MIP 2601
ASSIGNMENT 1
2026
Section A:
This theory was developed by Pierre van Hiele and Dina van Hiele-Geldof and it
explains how learners develop understanding in geometry through hierarchical levels of
thinking. The theory emphasizes that learners progress through levels sequentially and
that instruction must align with their current level to be effective.
The key ideas of the Van Hiele Model are that learning is level-based, not age-based.
Moreso, it also highlight that progression depends on instruction and experience, not
maturation. Furthermore, each level has its own language and reasoning style and
learners cannot skip levels.
Below are the five levels of geometric thought:-
, Level 0: Visualization (Recognition)
Learners identify shapes based on appearance.
Example: A learner says, “This is a square because it looks like a box.”
They cannot yet describe properties.
Level 1: Analysis (Descriptive)
Learners identify properties of shapes.
Example: “A rectangle has four sides and four right angles.”
However, they do not yet understand relationships between shapes.
Level 2: Informal Deduction (Relational)
Learners understand relationships between properties and classes of shapes.
Example: “A square is a rectangle because it has all the properties of a rectangle.”
Level 3: Formal Deduction
Learners can form logical proofs and understand theorems (usually high school level).
Level 4: Rigor
Learners work with abstract systems of geometry (university level).
In conclusion , in the Intermediate Phase (Grades 4–6), teaching should focus mainly
on Levels 0–2.
Section B:
A short diagnostic task to assess learners’ Van Hiele levels in a Grade 5 class is
highlighted below.
Diagnostic Activity
Use this worksheet which had different 2D shapes (triangles, squares, rectangles,
rhombuses in different orientations).And then answer the questions that follow:-
ASSIGNMENT 1
2026
Section A:
This theory was developed by Pierre van Hiele and Dina van Hiele-Geldof and it
explains how learners develop understanding in geometry through hierarchical levels of
thinking. The theory emphasizes that learners progress through levels sequentially and
that instruction must align with their current level to be effective.
The key ideas of the Van Hiele Model are that learning is level-based, not age-based.
Moreso, it also highlight that progression depends on instruction and experience, not
maturation. Furthermore, each level has its own language and reasoning style and
learners cannot skip levels.
Below are the five levels of geometric thought:-
, Level 0: Visualization (Recognition)
Learners identify shapes based on appearance.
Example: A learner says, “This is a square because it looks like a box.”
They cannot yet describe properties.
Level 1: Analysis (Descriptive)
Learners identify properties of shapes.
Example: “A rectangle has four sides and four right angles.”
However, they do not yet understand relationships between shapes.
Level 2: Informal Deduction (Relational)
Learners understand relationships between properties and classes of shapes.
Example: “A square is a rectangle because it has all the properties of a rectangle.”
Level 3: Formal Deduction
Learners can form logical proofs and understand theorems (usually high school level).
Level 4: Rigor
Learners work with abstract systems of geometry (university level).
In conclusion , in the Intermediate Phase (Grades 4–6), teaching should focus mainly
on Levels 0–2.
Section B:
A short diagnostic task to assess learners’ Van Hiele levels in a Grade 5 class is
highlighted below.
Diagnostic Activity
Use this worksheet which had different 2D shapes (triangles, squares, rectangles,
rhombuses in different orientations).And then answer the questions that follow:-
