According to Van Hiele level of Geometric thought the five levels of geometric understanding are visualization, analysis, informal deduction, formal deduction and rigour. Students of class VII are asked to classify the quadrilaterals according to their properties. These students are 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 dimensionalshapes. Level 2: Informal DeductionChildren 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'. Theycan 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: DeductionStudents 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 theprevious 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 themathematical theories. This is generally the level of university mathematics majoring in geometry.