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. Generally, 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 their spatial sense

 Develop dynamic imagery

 Develop logical thinking, and

 Build and develop problem solving skills

The national curriculum for secondary schools in Trinidad and Tobago is designed to support the attainment of the following 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)

It outlines these various purposes specific to geometry in the relevant section(s). These specific puposes include the following:

 To 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 of situations (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 Standards goes on to discuss geometry in Chapter 3: Geometry. It explains that mathematics instructional programs should include attention to geometry and spatial sense so that all students will be capable of

 analyzing characteristics and properties of two- and three-dimensional geometric objects;

 selecting and using different representational systems, including coordinate geometry and graph theory;  recognizing the usefulness of transformations and symmetry in analyzing mathematical situations;

 using visualization and spatial reasoning to solve problems both within and outside of mathematics.

Therefore, the purpose of geometry evidently spans a wide range: from the individual’s development in their thinking, to the various advancements made possible in society as a result. These purposes are recognised not only nationally in Trinidad and Tobago but also, from research, globally as well.