Understanding decimal proportions: discrete representations, parallel access, and privileged processing of zero.

ABSTRACT

Much of the research on mathematical cognition has focused on the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, with considerably less attention paid to more abstract number classes. The current research investigated how people understand decimal proportions--rational numbers between 0 and 1 expressed in the place-value symbol system. The results demonstrate that proportions are represented as discrete structures and processed in parallel. There was a semantic interference effect When understanding a proportion expression (e.g., "0.29"), both the correct proportion referent (e.g., 0.29) and the incorrect natural number referent (e.g., 29) corresponding to the visually similar natural number expression (e.g., "29") are accessed in parallel, and when these referents lead to conflicting judgments, performance slows. There was also a syntactic interference effect, generalizing the unit-decade compatibility effect for natural numbers When comparing two proportions, their tenths and hundredths components are processed in parallel, and when the different components lead to conflicting judgments, performance slows. The results also reveal that zero decimals--proportions ending in zero--serve multiple cognitive functions, including eliminating semantic interference and speeding processing. The current research also extends the distance, semantic congruence, and SNARC effects from natural numbers to decimal proportions. These findings inform how people understand the place-value symbol system, and the mental implementation of mathematical symbol systems more generally.