The elementary ideas in mathematics are abstractions drawn from the experiences an individual has with his physical environment. These experiences are prima rily of two kinds. There are, first, those experiences that arc associated with counting. They arise naturally in dea ling with collections of discrete objects and lead ultim ately to the abstract notion of the counting numbers and the operations on the counting numbers. That is, the experiences of this type a re those that induce us to in vent the counting numbers a nd the usual arithmetic of this system and its extensions. The second category of experiences includes those of a spatial nature. They are related to our perceptions of size, shape, and form. The child discovers that this pencil is too long to fit in that box; that this peg will just fit in that hole; that the faces of two of his blocks fit exactly on each other, and so on. These are the experiences that motivate us to identify and discuss various figures and to give names to the common ones like line segment, line, ray, plane, triangle, circle, and sphere. Thus the developing space percept ion of the individual leads to the creation of the mathematical ideas normally associated with the word “geometry.”
Dr. Jackson is a professor of mathematics at the University of Maryland.
