1 Common misconceptions about proportional reasoning

Pause for thought To start thinking about the presence of proportional reasoning in everyday life, make a note of all the situations you come across where you use proportional reasoning over the period of a day. For example: ‘I made a smaller amount of chapattis – about half of normal. I adjusted the amount of flour I needed to halve the quantity as well.’ You could ask your students to do the same and bring their examples to the next lesson.

The core idea in proportional reasoning is that it uses multiplication and division to compare quantities and to describe how these quantities relate to each other. So the width of one leaf can be four times as big as the width of another; the height of a picture one-third of another one, the age of a child one-and-a-half times that of another child, etc.

Researchers suggest that the main issue with learning about proportional reasoning is that students’ understanding of multiplication is often based on the repeated addition of integers, which is limiting when learning to engage in proportional reasoning (Watson et al., 2013). When students are comparing, for example, the age of Child A who is eight years old with another Child B who is 12 years old they can find it easier to compare by using the difference in age (four years) than by describing the relationship in a multiplicative way (Child B is therefore 1.5 times as old as Child A).

The teaching challenge is thus to provide students with an understanding of multiplicative reasoning that does not use repeated addition.