MATHEMATICS FOR INTERMEDIATE
PHASE TEACHERS III
MIP2601 Assignment 1 solutions 2026
Dear Student
Tutorial letter 102 contains the formative assessment 1 with the unique
number: 601617 which you are
expected to complete for the year 2025. The due date for the
assignment is 13 May 2026, at 7:00 p.m.
this assignment contain some pictures for more clear understanding
,Section A: Conceptual Understanding of the Van Hiele Model
Origin of the Van Hiele Model
The Van Hiele model of geometric thinking was developed in the 1950s by Dutch
mathematics educators Pierre van Hiele and Dina van Hiele-Geldof. Their research
focused on understanding why many learners struggled to learn geometry. They
discovered that learners do not immediately understand geometric concepts in a
formal way. Instead, learners progress through different levels of geometric thinking,
and each level represents a different way of understanding shapes and geometric
relationships.
The key idea of the Van Hiele model is that learners move through these levels
sequentially, and they cannot skip a level. Progression from one level to another
depends mainly on instruction and learning experiences, rather than age. This means
that teachers play an important role in designing activities that help learners gradually
develop deeper geometric understanding. The model is particularly useful in the
Intermediate Phase because it helps teachers understand how learners recognise
shapes, analyse their properties, and eventually reason about relationships between
shapes.
The Five Levels of the Van Hiele Model
The Van Hiele theory describes five levels of geometric thinking. Each level represents
a more advanced form of reasoning and understanding in geometry.
Level 0: Visualisation (Recognition)
At the visualisation level, learners recognise shapes based on their overall appearance
rather than their properties. They identify shapes by what they look like and may
associate them with familiar objects.
For example, a learner may recognise a square because it looks like a window or a box.
However, the learner may not yet understand that a square has four equal sides and
four right angles.
Example from geometry:
Learners are shown different shapes and asked to identify them as triangles, rectangles,
or circles. At this level, learners simply recognise the shapes visually without analysing
their characteristics.
, Level 1: Analysis
At the analysis level, learners begin to identify and describe the properties of shapes.
They start to understand that shapes have specific characteristics such as the number
of sides, angles, and parallel lines.
For example, learners may describe a rectangle by saying that:
• it has four sides,
• opposite sides are equal, and
• it has four right angles.
Although learners can describe these properties, they may not yet understand how the
properties are related.
Example from geometry:
Learners examine different quadrilaterals and list their properties, such as the number
of sides and types of angles.
Level 2: Informal Deduction (Relational Thinking)
At this level, learners begin to understand relationships between shapes and their
properties. They can compare shapes and explain how they are related.
For example, learners may understand that:
PHASE TEACHERS III
MIP2601 Assignment 1 solutions 2026
Dear Student
Tutorial letter 102 contains the formative assessment 1 with the unique
number: 601617 which you are
expected to complete for the year 2025. The due date for the
assignment is 13 May 2026, at 7:00 p.m.
this assignment contain some pictures for more clear understanding
,Section A: Conceptual Understanding of the Van Hiele Model
Origin of the Van Hiele Model
The Van Hiele model of geometric thinking was developed in the 1950s by Dutch
mathematics educators Pierre van Hiele and Dina van Hiele-Geldof. Their research
focused on understanding why many learners struggled to learn geometry. They
discovered that learners do not immediately understand geometric concepts in a
formal way. Instead, learners progress through different levels of geometric thinking,
and each level represents a different way of understanding shapes and geometric
relationships.
The key idea of the Van Hiele model is that learners move through these levels
sequentially, and they cannot skip a level. Progression from one level to another
depends mainly on instruction and learning experiences, rather than age. This means
that teachers play an important role in designing activities that help learners gradually
develop deeper geometric understanding. The model is particularly useful in the
Intermediate Phase because it helps teachers understand how learners recognise
shapes, analyse their properties, and eventually reason about relationships between
shapes.
The Five Levels of the Van Hiele Model
The Van Hiele theory describes five levels of geometric thinking. Each level represents
a more advanced form of reasoning and understanding in geometry.
Level 0: Visualisation (Recognition)
At the visualisation level, learners recognise shapes based on their overall appearance
rather than their properties. They identify shapes by what they look like and may
associate them with familiar objects.
For example, a learner may recognise a square because it looks like a window or a box.
However, the learner may not yet understand that a square has four equal sides and
four right angles.
Example from geometry:
Learners are shown different shapes and asked to identify them as triangles, rectangles,
or circles. At this level, learners simply recognise the shapes visually without analysing
their characteristics.
, Level 1: Analysis
At the analysis level, learners begin to identify and describe the properties of shapes.
They start to understand that shapes have specific characteristics such as the number
of sides, angles, and parallel lines.
For example, learners may describe a rectangle by saying that:
• it has four sides,
• opposite sides are equal, and
• it has four right angles.
Although learners can describe these properties, they may not yet understand how the
properties are related.
Example from geometry:
Learners examine different quadrilaterals and list their properties, such as the number
of sides and types of angles.
Level 2: Informal Deduction (Relational Thinking)
At this level, learners begin to understand relationships between shapes and their
properties. They can compare shapes and explain how they are related.
For example, learners may understand that:
