that definitions are arbitrary and need not actually refer to any concrete realization. Permission also needed to be gained for the possible publication of the study. Properties are not yet ordered at this level.

I have taken a deductive approach in writing my literature review see can 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.

However, Haggerty asserts not all geometrical learning is linear and discrete; it can be discontinuous as pupils develop at different rates. 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.

# Van Hiele model – Wikipedia

A possible criticism of the Piagetian and Van Hiele models is that they are heavily generalised and do not account for variations in ability. 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. If the horizontal base of the triangle is on top and the opposing vertex below, the child may recognize it as a triangle, but claim it is “upside down”.

The fusion of these 2 approaches may thesia complementary as it could allow me thrsis gain a deep knowledge of what I have researched and enact what I have learned in my classroom practice Weick, However, all students were selected free of bias and no discrimination was made at all, particularly for cultural factors such as religion and race.

They have proposed renaming this level the syncretic level. However, they do not yet understand the intrinsic meaning of deduction.

Theeis ethnicity of most of the pupils at the schools surveyed was White British. thewis

## Van Hiele model

Children view figures yhesis without analyzing their properties. For all of these reasons, I decided to conduct a research study investigating how children learn shape.

Once children have grasped the basic notions of angle and shapes, they can begin to make links between them. The Soviets did research on the theory in the s and integrated their findings into their curricula. Scientific Study, 98 Pages, Grade: Van Hiele termed this level as analysis where pupils could understand the properties of shape but not yet link them. This arguably indicates that numeracy skills are not ideal in the current environment; so it may be beneficial to gain a detailed knowledge of how pupils learn so standards and attainment can be increased.