Humans have an intuitive sense of number that allows them, for example, to readily identify which of two containers has more objects without counting. This ability is present at birth, and gradually improves throughout childhood_ScienceDaily
Johns Hopkins scientists have tested the Approximate Number Sense (ANS) in human pre-schoolers, then compared their ANS scores with later standard tests of math ability administered in school at age 6. They discovered a high correlation between the ANS score in preschool and the later math ability scores at age 6.
The Approximate Number System (ANS) is a primitive mental system of nonverbal representations that supports an intuitive sense of number in human adults, children, infants, and other animal species. The numerical approximations produced by the ANS are characteristically imprecise and, in humans, this precision gradually improves from infancy to adulthood. Throughout development, wide ranging individual differences in ANS precision are evident within age groups. These individual differences have been linked to formal mathematics outcomes, based on concurrent, retrospective, or short-term longitudinal correlations observed during the school age years. However, it remains unknown whether this approximate number sense actually serves as a foundation for these school mathematics abilities. Here we show that ANS precision measured at preschool, prior to formal instruction in mathematics, selectively predicts performance on school mathematics at 6 years of age. In contrast, ANS precision does not predict non-numerical cognitive abilities. To our knowledge, these results provide the first evidence for early ANS precision, measured before the onset of formal education, predicting later mathematical abilities.The authors were unable to determine whether ANS skills could be improved through early childhood intervention. But their findings add to a growing body of knowledge demonstrating a wide range of cognitive abilities between individuals, starting from a very early age. One should note that ANS precision correlates only to later math skills, and not to language skills.
...Further longitudinal studies are needed to evaluate whether and how mediators of the relationship between ANS skills and symbolic mathematics vary as a function of other child characteristics, and how ANS skills might predict not only math performance at a given time but also trajectories of growth in formal mathematics skills over development. _PLoS (Full paper)
It is important for scientists and educators to determine how much of individual cognitive capacity can be improved, and how much is relatively fixed. This should be done on an individual-to-individual basis to avoid prejudgement, and to better customise and optimise the education experience for each child.
This Johns Hopkins study offers some suggestive hints as to the nature of pre-verbal and non-verbal metaphor development in young children, prior to any formal math training.