Answer to Question #351004 in Geometry for Nkomi

Question

How learners thinks about the triangles at level 1,2 and 3 of van hiele levels of geometric thought

Answer 1

Solution:

Let's describe Pierre van Hiele 1-3 levels in generally:

Level 1 Analysis (Description): At this level pupils (students) start analyzing and naming properties of geometric figures. They do not see relationships between properties, they think all properties are important (there is no difference between necessary and sufficient properties). They do not see a need for proof of facts discovered empirically. They can measure, fold and cut paper, use geometric software etc.

Level 2 Abstraction: At this level pupils or students perceive relationships between properties and figures. They create meaningful definitions. They are able to give simple arguments to justify their reasoning. They can draw logical maps and diagrams. They use sketches, grid paper, geometric SW.

Level 3 Deduction: At this level students can give deductive geometric proofs. They are able to differentiate between necessary and sufficient conditions. They identify which properties are implied by others. They understand the role of definitions, theorems, axioms and proofs.

Now, we will try to describe 1-3 levels for thinking about triangles:

Level 1: descriptions often have a lot of properties listed (more than are needed): these triangles all have tree sides (A and B) that are the same length, and they can be split right down the middle to create mirror images.

Level 2:  descriptions often have more efficient lists of properties. The descriptions are usually more careful and include more mathematical vocabulary: triangles that have 90 degrees or equilateral triangles all sides are equal.

Level 3: in this level students able to differentiate between necessary and sufficient conditions. For example, relation between angles and sides of triangles.