Introduction to algebra

The equals sign in algebra - part 2

In algebra, however, the equals sign must be seen as representing equivalence. It means that what is written on one side ‘is the same as’ what is written on the other side. Of course, it has this meaning in arithmetic as well: 3 + 5 = 8 does mean that 3 + 5 is the same as 8. But pupils rarely use it to mean this; their experience reinforces the perception of the equals sign as an instruction to perform an operation with some numbers. In algebraic statements it is the idea of equivalence that is strongest in the way the equals sign is used. For example, when we write p + q = r, this is not actually an instruction to add p and q. In fact, we may not have to do anything at all with the statement. It is simply a statement of equivalence between one variable and the sum of two others.

This apparent lack of closure is a cause of consternation to some pupils. If the answer to an algebra question is p + q, they will have the feeling that there is still something to be done, because they are so wedded to the idea that the addition sign is an instruction to do something to the p and the q.

Remember to reinforce through your own language the idea that the equals sign means ‘is the same as’, even in the early stages of recording the results of calculations.