According to Van Hiele level of Geomatric 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.

Options

A. Formal Deduction
B. Visualization
C. Analysis
D. Informal Deduction

Answer

To determine the level of geometric thought that students of class VII are at when they classify quadrilaterals according to their properties, we can analyze the levels defined by Van Hiele.

1. **Understanding the Levels**: The Van Hiele levels of geometric thought are:
- Level 0: Visualization
- Level 1: Analysis
- Level 2: Informal Deduction
- Level 3: Formal Deduction
- Level 4: Rigor

2. **Identifying the Task**: The students are asked to classify quadrilaterals based on their properties. This involves recognizing the properties of different quadrilaterals (like squares, rectangles, rhombuses, etc.) and categorizing them accordingly.

3. **Analyzing the Levels**:
- **Level 0 (Visualization)**: This level involves recognizing shapes without understanding their properties. It is about seeing and naming shapes.
- **Level 1 (Analysis)**: At this level, students can analyze the properties of shapes but may not yet understand the relationships between different shapes.
- **Level 2 (Informal Deduction)**: This level involves understanding relationships between shapes and properties. Students can classify shapes based on their properties and make informal deductions about them.
- **Level 3 (Formal Deduction)**: This level involves a more rigorous understanding of geometric properties and theorems, where students can prove relationships formally.
- **Level 4 (Rigor)**: This level involves a deep understanding of geometry, including axiomatic systems and rigorous proofs.

4. **Conclusion**: Since the task requires students to classify quadrilaterals based on their properties, they are engaging in analysis and informal deduction. They are not just recognizing shapes (Level 0) or merely analyzing them without understanding relationships (Level 1). They are making connections between the properties of different quadrilaterals, which aligns with Level 2, Informal Deduction.

Thus, the students of class VII are at **Level 2 (Informal Deduction)** of Van Hiele's geometric thought.