PREVIEW
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 allows
for a systematic and structured approach
to geometric learning, ensuring that
learners have a strong foundation before
moving on to more complex ideas.
MIP2601 NATALIE FOXX
ASSIGNMENT 2 2024
, Question 1: Geometric thinking
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
allows for a systematic and structured approach to geometric learning, ensuring
that learners have a strong foundation before moving on to more complex
ideas.
1.3 What are the 5 implications of Van Hiele’s framework in the teaching and
learning of geometry in the Intermediate Phase mathematics? (10)
a) The framework helps teachers understand the different levels of geometric
thinking in students and tailor their teaching to each level.
b) It emphasizes the importance of hands-on, experiential learning in order to
move students from one level to the next.
c) It highlights the need for students to develop logical reasoning and
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 allows
for a systematic and structured approach
to geometric learning, ensuring that
learners have a strong foundation before
moving on to more complex ideas.
MIP2601 NATALIE FOXX
ASSIGNMENT 2 2024
, Question 1: Geometric thinking
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
allows for a systematic and structured approach to geometric learning, ensuring
that learners have a strong foundation before moving on to more complex
ideas.
1.3 What are the 5 implications of Van Hiele’s framework in the teaching and
learning of geometry in the Intermediate Phase mathematics? (10)
a) The framework helps teachers understand the different levels of geometric
thinking in students and tailor their teaching to each level.
b) It emphasizes the importance of hands-on, experiential learning in order to
move students from one level to the next.
c) It highlights the need for students to develop logical reasoning and
