Proportional reasoning: Connections to ratio and proportion
Before considering proportional reasoning, consider the meaning of the words ratio and proportion. In its barest form, ratio describes a situation in comparative terms, and proportion is when this comparison is used to describe a related situation in the same comparative terms. For example, if we say that the ratio of boys to girls in the class is 2 to 3, we are comparing the number of boys to the number of girls.
When we know that there are 30 children in the class we know that, proportionally, the number of boys is 12 and the number of girls is 18. We are using the base comparison to apply it to the whole situation. In order to understand this relationship proportional reasoning is used. Proportional thinking and reasoning is knowing the multiplicative relationship between the base ratio and the proportional situation to which it is applied.
Proportional reasoning is being able to make comparisons between entities in multiplicative terms. This means that the relationship between the two entities is conceptualised as a multiplicative relationship. For many young children, comparisons between entities are described in additive terms, and they compare groups using additive or subtractive language. For example, when comparing the number of boys to girls as in the example above (ratio of boys to girls 2:3), they may say that there is always one extra girl for each group of boys. So, if there were 4 boys, there would be five girls. Being able to describe proportional situations using multiplicative language is an indicator of proportional reasoning.