Thesis

CHAPTER 1

THE PROBLEM AND ITS BACKGROUND

Introduction

Geometry is one of the very useful branches of mathematics. It is the area of mathematics that deals with points, lines and shapes. It is also concerned with questions of size, relative position of figures, and the properties of space. Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry. H. M. S. Coxeter (2003)

The role of geometry in the development of mathematical idea is very important. The geometrical skills and visual icons are basic instruments and source of inspiration for many mathematicians (Chazan & Yeryshalmy in Protopapas, 2003). The content of geometry is appropriate both for the development of lower level of mathematical thinking, (i.e. the recognition of shape), as well as for higher order thinking, (i.e. the discovery of the properties of shapes), the construction of geometrical models and the solution of mathematical problems (NCTM, 1999). The representation of geometrical objects and the relationships between geometrical objects and their representations constitute important problems in geometry (Mesquita, 1998).

Geometry holds great importance in the forever-expanding world of mathematics. It enables us to picture what is happening in problems we may encounter in the study of mathematics. The study of geometry helps us develop the ability to visualize shapes, volume, area, and so on. Geometric proofs play an important role in the expansion and understanding of many branches of mathematics, from Venn diagrams in set theory to area under the graph in calculus. Geometry is a good training ground for students as well as mathematics teachers to make use of concrete materials and activities. Those same...