MIP2601
A S S I G N M E N T 2
D U E 1 0 J U N E 2 0 2 4
, Assignment Unique number Due date
2 648210 12 June 2024, Time:
19:00
Question1: Geometricthinking
Read the following statement referring to Van Hiele’s Level 3: Deduction, and then
answer the questions that follow.
Learners can now develop sequences of statements that logically justify conclusions.
Given an isosceles triangle for example, learners can prove that the angles opposite the
congruent sides are equal.
1.1. Clements and Batista (1994) classify Van Hiele levels from 1 to 5. Using examples,
discuss the levels 1 to 3 in detail.
Geometric Thinking
1.1 Discussing Levels 1 to 3 of the Van Hiele Model in Detail
Level 1: Visualization
At this level, learners recognize basic geometric shapes and connect them to real-world
objects. For instance, they might identify a square as resembling a window. However, they
do not yet understand the properties or relationships between shapes.
Example: A child sees a circle and describes it as a "round pizza."
Level 2: Analysis
At Level 2, learners begin to attach properties to shapes. They can identify characteristics
such as the number of sides or angles in a shape. They may also engage in hands-on
activities like folding and cutting paper to explore geometric concepts further.
Example: A learner can state that a square has four sides that are all the same length.
Level 3: Informal Deduction
In this stage, learners can find relationships between shapes and their properties. They start
to make logical deductions based on their understanding of geometric principles. Activities
, like completing Venn diagrams to compare shapes help reinforce their deductive reasoning
skills.
Example: Given an isosceles triangle, learners can prove that the angles opposite the
congruent sides are equal.
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape),
what does it mean to say that the levels are hierarchical?
In the Curriculum and Assessment Policy Statement (CAPS) for Intermediate Phase
Mathematics (Space and Shape), the levels of the Van Hiele Model are considered
hierarchical. This means that learners must progress through each level sequentially,
building upon their understanding at each stage.
Example: In CAPS, learners first develop a visual understanding of shapes and their
properties (Level 1). Then, they analyze shapes and begin to recognize their attributes (Level
2). Finally, they reach Level 3, where they can make logical deductions and prove geometric
relationships. Each level serves as a foundation for the next, with Level 3 building upon the
skills and concepts developed in Levels 1 and 2.
Following a hierarchical progression, learners develop a deeper and more sophisticated
understanding of geometric thinking, ultimately leading to proficiency in geometry at the
Intermediate Phase level.
A S S I G N M E N T 2
D U E 1 0 J U N E 2 0 2 4
, Assignment Unique number Due date
2 648210 12 June 2024, Time:
19:00
Question1: Geometricthinking
Read the following statement referring to Van Hiele’s Level 3: Deduction, and then
answer the questions that follow.
Learners can now develop sequences of statements that logically justify conclusions.
Given an isosceles triangle for example, learners can prove that the angles opposite the
congruent sides are equal.
1.1. Clements and Batista (1994) classify Van Hiele levels from 1 to 5. Using examples,
discuss the levels 1 to 3 in detail.
Geometric Thinking
1.1 Discussing Levels 1 to 3 of the Van Hiele Model in Detail
Level 1: Visualization
At this level, learners recognize basic geometric shapes and connect them to real-world
objects. For instance, they might identify a square as resembling a window. However, they
do not yet understand the properties or relationships between shapes.
Example: A child sees a circle and describes it as a "round pizza."
Level 2: Analysis
At Level 2, learners begin to attach properties to shapes. They can identify characteristics
such as the number of sides or angles in a shape. They may also engage in hands-on
activities like folding and cutting paper to explore geometric concepts further.
Example: A learner can state that a square has four sides that are all the same length.
Level 3: Informal Deduction
In this stage, learners can find relationships between shapes and their properties. They start
to make logical deductions based on their understanding of geometric principles. Activities
, like completing Venn diagrams to compare shapes help reinforce their deductive reasoning
skills.
Example: Given an isosceles triangle, learners can prove that the angles opposite the
congruent sides are equal.
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape),
what does it mean to say that the levels are hierarchical?
In the Curriculum and Assessment Policy Statement (CAPS) for Intermediate Phase
Mathematics (Space and Shape), the levels of the Van Hiele Model are considered
hierarchical. This means that learners must progress through each level sequentially,
building upon their understanding at each stage.
Example: In CAPS, learners first develop a visual understanding of shapes and their
properties (Level 1). Then, they analyze shapes and begin to recognize their attributes (Level
2). Finally, they reach Level 3, where they can make logical deductions and prove geometric
relationships. Each level serves as a foundation for the next, with Level 3 building upon the
skills and concepts developed in Levels 1 and 2.
Following a hierarchical progression, learners develop a deeper and more sophisticated
understanding of geometric thinking, ultimately leading to proficiency in geometry at the
Intermediate Phase level.
