MIP2601
Assignment 2
2025 - DUE12
June 2025
user
, QUESTION 1: GEOMETRIC THINKING
1.1 Van Hiele‟s Levels (1–3)
Level 1: Visualisation (Recognition Level)
At this level, learners recognise shapes based on their appearance without
understanding properties. They identify figures visually as whole objects rather than
by individual attributes.
Example: A learner identifies a shape as a "square" simply because it looks like
one. If it’s rotated or skewed, they might not recognise it as a square anymore.
Level 2: Analysis (Descriptive Level)
Learners begin recognising and describing geometric figures by their properties,
like sides and angles. They do not yet understand relationships between these
properties.
Example: A learner can state a square has four equal sides and four right angles,
but may not realise all squares are rectangles.
Level 3: Informal Deduction (Abstraction Level)
Learners begin understanding relationships between properties. They can classify
shapes based on logical reasoning, making connections between properties.
Example: A learner understands all squares are rectangles because squares share
all properties of rectangles (four right angles, opposite sides equal), plus have all
sides equal.
1.2 Hierarchical Nature of Van Hiele‟s Levels
The Van Hiele levels are hierarchical, meaning:
Each level builds logically upon the previous level.
Assignment 2
2025 - DUE12
June 2025
user
, QUESTION 1: GEOMETRIC THINKING
1.1 Van Hiele‟s Levels (1–3)
Level 1: Visualisation (Recognition Level)
At this level, learners recognise shapes based on their appearance without
understanding properties. They identify figures visually as whole objects rather than
by individual attributes.
Example: A learner identifies a shape as a "square" simply because it looks like
one. If it’s rotated or skewed, they might not recognise it as a square anymore.
Level 2: Analysis (Descriptive Level)
Learners begin recognising and describing geometric figures by their properties,
like sides and angles. They do not yet understand relationships between these
properties.
Example: A learner can state a square has four equal sides and four right angles,
but may not realise all squares are rectangles.
Level 3: Informal Deduction (Abstraction Level)
Learners begin understanding relationships between properties. They can classify
shapes based on logical reasoning, making connections between properties.
Example: A learner understands all squares are rectangles because squares share
all properties of rectangles (four right angles, opposite sides equal), plus have all
sides equal.
1.2 Hierarchical Nature of Van Hiele‟s Levels
The Van Hiele levels are hierarchical, meaning:
Each level builds logically upon the previous level.
