MIP2601
Assignment 1
Unique No: 601617
Due 13 May 2026
, Van Hiele Levels of Geometric Thought Assignment
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 by Dutch educators Pierre van Hiele and Dina van
Hiele-Geldof in the 1950s while researching how learners understand geometry. They
observed that learners do not grasp geometry simply by getting older. Instead, they
move through identifiable levels of geometric thinking based on instruction and
experience rather than age (Van Hiele, 1986).
The core idea behind the model is that learners progress through structured levels of
reasoning. Each level reflects how learners see shapes, use language and justify
geometric ideas. A learner cannot skip levels because understanding at a higher level
depends on the thinking developed at the previous one.
Level 0: Visualisation (Recognition) At this level, learners recognise shapes based on
their appearance rather than properties. Thinking is visual and intuitive.
Example A learner identifies a triangle because it “looks like a triangle” but cannot
explain its properties. A square is recognised because it looks like a box shape, not
because it has equal sides or right angles.
Typical learner language “This is a rectangle because it looks like one.”
Level 1: Analysis (Descriptive) Learners begin to notice properties of shapes. They
can describe characteristics but do not yet see relationships between properties.
Example A learner can say that a rectangle has four sides and opposite sides are equal.
However, they may not understand that a square is also a rectangle because they
cannot connect properties logically.
Typical learner language “A square has four equal sides and four corners.”
Assignment 1
Unique No: 601617
Due 13 May 2026
, Van Hiele Levels of Geometric Thought Assignment
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 by Dutch educators Pierre van Hiele and Dina van
Hiele-Geldof in the 1950s while researching how learners understand geometry. They
observed that learners do not grasp geometry simply by getting older. Instead, they
move through identifiable levels of geometric thinking based on instruction and
experience rather than age (Van Hiele, 1986).
The core idea behind the model is that learners progress through structured levels of
reasoning. Each level reflects how learners see shapes, use language and justify
geometric ideas. A learner cannot skip levels because understanding at a higher level
depends on the thinking developed at the previous one.
Level 0: Visualisation (Recognition) At this level, learners recognise shapes based on
their appearance rather than properties. Thinking is visual and intuitive.
Example A learner identifies a triangle because it “looks like a triangle” but cannot
explain its properties. A square is recognised because it looks like a box shape, not
because it has equal sides or right angles.
Typical learner language “This is a rectangle because it looks like one.”
Level 1: Analysis (Descriptive) Learners begin to notice properties of shapes. They
can describe characteristics but do not yet see relationships between properties.
Example A learner can say that a rectangle has four sides and opposite sides are equal.
However, they may not understand that a square is also a rectangle because they
cannot connect properties logically.
Typical learner language “A square has four equal sides and four corners.”
