The componential nature of arithmetical cognition: some important questions.

Research on typically developing children and adults and people with developmental and acquired dyscalculia converges in indicating that arithmetical ability is not unitary but is made up of many different components. Categories of components include non-symbolic quantity representation and processing; symbolic quantity representation and processing; counting procedures and principles; arithmetic operations; arithmetical knowledge and understanding; multiple forms and applications of conceptual knowledge of arithmetic; and domain-general abilities such as attention, executive functions and working memory. There is much evidence that different components can and often do show considerable functional independence, not only in developmental and acquired dyscalculia, but in typically achieving children and adults. At the same time, it is possible to find complex interactions and bidirectional relationships between the different components, including between domain-specific and apparently domain-general abilities. There is a great deal that still needs to be discovered. In particular, we need to learn more about the origins in infancy of subitizing and approximate magnitude comparison, the extent to which these interact, the extent to which they may be further divisible, and the extent and ways in which they themselves may develop with age and the extent to which they may influence later-developing components. There also needs to be a lot more research on exactly how domain-general and domain-specific abilities contribute to mathematical development, and how they interact with one another.