MIP2601
Assignment 1 2026
Unique number:
Due Date: 13 May 2026
Detailed solutions, explanations, workings
and references.
+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
Varsity Cube 2026 +27 81 278 3372
Assignment 1 2026
Unique number:
Due Date: 13 May 2026
Detailed solutions, explanations, workings
and references.
+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
Varsity Cube 2026 +27 81 278 3372
