The concepts of shape, size and position has been familiar to human beings from the earliest stage. Even at the Primary level of education children are learning through perception and purposive action. The main aim is to acquaint children with the organization of spatial experiences.
Herbert recommended the training in sense perception on squares, triangles etc. In the Montessori Methods, the perception of forms is an integral part of programme of sense-training by means of Geometrical insets and other apparatus. Froebel’s gifts give the pupils opportunities to handle and learn the properties of the sphere, the cube, and the square, card-board modeling and paper-folding bring out the idea of the right angles. Games and folk-dances introduce the idea of circles, squares, parallels and diagonals.
The aims and functions of Geometry in the Secondary Schools follow these adopted at the Primary stage. The major objective of instruction in Geometry in the Secondary Schools is to teach pupils to think clearly and logically, to be critical and to generalize correctly. In other words, Geometry in Secondary Schools should train the students to seek and to discover truth and to understand the meaning of exactness and precision in mathematical reasoning.
In the teaching of theoretical geometry, the teacher points out the gaps in the process of reasoning by helping them to state the “why” and “how” of steps of the proof. This gives students and idea of logical proof of accuracy and clear reasoning.