MIP2601 Assignment 2 (COMPLETE ANSWERS) 2024 - 12 June 2024; 100% TRUSTED workings, explanations and solutions. .............. 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 devel...
MIP2601 Assignment
2 (COMPLETE
ANSWERS) 2024 - 12
June 2024; 100%
TRUSTED workings,
explanations and
solutions.
ADMIN
[COMPANY NAME]
, 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
Level 1: Visualization
• Description: At this level, learners recognize shapes and objects based on their
appearance. They can identify and name various shapes but do not understand their
properties or relationships.
• Example: A learner can identify a square, a triangle, and a circle by looking at them, but
they cannot explain why a square has right angles or why all sides of a triangle add up to
180 degrees.
Level 2: Analysis
• Description: Learners start to understand properties and attributes of shapes. They can
classify shapes based on their properties and begin to see relationships between different
shapes.
• Example: A learner can explain that a square has four equal sides and four right angles.
They can differentiate between a square and a rectangle based on these properties.
Level 3: Deduction
• Description: Learners can develop sequences of logical statements to justify conclusions.
They understand the properties of shapes and can use deductive reasoning to prove
geometric relationships.
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