Meaning of theses
Jump to navigation Jump to search In mathematics education, the Van Hiele model is a theory meaning of theses describes how students learn geometry.
Therefore the system of relations is an independent construction having no rapport with other experiences of the child. This means that the student knows only what has been taught to him and what has been deduced from it. He has not learned to establish connections between the system and the sensory world. 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.
Students cannot be expected to prove geometric theorems until they have built up an extensive understanding of the systems of relationships between geometric ideas. The five van Hiele levels are sometimes misunderstood to be descriptions of how students understand shape classification, but the levels actually describe the way that students reason about shapes and other geometric ideas. 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. Children at Level 0 will often say all of these shapes are triangles, except E, which is too «skinny». They may say F is «upside down». Students at Level 1 will recognize that only E and F are valid triangles.
Visualization: At this level, the focus of a child’s thinking is on individual shapes, which the child is learning of classify by judging their holistic appearance. Children simply say, «That is a circle,» usually without further description. Analysis: At this level, the shapes become bearers of their properties. The objects of thought are classes of theses, which meaning child has learned to analyze as having properties. A person at this level might say, «A square has 4 equal sides and 4 equal angles.
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Its diagonals are congruent and perpendicular, and they bisect each other. The properties are more important than the appearance of the shape. Abstraction: At this level, properties are ordered. The objects of thought are geometric properties, which the student has learned to connect deductively. The student understands that properties are related and one set of properties may imply another property.
Students can reason with simple arguments about geometric figures. Deduction: Students at this level understand the meaning of deduction. Learners can construct geometric proofs at a secondary school level and understand their meaning. Rigor: At this level, geometry is understood at the level of a mathematician. Students understand that definitions are arbitrary and need not actually refer to any concrete realization. The object of thought is deductive geometric systems, for which the learner compares axiomatic systems.
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