MIP2601
Assignment 1 2026
Unique number:
Due Date: 13 May 2026
SECTION A
The Van Hiele theory 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 the difficulty teachers experienced in helping learners
understand geometric concepts. They observed that learners did not struggle because
geometry was too difficult, but because teaching often did not match learners’ levels of
thinking. The Van Hiele model therefore explains how learners’ geometric understanding
develops in a sequence of levels and how teaching can support movement from one level to
the next. This theory has since been widely recognised and applied in geometry education
internationally and forms an important foundation for teaching geometry in the Intermediate
Phase (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Theory
The central idea of the Van Hiele theory is that geometric thinking develops through a series
of hierarchical levels. Learners cannot skip levels, and progression depends more on
learning experiences and instruction than on age alone.
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.
, For additional support +27 81 278 3372
SECTION A
The Van Hiele theory 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 the difficulty teachers experienced in
helping learners understand geometric concepts. They observed that learners did
not struggle because geometry was too difficult, but because teaching often did not
match learners’ levels of thinking. The Van Hiele model therefore explains how
learners’ geometric understanding develops in a sequence of levels and how
teaching can support movement from one level to the next. This theory has since
been widely recognised and applied in geometry education internationally and forms
an important foundation for teaching geometry in the Intermediate Phase (MIP2601
Study Guide, 2020).
Key Ideas of the Van Hiele Theory
The central idea of the Van Hiele theory is that geometric thinking develops through
a series of hierarchical levels. Learners cannot skip levels, and progression depends
more on learning experiences and instruction than on age alone. Each level has its
own language, ways of reasoning, and understanding of geometry. Teaching that is
not aligned with a learner’s current level is likely to be ineffective, as learners cannot
understand concepts that belong to higher levels of thinking. The theory also
emphasises the role of carefully structured activities that allow learners to explore,
describe, analyse, and reason about shapes (MIP2601 Study Guide, 2020).
Level 0: Visualisation
At the visualisation level, learners recognise geometric shapes based on their overall
appearance. They identify shapes such as squares, triangles, and circles 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 a square that is rotated.
Learners at this level do not distinguish between shapes using formal properties.
This level is typically expected in the Foundation Phase (MIP2601 Study Guide,
2020).
Level 1: Analysis
Assignment 1 2026
Unique number:
Due Date: 13 May 2026
SECTION A
The Van Hiele theory 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 the difficulty teachers experienced in helping learners
understand geometric concepts. They observed that learners did not struggle because
geometry was too difficult, but because teaching often did not match learners’ levels of
thinking. The Van Hiele model therefore explains how learners’ geometric understanding
develops in a sequence of levels and how teaching can support movement from one level to
the next. This theory has since been widely recognised and applied in geometry education
internationally and forms an important foundation for teaching geometry in the Intermediate
Phase (MIP2601 Study Guide, 2020).
Key Ideas of the Van Hiele Theory
The central idea of the Van Hiele theory is that geometric thinking develops through a series
of hierarchical levels. Learners cannot skip levels, and progression depends more on
learning experiences and instruction than on age alone.
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.
, For additional support +27 81 278 3372
SECTION A
The Van Hiele theory 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 the difficulty teachers experienced in
helping learners understand geometric concepts. They observed that learners did
not struggle because geometry was too difficult, but because teaching often did not
match learners’ levels of thinking. The Van Hiele model therefore explains how
learners’ geometric understanding develops in a sequence of levels and how
teaching can support movement from one level to the next. This theory has since
been widely recognised and applied in geometry education internationally and forms
an important foundation for teaching geometry in the Intermediate Phase (MIP2601
Study Guide, 2020).
Key Ideas of the Van Hiele Theory
The central idea of the Van Hiele theory is that geometric thinking develops through
a series of hierarchical levels. Learners cannot skip levels, and progression depends
more on learning experiences and instruction than on age alone. Each level has its
own language, ways of reasoning, and understanding of geometry. Teaching that is
not aligned with a learner’s current level is likely to be ineffective, as learners cannot
understand concepts that belong to higher levels of thinking. The theory also
emphasises the role of carefully structured activities that allow learners to explore,
describe, analyse, and reason about shapes (MIP2601 Study Guide, 2020).
Level 0: Visualisation
At the visualisation level, learners recognise geometric shapes based on their overall
appearance. They identify shapes such as squares, triangles, and circles 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 a square that is rotated.
Learners at this level do not distinguish between shapes using formal properties.
This level is typically expected in the Foundation Phase (MIP2601 Study Guide,
2020).
Level 1: Analysis
