"The student learns by rote to operate with [mathematical] relations that he does not understand, and of which he has not seen the origin…. 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. He will not know how to apply what he has learned in a new situation. "- Pierre van Hiele, 1959
Level 0. Visualization: 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.
Level 1. Analysis: At this level, the shapes become bearers of their properties. The objects of thought are classes of shapes, which the child has learned to analyze as having properties
Level 2. Abstraction: At this level, properties are ordered. The objects of thought are geometric properties, which the student has learned to connect deductively.
Level 3. Deduction: Students at this level understand the meaning of deduction. The object of thought is deductive reasoning (simple proofs), which the student learns to combine to form a system of formal proofs
Level 4. 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 research for the model began in the 1950's with a husband and wife team in the Netherlands, Pierre and Dina van Hiele. The main theory emphasises that despite some natural development of spatial thinking, deliberate instruction is needed to move children through several levels of geometric understanding and reasoning skill. It is based on the firm belief that it is inappropriate to teach children Euclidean geometry following the same logical construction of axioms, definitions, theorems and proofs that Euclid used to construct the system. Children don't think on a formal deductive level, and therefore can only memorise geometric facts and 'rules', but not understand the relationships between the ideas, if taught using this approach.
So which level of van hiele geometric thinking , do you think you are?
Level 0. Visualization: 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.
Level 1. Analysis: At this level, the shapes become bearers of their properties. The objects of thought are classes of shapes, which the child has learned to analyze as having properties
Level 2. Abstraction: At this level, properties are ordered. The objects of thought are geometric properties, which the student has learned to connect deductively.
Level 3. Deduction: Students at this level understand the meaning of deduction. The object of thought is deductive reasoning (simple proofs), which the student learns to combine to form a system of formal proofs
Level 4. 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
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| Pierre Van Hiele |
The research for the model began in the 1950's with a husband and wife team in the Netherlands, Pierre and Dina van Hiele. The main theory emphasises that despite some natural development of spatial thinking, deliberate instruction is needed to move children through several levels of geometric understanding and reasoning skill. It is based on the firm belief that it is inappropriate to teach children Euclidean geometry following the same logical construction of axioms, definitions, theorems and proofs that Euclid used to construct the system. Children don't think on a formal deductive level, and therefore can only memorise geometric facts and 'rules', but not understand the relationships between the ideas, if taught using this approach.
So which level of van hiele geometric thinking , do you think you are?
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