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MIP2601 ASSIGNMENT 2 SEMESTER 1 2024
- Course
- MIP2601
- Institution
- University Of South Africa (Unisa)
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MIP2601ASSIGNMENT 02
Semester 1
2024
STUDENT NUMBER:
STUDENT NAMES:
UNIQUE NUMBER: 648210
DUE 12 JUNE 2024
TIME 19:00
Question 1: Geometric thinking
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)
Van Hiele level 1 focuses on recognition. Learners at this level can identify
and name geometric shapes, but they do not understand the relationships
between the shapes. For example, they can recognize a square, but they may
not understand that all sides of a square are equal.
Van Hiele level 2 involves analysis. Learners at this level can identify
properties and characteristics of geometric shapes. They can compare and
classify shapes based on their properties. For example, they can recognize
, that a rectangle has four right angles and opposite sides are equal.
Van Hiele level 3, as mentioned in the statement, is deduction. This is the
level where learners can develop logical sequences of statements to justify
conclusions. They understand the relationships and properties of geometric
shapes and can use deductive reasoning to prove statements. For example,
they can prove that the angles opposite the congruent sides of an isosceles
triangle are equal using deductive reasoning.
In summary, Van Hiele levels 1 to 3 progresses from simple recognition of
shapes to a deeper understanding of their properties and relationships,
ultimately leading to the ability to use deductive reasoning to prove geometric
statements.
1.2 Drawing from the CAPS Intermediate Phase Mathematics (Space and
Shape), what does it mean to say that the levels are hierarchical? (5)
In the context of the CAPS Intermediate Phase Mathematics, the levels in Van
Hiele's theory are hierarchical, which means that each level builds upon the
understanding and skills developed in the previous level. As learners progress
through the levels, they deepen their understanding of geometric concepts
and develop more advanced reasoning and deduction skills. This progression
allows for a systematic and structured approach to geometric learning,
ensuring that learners have a strong foundation before moving on to more
complex ideas.
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)
a) The framework helps teachers understand the different levels of
geometric thinking in students and tailor their teaching to each level.
b) It emphasizes the importance of hands-on, experiential learning in order
to move students from one level to the next.
c) It highlights the need for students to develop logical reasoning and
justification skills in geometry.
d) It encourages the use of concrete examples and manipulative to help
students visualize and understand geometric concepts.
e) It promotes the use of problem-solving and inquiry-based learning to
deepen students' understanding of geometry.
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)
Some early evidence of geometry can be found in ancient Egypt,
Mesopotamia, and Greece
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