MIP2601
Assignment 1 2026
Unique number:
Due date: 13 May 2026
SECTION A
The Van Hiele model of geometric thinking was developed in the 1950s by Pierre van
Hiele and Dina van Hiele-Geldof. The theory emerged from their concern about learners’
poor performance in geometry and their own difficulties as teachers in helping learners
understand geometric concepts. They realised that learners were not failing because
geometry was too difficult, but because it was taught at a level of thinking that learners
had not yet reached. The Van Hiele theory therefore explains how learners’ geometric
thinking develops in stages and how teaching should be aligned with these stages to
support learning (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Model
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen
as a replacement for individual research, critical analysis, or professional consultation. Students are encouraged
to perform their own research and seek advice from their instructors or academic advisors for specific
assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information in these study notes, the seller does not guarantee the completeness or correctness of all content.
The buyer is responsible for verifying the accuracy of the information and exercising their own judgment when
applying it to their assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's
policies regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and
sources of inspiration. Any direct reproduction of the content without proper citation and acknowledgment may
be considered academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences
arising from the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or
any other negative consequences resulting from the application or misuse of the information provided.
, SECTION A
The Van Hiele model of geometric thinking was developed in the 1950s by Pierre
van Hiele and Dina van Hiele-Geldof. The theory emerged from their concern about
learners’ poor performance in geometry and their own difficulties as teachers in
helping learners understand geometric concepts. They realised that learners were
not failing because geometry was too difficult, but because it was taught at a level of
thinking that learners had not yet reached. The Van Hiele theory therefore explains
how learners’ geometric thinking develops in stages and how teaching should be
aligned with these stages to support learning (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Model
The central idea of the Van Hiele model is that geometric understanding develops
through five hierarchical levels. Learners must move through the levels in
sequence, and progression depends more on instruction and experience than on
age. Each level has its own language, way of reasoning, and understanding of
geometry. If teaching is pitched above a learner’s level, meaningful learning will not
occur. Teachers therefore play a crucial role in guiding learners from one level to the
next through appropriate activities and language (MIP2601 Study Guide, 2020).
The Five Levels of Geometric Thinking
Level 0: Visualisation
At this level, learners recognise shapes based on their overall appearance. They
identify shapes such as squares, circles, and triangles by what they look like, rather
than by their properties. For example, a learner may identify a square because it
“looks like a box”, but may not recognise it if it is rotated. Learners cannot yet
distinguish between shapes such as squares and rectangles based on properties
(MIP2601 Study Guide, 2020).
Level 1: Analysis
Assignment 1 2026
Unique number:
Due date: 13 May 2026
SECTION A
The Van Hiele model of geometric thinking was developed in the 1950s by Pierre van
Hiele and Dina van Hiele-Geldof. The theory emerged from their concern about learners’
poor performance in geometry and their own difficulties as teachers in helping learners
understand geometric concepts. They realised that learners were not failing because
geometry was too difficult, but because it was taught at a level of thinking that learners
had not yet reached. The Van Hiele theory therefore explains how learners’ geometric
thinking develops in stages and how teaching should be aligned with these stages to
support learning (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Model
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen
as a replacement for individual research, critical analysis, or professional consultation. Students are encouraged
to perform their own research and seek advice from their instructors or academic advisors for specific
assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the
information in these study notes, the seller does not guarantee the completeness or correctness of all content.
The buyer is responsible for verifying the accuracy of the information and exercising their own judgment when
applying it to their assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's
policies regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and
sources of inspiration. Any direct reproduction of the content without proper citation and acknowledgment may
be considered academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences
arising from the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or
any other negative consequences resulting from the application or misuse of the information provided.
, SECTION A
The Van Hiele model of geometric thinking was developed in the 1950s by Pierre
van Hiele and Dina van Hiele-Geldof. The theory emerged from their concern about
learners’ poor performance in geometry and their own difficulties as teachers in
helping learners understand geometric concepts. They realised that learners were
not failing because geometry was too difficult, but because it was taught at a level of
thinking that learners had not yet reached. The Van Hiele theory therefore explains
how learners’ geometric thinking develops in stages and how teaching should be
aligned with these stages to support learning (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Model
The central idea of the Van Hiele model is that geometric understanding develops
through five hierarchical levels. Learners must move through the levels in
sequence, and progression depends more on instruction and experience than on
age. Each level has its own language, way of reasoning, and understanding of
geometry. If teaching is pitched above a learner’s level, meaningful learning will not
occur. Teachers therefore play a crucial role in guiding learners from one level to the
next through appropriate activities and language (MIP2601 Study Guide, 2020).
The Five Levels of Geometric Thinking
Level 0: Visualisation
At this level, learners recognise shapes based on their overall appearance. They
identify shapes such as squares, circles, and triangles by what they look like, rather
than by their properties. For example, a learner may identify a square because it
“looks like a box”, but may not recognise it if it is rotated. Learners cannot yet
distinguish between shapes such as squares and rectangles based on properties
(MIP2601 Study Guide, 2020).
Level 1: Analysis
