MIP2601 ASSIGNMENT
2 2024 - 12 JUNE 2024
QUESTIONS WITH COMPLETE ANSWERS
[DATE]
[Company address]
, MIP2601 Assignment 2 2024 - 12 June 2024
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)
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape), what does it
mean to say that the levels are hierarchical? (5) MIP2601/102/0/2024 4
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)
1.4 The development of the geometry we know today, started very early in the human history.
(a) Where in the world do we find some early evidence of geometry? (1)
(b) Approximately to what year does this evidence date back? (1)
(c) Give details of how geometry was practiced in your example. (2) (d) Where in the CAPS is this
type of GEOMETRY covered as a topic? (1) [Sub-Total=26]
1.1. Van Hiele Levels 1 to 3
Van Hiele’s model of geometric thought is composed of five levels of understanding, from Level 0
(Visualization) to Level 4 (Rigor). Here, we discuss Levels 1 to 3 in detail:
Level 1: Visualization
• Description: At this level, learners recognize shapes and objects based on their appearance and
are able to identify and name them. They do not understand the properties and relationships of
the shapes.
2 2024 - 12 JUNE 2024
QUESTIONS WITH COMPLETE ANSWERS
[DATE]
[Company address]
, MIP2601 Assignment 2 2024 - 12 June 2024
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)
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and Shape), what does it
mean to say that the levels are hierarchical? (5) MIP2601/102/0/2024 4
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)
1.4 The development of the geometry we know today, started very early in the human history.
(a) Where in the world do we find some early evidence of geometry? (1)
(b) Approximately to what year does this evidence date back? (1)
(c) Give details of how geometry was practiced in your example. (2) (d) Where in the CAPS is this
type of GEOMETRY covered as a topic? (1) [Sub-Total=26]
1.1. Van Hiele Levels 1 to 3
Van Hiele’s model of geometric thought is composed of five levels of understanding, from Level 0
(Visualization) to Level 4 (Rigor). Here, we discuss Levels 1 to 3 in detail:
Level 1: Visualization
• Description: At this level, learners recognize shapes and objects based on their appearance and
are able to identify and name them. They do not understand the properties and relationships of
the shapes.
