Intensive quantities: why they matter to developmental research

A distinction can be drawn between extensive and intensive quantities. Extensive quantities (e.g., volume, distance), which have been the focus of developmental research, depend upon additive combination. Intensive quantities (e.g., density, speed), which have been relatively neglected, derive from proportional relations between variables. Thus, while proportional relations can be expressed with extensive quantities, these relations are constitutive with intensive quantities. One consequence is that factors, which are theorized as marginal with extensive quantities, are conceptually central in intensive contexts, and may need to be recognized in developmental models. Two such factors, termed variable salience and relational focus, are examined here, via a study where 963 Scottish children aged 7-12 years were asked to solve 42 intensive quantity problems in comparison and missing value format. Reasoning improved with age, but at all ages it was strongly influenced by variable salience and relational focus. Moreover, the manner in which these two factors interacted with other factors differed from what might be expected from models of proportional reasoning with extensive quantities. Based upon these results, it is argued that the distinction between extensive and intensive quantities is theoretically significant, and intensive quantities need to be granted more attention in the future.