, MIP2601 ASSIGNMENT 02
UNIQUE NUMBER 648210
DUE 12JUNE 2024 TIME 19:00
Question 1: Geometric thinking
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. (6)
Van Hiele level 1 focuses on recognition. Learners at this level can identify and name geometric
shapes, but they do not understand the relationships between the shapes. For example, they can
recognize a square, but they may not understand that all sides of a square are equal.
Van Hiele level 2 involves analysis. Learners at this level can identify properties and characteristics of
geometric shapes. They can compare and classify shapes based on their properties. For example,
they can recognize that a rectangle has four right angles and opposite sides are equal.
Van Hiele level 3, as mentioned in the statement, is deduction. This is the level where learners can
develop logical sequences of statements to justify conclusions. They understand the relationships
and properties of geometric shapes and can use deductive reasoning to prove statements. For
example, they can prove that the angles opposite the congruent sides of an isosceles triangle are
equal using deductive reasoning.
In summary, Van Hiele levels 1 to 3 progresses from simple recognition of shapes to a deeper
understanding of their properties and relationships, ultimately leading to the ability to use deductive
reasoning to prove geometric statements.
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape), what does it
mean to say that the levels are hierarchical? (5)
In the context of the CAPS Intermediate Phase Mathematics, the levels in Van Hiele's theory are
hierarchical, which means that each level builds upon the understanding and skills developed in the
previous level. As learners progress through the levels, they deepen their understanding of
geometric concepts and develop more advanced reasoning and deduction skills. This progression
UNIQUE NUMBER 648210
DUE 12JUNE 2024 TIME 19:00
Question 1: Geometric thinking
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. (6)
Van Hiele level 1 focuses on recognition. Learners at this level can identify and name geometric
shapes, but they do not understand the relationships between the shapes. For example, they can
recognize a square, but they may not understand that all sides of a square are equal.
Van Hiele level 2 involves analysis. Learners at this level can identify properties and characteristics of
geometric shapes. They can compare and classify shapes based on their properties. For example,
they can recognize that a rectangle has four right angles and opposite sides are equal.
Van Hiele level 3, as mentioned in the statement, is deduction. This is the level where learners can
develop logical sequences of statements to justify conclusions. They understand the relationships
and properties of geometric shapes and can use deductive reasoning to prove statements. For
example, they can prove that the angles opposite the congruent sides of an isosceles triangle are
equal using deductive reasoning.
In summary, Van Hiele levels 1 to 3 progresses from simple recognition of shapes to a deeper
understanding of their properties and relationships, ultimately leading to the ability to use deductive
reasoning to prove geometric statements.
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape), what does it
mean to say that the levels are hierarchical? (5)
In the context of the CAPS Intermediate Phase Mathematics, the levels in Van Hiele's theory are
hierarchical, which means that each level builds upon the understanding and skills developed in the
previous level. As learners progress through the levels, they deepen their understanding of
geometric concepts and develop more advanced reasoning and deduction skills. This progression
