MIP2601
Assignment 1
Unique No: 601617
Due 13 May 2026
, Section A: Conceptual
Q1. Explain the origin, key ideas and the five levels of the Van Hiele model.
Discuss the characteristics of each level with examples from geometry.
The Van Hiele model was developed in the 1950s by Dutch educators Pierre van Hiele
and Dina van Hiele-Geldof. They observed that learners do not understand geometry
simply by age or exposure, but by progressing through distinct levels of geometric
thinking. Each level reflects how learners reason about shapes, not just what they know
(Van Hiele, 1986).
The core idea is that learners move through hierarchical levels. They cannot skip a
level, and teaching must match the learner’s current level to be effective. Language and
experiences play a key role in helping learners move from one level to the next (Fuys,
Geddes & Tischler, 1988).
The five levels are explained below.
Level 0: Visualisation At this level, learners recognise shapes by their appearance. They
see a shape as a whole but do not analyse its properties. For example, a learner may
say a square is a square “because it looks like a box”. If the square is rotated, they may
no longer recognise it as a square. In a Grade 5 class, learners might correctly pick out
triangles from pictures but struggle to explain why a shape is a triangle.
Level 1: Analysis Learners begin to focus on properties of shapes. They can identify
features such as sides, angles and parallel lines but do not yet see relationships
between properties. For instance, a learner can state that a rectangle has four right
angles and opposite sides equal, but may not understand that all squares are
rectangles. Classroom example: learners sort shapes based on properties such as
number of sides or equal lengths.
Level 2: Informal Deduction Learners start to understand relationships between
properties and between different shapes. They can follow logical reasoning but still rely
on informal arguments. For example, a learner can explain that a square is a rectangle
because it has all the properties of a rectangle plus equal sides. In Grade 5, learners
Assignment 1
Unique No: 601617
Due 13 May 2026
, Section A: Conceptual
Q1. Explain the origin, key ideas and the five levels of the Van Hiele model.
Discuss the characteristics of each level with examples from geometry.
The Van Hiele model was developed in the 1950s by Dutch educators Pierre van Hiele
and Dina van Hiele-Geldof. They observed that learners do not understand geometry
simply by age or exposure, but by progressing through distinct levels of geometric
thinking. Each level reflects how learners reason about shapes, not just what they know
(Van Hiele, 1986).
The core idea is that learners move through hierarchical levels. They cannot skip a
level, and teaching must match the learner’s current level to be effective. Language and
experiences play a key role in helping learners move from one level to the next (Fuys,
Geddes & Tischler, 1988).
The five levels are explained below.
Level 0: Visualisation At this level, learners recognise shapes by their appearance. They
see a shape as a whole but do not analyse its properties. For example, a learner may
say a square is a square “because it looks like a box”. If the square is rotated, they may
no longer recognise it as a square. In a Grade 5 class, learners might correctly pick out
triangles from pictures but struggle to explain why a shape is a triangle.
Level 1: Analysis Learners begin to focus on properties of shapes. They can identify
features such as sides, angles and parallel lines but do not yet see relationships
between properties. For instance, a learner can state that a rectangle has four right
angles and opposite sides equal, but may not understand that all squares are
rectangles. Classroom example: learners sort shapes based on properties such as
number of sides or equal lengths.
Level 2: Informal Deduction Learners start to understand relationships between
properties and between different shapes. They can follow logical reasoning but still rely
on informal arguments. For example, a learner can explain that a square is a rectangle
because it has all the properties of a rectangle plus equal sides. In Grade 5, learners
