MIP2601
ASSIGNMENT 2
2024 - 12 JUNE
2024
[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.
• Example: A learner at this level can identify a square because it looks like a square they have seen
before but cannot explain why it is a square in terms of properties such as having four equal sides and
right angles.
Level 2: Analysis
ASSIGNMENT 2
2024 - 12 JUNE
2024
[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.
• Example: A learner at this level can identify a square because it looks like a square they have seen
before but cannot explain why it is a square in terms of properties such as having four equal sides and
right angles.
Level 2: Analysis
