Exam (elaborations)
MIP2601 Assignment 2 (COMPLETE ANSWERS) 2024 - 12 June 2024
- Course
- MIP2601
- Institution
- University Of South Africa
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MIP2601Assignment 2
(COMPLETE
ANSWERS)
2024 - 12 June
2024
CONTACT: biwottcornelius@gmail.com
, 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 Levels 1 to 3 of Van Hiele's geometric thinking model represent different stages of
understanding geometry.
Level 1: Visualization: At this level, learners recognize shapes based on their
appearance and characteristics. For example, they can identify basic shapes like squares,
triangles, and circles, but their understanding is limited to visual recognition without
deeper comprehension of properties or relationships.
Level 2: Analysis: Learners at this stage start to understand the properties and
relationships of geometric figures. They can compare shapes, identify basic properties
like congruence or symmetry, and classify shapes based on these properties.
Level 3: Deduction: This is the level where learners can logically justify conclusions
based on sequences of statements. They can prove geometric theorems and propositions
using deductive reasoning. For instance, they can prove that the angles opposite the
congruent sides of an isosceles triangle are equal through a logical sequence of steps.
1.2 In the context of CAPS Intermediate Phase Mathematics (Space and Shape), the hierarchical
nature of the Van Hiele levels means that understanding at each level builds upon the previous
one. For instance, before students can engage in deductive reasoning (Level 3), they need to have
a solid grasp of geometric properties and relationships (Level 2), which, in turn, relies on their
ability to recognize shapes and their characteristics (Level 1). Each level serves as a foundation
for the next, with increasing complexity and depth of understanding.
1.3 Implications of Van Hiele’s framework in the teaching and learning of geometry in the
Intermediate Phase mathematics include:
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