PURPOSE OF GEOMETRY
Geometry is used daily by everyone as it is evident in art, architecture, engineering,
robotics, land surveys, as astronomy, sculptures, space, nature, sports, machines, cars and much
more. It is the main reason for construction of buildings of wonders such as the Pyramids of
Egypt, Machu Picchu, Great Wall of China, Taj Mahal, Bali and Bagan Temples.
Apart from obvious uses of geometry, it also has a wide range of applications in scientific
and technological fields. Without the concept of geometry there could not have been any
technology to enjoy. Not only is it used for studies in angles and triangles, perimeter , area and
volume, but also to determined measurement, speed, velocity, momentum, direction, distance
and probabilistic measure in astronomical bodies.
Geometry also sharpens thinking skills by teaching the process of logical reasoning,
spatial reasoning, problem solving skills and deductive thinking because geometry trains the
mind in clear and rigorous thinking.
In schools students study geometry for a wide range of purposes and not just to perform
geometric tasks. When students study geometry they are able to:
Prepare themselves for further studies in mathematics and science
Represent aspects of the world they live in with greater accuracy.
Describe the world they live in with greater accuracy
Develop spatial sense
Develop dynamic imagery
Develop logical thinking
Build and develop problem solving skills
The national curriculum for secondary schools in Trinidad and Tobago is designed to support the
attainment of six Essential Learning Outcomes:
1. Aesthetic Expression (AE)
2. Communication (C)
3. Citizenship (CIT)
4. Personal Development (PD)
5. Problem Solving (PS)
6. Technological Competence (TC)
Geometry is used to acquire all of the above in the following ways:
Enhance students problem-solving skills through the use of algebraic thinking and the
use of models (PS);
To enhance problem-solving skills through the use of abstract reasoning and mental
visualization (PS);
To enhance critical thinking and enquiry skills (PS);
To stimulate intellectual curiosity (PS);
To enhance spatial reasoning in analysing patterns and relationships of points in space
(PS);
enhance problem-solving skills through the use of geometric models (PS);
To enhance technological skills (TC);
To develop skills in using charts, graphs, and symbols to communicate (C);
To facilitate the construction of new knowledge through problem solving (PS);
To enhance the skills required to analyse and evaluate mathematical thinking of others
(PS, C);
To adapt and share mathematical information using a variety of sources as well as
existing and developing technologies (TC);
To enhance the skills required to understand, interpret, and analyse change in a variety
ofsituations (PD, TC);
To develop understanding and appreciation of the role of mathematics in past, present,
and future social, political, and economic contexts (CIT);
To apply knowledge of mathematics concepts and procedures to address authentic issues
in various cultural, environmental, and global contexts (CIT)
The new NCTM Standards explicitly include visualization as an item under Chapter 3:
Geometry. In the detailed description for grades preK–12 (or secondary levels in the case of
Trinidad and Tobago), the Council elaborates:
“Over the grades, students should become comfortable analyzing and drawing perspective views,
counting component parts, and describing attributes that cannot be seen but can be inferred.
Students need to learn to physically and mentally change the position, orientation, and size of
objects in systematic ways as they develop their understandings about congruence, similarity,
and transformations”.
The new NCTM Standards discuss geometry in Chapter 3: Geometry:
Mathematics instructional programs should include attention to geometry and spatial sense so
that all students
analyze characteristics and properties of two- and three-dimensional geometric objects;
select and use different representational systems, including coordinate geometry and
graph theory;
recognize the usefulness of transformations and symmetry in analyzing mathematical
situations;
use visualization and spatial reasoning to solve problems both within and outside of
mathematics.
Therefore the purpose of geometry spans a wide range and includes scientific and technological
advancements throughout civilisation to the development of the individual.