According to Van Hiele level of geometric thought, the five levels are—visualization, analysis, informal deducation, formal deducation and rigour. Some polygons are given to a child of Class III for sorting.
He classified the polygons on the basis of the number of sides. This child is at ______ level of Van-Hiele Geometrical thought
In Mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The van Hiele model consists of five levels of thinking processes. A brief overview of the model is given below.
Level 0: Visualisation Children can recognise geometric figures by their shape or physical appearance and not by their parts or properties.
Level 1: Analysis Children at this level are able to appreciate that the collection of figures goes together because of properties. They also become more proficient in describing the attributes of two and three dimensional shapes.
Level 2: Informal Deduction Children at this stage are able to establish relationships among the properties of the figures. 'If all four angles are right angles the shape must be a rectangle'. They can also formulate relationships among shapes. 'If it is a square, it must be a rectangle'. They are able to give logical arguments to justify their reasoning.
Level 3: Deduction Students at this stage are able to go further than giving informal deductive arguments as in the earlier stage. Here, they begin to appreciate the importance and use of axioms, definitions, corollaries and postulates in order to proof a certain geometric truth. This level of thought is typical of secondary school geometry class.
Level 4: Rigor At this level the object of attention is the differences and relationships between different axiomatic systems that are used to derive mathematical theories. In the previous stage the students are expected to know how to form deductive arguments to proof a theory. In this stage they go further by questioning the initial assumptions or axioms that are used to form the mathematical theories. This is generally the level of university mathematics majoring in geometry.