MIP2601 Assignment
2 2024 - 12 June
2024
QUESTIONS WITH COMPLETE ANSWERS
[School]
[Course title]
,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
• Description: Learners begin to identify properties and attributes of shapes. They
can differentiate shapes based on these properties and start to understand and use
the correct terminology. They can analyze components and recognize properties
but do not yet understand how properties interact.
• Example: A learner can recognize that a square has four equal sides and four right
angles, and can distinguish it from a rectangle, which has right angles but not
necessarily equal sides.
Level 3: Informal Deduction
• Description: At this level, learners can understand relationships between
properties of shapes and use these relationships to solve problems. They can make
and test hypotheses and develop logical sequences of statements to justify
conclusions.
• Example: A learner can prove that in an isosceles triangle, the angles opposite the
congruent sides are equal by logically connecting the properties of the triangle and
using reasoning.
2 2024 - 12 June
2024
QUESTIONS WITH COMPLETE ANSWERS
[School]
[Course title]
,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
• Description: Learners begin to identify properties and attributes of shapes. They
can differentiate shapes based on these properties and start to understand and use
the correct terminology. They can analyze components and recognize properties
but do not yet understand how properties interact.
• Example: A learner can recognize that a square has four equal sides and four right
angles, and can distinguish it from a rectangle, which has right angles but not
necessarily equal sides.
Level 3: Informal Deduction
• Description: At this level, learners can understand relationships between
properties of shapes and use these relationships to solve problems. They can make
and test hypotheses and develop logical sequences of statements to justify
conclusions.
• Example: A learner can prove that in an isosceles triangle, the angles opposite the
congruent sides are equal by logically connecting the properties of the triangle and
using reasoning.
