Question

Describe van Hiele Level 1 (analysis), Level 2 (informal deduction) and Level 3 (deduction). Demonstrate the difference by using a scalene, isosceles and equilateral triangle as an example to explain learner thinking at the three different levels.

Answer 1

The van Hiele theory describes how young people in schools learn geometry.

How to explain the theory?

Van Hiele theory postulates five levels of geometric thinking which are visualization, analysis, abstraction, formal deduction, and rigor. The levels use their own language and symbols

Analysis: At this level, students start analyzing and naming the properties of geometric figures.

Informal deduction: At this level pupils or students perceive relationships between properties and figures.

Deduction: At this level, students can give deductive geometric proofs. They are able to differentiate between necessary and sufficient conditions.

An equilateral triangle has all sides equal. In an isosceles triangle, two sides are the same length. In a scalene triangle, none of the sides are the same length.

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