Spatial Development, Geometry & Trigonometry in
Intermediate and Senior Phase Mathematics
MAE102K
Department of Mathematics Education
Assignment 02 Semester 01 2022 (compulsory)
Unique Number: 173860
Due Date: 13 April 2022
Terms of use:
• To be used ONLY for comparison purposes (As a guideline)
• Do not duplicate or distribute without written consent from the author. (That includes
distribution on WhatsApp/Telegram etc.
•
Question 1
1.1 Explain the first three levels of Van Hiele’s geometric thinking that Intermediate and Senior
Phase learners go through. (9)
Answer:
, Level 0: Visualization: Recognize and name figures based on the global visual characteristics of
the figure. (Classes of shapes)
• Figures are judged by appearance
• Grouping of shapes that seem to be “alike”.
- A square is a square “because it looks like a square”.
- Rotated square is not a square to this level of thinker.
Level 1: Analysis: At this level pupils (students) start analyzing and naming properties of
geometric figures. (Properties of shapes)
• Descriptive level
• Properties of shapes
- A square is a square because it is a rectangle with four congruent sides.
• Relationships among properties not developed.
- Won’t see the relationship between squares, rectangles, and parallelograms.
Level 2: Informal deduction: Students perceive relationships between properties and figures.
(Relationships between properties)
• Relationships among properties of geometric ideas developed.
• Able to justify relationships based on properties.
- “If all four angles are right angles, the shape must be a rectangle. If it is a square,
all angles are right angles. If it is a square, it must be a rectangle.”
Refer to page 513-514 of the prescribed textbook:
The van Hiele Levels of Geometric Thought
The van Hiele model is a five-level hierarchy of understanding spatial ideas (see Figure 20.1).
Each level describes the thinking processes used in geometric contexts. Specifically, the levels
describe how we think and what types of geometric ideas we think about (called objects of
thought) and what students can do (products of thought). The levels are developmental—
learners of any age begin at level 0 and progress to the next level through experiences with
geometrical ideas. Characteristics of the van Hiele levels are provided in Table 20.1.
Intermediate and Senior Phase Mathematics
MAE102K
Department of Mathematics Education
Assignment 02 Semester 01 2022 (compulsory)
Unique Number: 173860
Due Date: 13 April 2022
Terms of use:
• To be used ONLY for comparison purposes (As a guideline)
• Do not duplicate or distribute without written consent from the author. (That includes
distribution on WhatsApp/Telegram etc.
•
Question 1
1.1 Explain the first three levels of Van Hiele’s geometric thinking that Intermediate and Senior
Phase learners go through. (9)
Answer:
, Level 0: Visualization: Recognize and name figures based on the global visual characteristics of
the figure. (Classes of shapes)
• Figures are judged by appearance
• Grouping of shapes that seem to be “alike”.
- A square is a square “because it looks like a square”.
- Rotated square is not a square to this level of thinker.
Level 1: Analysis: At this level pupils (students) start analyzing and naming properties of
geometric figures. (Properties of shapes)
• Descriptive level
• Properties of shapes
- A square is a square because it is a rectangle with four congruent sides.
• Relationships among properties not developed.
- Won’t see the relationship between squares, rectangles, and parallelograms.
Level 2: Informal deduction: Students perceive relationships between properties and figures.
(Relationships between properties)
• Relationships among properties of geometric ideas developed.
• Able to justify relationships based on properties.
- “If all four angles are right angles, the shape must be a rectangle. If it is a square,
all angles are right angles. If it is a square, it must be a rectangle.”
Refer to page 513-514 of the prescribed textbook:
The van Hiele Levels of Geometric Thought
The van Hiele model is a five-level hierarchy of understanding spatial ideas (see Figure 20.1).
Each level describes the thinking processes used in geometric contexts. Specifically, the levels
describe how we think and what types of geometric ideas we think about (called objects of
thought) and what students can do (products of thought). The levels are developmental—
learners of any age begin at level 0 and progress to the next level through experiences with
geometrical ideas. Characteristics of the van Hiele levels are provided in Table 20.1.
