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MIP2601 Assignment 2 2024 - 12 June 2024
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MIP2601 Assignment 2 2024 - 12 June 2024 QUESTIONS WITH DETAILED ANSWERS
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+254792947610MIP2601
Assignment 2
2024 - 12 June
2024
QUESTIONS WITH DETAILED ANSWERS
,MIP2601 Assignment 2 2024 - 12 June 2024
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
MIP2601 Assignment 2 2024 - 12 June 2024
, MIP2601 Assignment 2 2024 - 12 June 2024
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.
MIP2601 Assignment 2 2024 - 12 June 2024
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