MIP2601
ASSIGNMENT 1
ANSWERS 2026
MIP2601 ASSIGNMENT 1 ANSWERS
2026
, MIP2601 ASSIGNMENT 1
A. Conceptual explanation of the Van Hiele model
Origin and key ideas
- Origin: The Van Hiele model was developed in the 1950s by Dutch educators Dina
van Hiele-Geldof and her husband Pierre van Hiele. It emerged from their studies of
how students think about geometry and how instruction should match and advance
that thinking.
- Core ideas:
- Geometry learning is a progression through qualitatively different ways of thinking,
not just a set of topics to be memorized.
- Learners move through levels as they engage with carefully designed tasks;
instruction must be adapted to the learner’s current level and provide appropriate
next-step tasks to progress.
- Levels describe the nature of thinking (how students think about shapes and their
properties, relationships, proofs, and axioms), not simply what content a student can
“name.”
- The process is sequential: students typically need to experience and practice at
one level before they can meaningfully engage with the next level.
The five levels (names often numbered 0–4 in contemporary classroom use)
- Level 0: Visualization (also called Visual Thinking)
- What characterizes it: Thinking is based on the overall appearance of shapes;
students recognize figures by how they look, not by their properties or relationships.
- Typical behaviors: Saying “that is a triangle” because it looks like a triangle,
regardless of side lengths or angles; confusing shapes that look similar; difficulty
distinguishing figures by properties.
- Example in geometry: A student sees a triangle and a trapezoid and identifies only
by overall shape, not by the number of sides.
B: Diagnostic Task analysis
1) Quick orientation: Van Hiele levels (reminder)
ASSIGNMENT 1
ANSWERS 2026
MIP2601 ASSIGNMENT 1 ANSWERS
2026
, MIP2601 ASSIGNMENT 1
A. Conceptual explanation of the Van Hiele model
Origin and key ideas
- Origin: The Van Hiele model was developed in the 1950s by Dutch educators Dina
van Hiele-Geldof and her husband Pierre van Hiele. It emerged from their studies of
how students think about geometry and how instruction should match and advance
that thinking.
- Core ideas:
- Geometry learning is a progression through qualitatively different ways of thinking,
not just a set of topics to be memorized.
- Learners move through levels as they engage with carefully designed tasks;
instruction must be adapted to the learner’s current level and provide appropriate
next-step tasks to progress.
- Levels describe the nature of thinking (how students think about shapes and their
properties, relationships, proofs, and axioms), not simply what content a student can
“name.”
- The process is sequential: students typically need to experience and practice at
one level before they can meaningfully engage with the next level.
The five levels (names often numbered 0–4 in contemporary classroom use)
- Level 0: Visualization (also called Visual Thinking)
- What characterizes it: Thinking is based on the overall appearance of shapes;
students recognize figures by how they look, not by their properties or relationships.
- Typical behaviors: Saying “that is a triangle” because it looks like a triangle,
regardless of side lengths or angles; confusing shapes that look similar; difficulty
distinguishing figures by properties.
- Example in geometry: A student sees a triangle and a trapezoid and identifies only
by overall shape, not by the number of sides.
B: Diagnostic Task analysis
1) Quick orientation: Van Hiele levels (reminder)
