Individual differences in non-verbal number acuity correlate with maths achievement

@article{Halberda2008IndividualDI,
  title={Individual differences in non-verbal number acuity correlate with maths achievement},
  author={Justin Halberda and Mich{\`e}le M. M. Mazzocco and Lisa Feigenson},
  journal={Nature},
  year={2008},
  volume={455},
  pages={665-668}
}
Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals—these groups can all represent the approximate number of items in visual or auditory arrays without verbally… 

Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children

TLDR
It is demonstrated that although when measured concurrently the same relationship holds in children, it does not hold in adults and that nonverbal number representations do not hold the key to explaining the wide variety of mathematical performance levels in adults.

Acquisition of the Cardinal Principle Coincides with Improvement in Approximate Number System Acuity in Preschoolers

TLDR
These findings suggest that experience with culture and language is intimately linked to changes in the properties of a core cognitive system, particularly the Approximate Number System.

Preschool acuity of the approximate number system correlates with school math ability.

TLDR
It is found that children's ANS acuity correlated with their math ability, even when age and verbal skills were controlled for, providing evidence for a relationship between the primitive sense of number and math ability starting early in life.

Education Enhances the Acuity of the Nonverbal Approximate Number System

TLDR
It is found that education significantly enhances the acuity with which sets of concrete objects are estimated, and it is hypothesized that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction.

Training the Approximate Number System Improves Math Proficiency

TLDR
In the two experiments reported here, it is shown that ANS training on approximate addition and subtraction of arrays of dots selectively improved symbolic addition and subtracting in symbolic math.

Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children.

TLDR
These findings argue against an exclusive role for non-symbolic number in supporting early mathematical understanding and suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non-numerical magnitude.

The approximate number system and its relation to early math achievement: evidence from the preschool years.

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