1 Variables and constants in school mathematics
Understanding the role of variables and constants is essential for developing mathematical reasoning and understanding. It is required to manipulate algebraic expressions and also enables students ‘ to express mathematical relations in different ways, and know more about them’ (Watson et al., 2013, p. 15).
Technically, there are ‘dependent’ variables, ‘independent’ variables and constants. The unknown, x, is conventionally used to denote the independent variable, and is conventionally plotted along the horizontal axis when drawing a graph.
For example, in the expression:
y = x + 4
where x and y are integers:
- x is the independent variable and can stand for any value in the set for which the expression is defined. In this example this means it can be any integer.
- y is described as a dependent variable. It is dependent because its value will depend on the value of x. It is a variable because, like x, it can stand for any value in the set for which the expression is defined. In this example this means it can be any integer.
- 4 is the constant, that is, a fixed quantity, whatever the values of the independent or dependent variables.
Research suggests that one of the main issues that students encounter in learning about variables and constants, and manipulating algebra in general, is not understanding the relationships between quantities and variables in algebraic expressions. This unit aims to develop this understanding by giving meaning to variables and constants by making students think and talk about connections between numbers and algebraic expressions.