ABSTRACT
As soon as people began to represent objects by using pebbles or other small tokens, they became aware that they could count them more easily by arranging the stones in patterns. The easiest shapes are rectangles or squares, and this leads to the discovery of some elementary properties of numbers. The introduction of algebraic notation introduces a level of abstraction in mathematics which is both powerful and potentially confusing. This chapter considers two very different situations in which algebraic notation is used and try to unravel some of the complexities. It deals with some techniques for working with algebraic expressions which are useful in problem-solving situations. Number sequences can be derived from growth patterns. Mathematicians were manipulating rational numbers, decimal fractions, positive and negative quantities, algebraic numbers, positive and negative square roots, trigonometric and imaginary quantities with ease, but without any logical justification.
