The relationship between number sense and mathematics achievement in children and adults

There is growing evidence that humans have an inbuilt 'number sense' system that supports approximate numerical operations. Findings suggest that when we learn to deal with symbolic numerals, they may be mapped onto the pre-existing non-symbolic system. Theorists have speculated that this non-symbolic system might be the cognitive basis of all higher mathematics. However, the relationship between 'number sense' and formal mathematics ability remains somewhat unclear. If symbolic arithmetic is aided by the use of a nonsymbolic
system, then children's understanding of number could be facilitated by improving mapping between systems. In the present study, seven- to nine-year old and adult participants were assessed for non-symbolic acuity, formal mathematics ability and IQ. In children, there was a positive relationship between formal mathematics ability and nonsymbolic comparison accuracy when controlling for IQ. In adults, however, this relationship was not present. This pattern of findings suggests a developmental shift in the relationship
between formal mathematics ability and non-symbolic acuity. In particular it seems that if 'number sense' is the cognitive basis of mathematical ability, it fulfils only a bootstrapping role.