lOMoARcPSD|51776212
, lOMoARcPSD|51776212
MIP2601/102/0/2026
MIP2601 Assignment 1 2026 - DUE 13 May 2026 [complete answers]
ASSIGNMENT 1
UNDERSTANDING AND APPLYING THE VAN HIELE FRAMEWORK IN INTERMEDIATE
PHASE MATHEMATICS EDUCATION
MIP2601 Assignment 1 (2026)
Understanding and Applying the Van Hiele Framework in Intermediate Phase
Mathematics Education
Section A: Conceptual Understanding of the Van Hiele Model (20 Marks)
The Van Hiele theory of geometric thinking was developed in the 1950s by Dutch
educators Pierre van Hiele and Dina van Hiele-Geldof at Utrecht University. Their
research focused on understanding why many learners struggled with geometry despite
being able to perform arithmetic successfully. They discovered that learners progress
through distinct and hierarchical levels of geometric thinking. Importantly, progression
depends more on instruction and experience than on age or maturity.
The Van Hiele model proposes five levels of geometric thought. Learners move
sequentially through these levels, and instruction must align with their current level to
promote advancement.
Level 0: Visualisation (Recognition)
At this level, learners recognise shapes based on their overall appearance rather than
their properties. For example, a Grade 5 learner may say, “This is a rectangle because it
looks like a door.” They do not yet analyse attributes such as parallel sides or right
angles.
Characteristics:
Shapes are identified holistically.
Language is informal.
Reasoning is based on visual prototypes.
Example: A learner may reject a rotated square as a square because it “looks like a
diamond.”
Level 1: Analysis (Descriptive)
2
, lOMoARcPSD|51776212
MIP2601/102/0/2026
MIP2601 Assignment 1 2026 - DUE 13 May 2026 [complete answers]
ASSIGNMENT 1
UNDERSTANDING AND APPLYING THE VAN HIELE FRAMEWORK IN INTERMEDIATE
PHASE MATHEMATICS EDUCATION
MIP2601 Assignment 1 (2026)
Understanding and Applying the Van Hiele Framework in Intermediate Phase
Mathematics Education
Section A: Conceptual Understanding of the Van Hiele Model (20 Marks)
The Van Hiele theory of geometric thinking was developed in the 1950s by Dutch
educators Pierre van Hiele and Dina van Hiele-Geldof at Utrecht University. Their
research focused on understanding why many learners struggled with geometry despite
being able to perform arithmetic successfully. They discovered that learners progress
through distinct and hierarchical levels of geometric thinking. Importantly, progression
depends more on instruction and experience than on age or maturity.
The Van Hiele model proposes five levels of geometric thought. Learners move
sequentially through these levels, and instruction must align with their current level to
promote advancement.
Level 0: Visualisation (Recognition)
At this level, learners recognise shapes based on their overall appearance rather than
their properties. For example, a Grade 5 learner may say, “This is a rectangle because it
looks like a door.” They do not yet analyse attributes such as parallel sides or right
angles.
Characteristics:
Shapes are identified holistically.
Language is informal.
Reasoning is based on visual prototypes.
Example: A learner may reject a rotated square as a square because it “looks like a
diamond.”
Level 1: Analysis (Descriptive)
2
