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

  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},
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

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

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.

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

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

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.

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.




Variability signatures distinguish verbal from nonverbal counting for both large and small numbers

The unexpected power-law relation between target value and mean number of presses in nonverbal counting suggests a new hypothesis about the development of the function relating number symbols to mental magnitudes.

Core systems of number

Handbook of mathematical cognition

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M.

Developmental change in the acuity of the "Number Sense": The Approximate Number System in 3-, 4-, 5-, and 6-year-olds and adults.

It is shown that the resolution of the Approximate Number System continues to increase throughout childhood, with adultlike levels of acuity attained surprisingly late in development.

Numerical Subtraction in the Pigeon: Evidence for a Linear Subjective Number Scale

The results indicate that subjective number is linearly, not logarithmically, related to objective number.

Bootstrapping & the origin of concepts

beings create scienti1⁄2c theories, mathematics, literature, moral systems, and complex technology. And only humans have the capacity to acquire such culturally constructed knowledge in the normal

Exact and Approximate Arithmetic in an Amazonian Indigene Group

This work studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words, and implies a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.

Ordering of the numerosities 1 to 9 by monkeys.

Rhesus monkeys represent the numerosities 1 to 9 on an ordinal scale and detect their ordinal disparity, and use numerical representations computationally to represent visual stimuli.

Numerical Cognition Without Words: Evidence from Amazonia

Results of numerical tasks with varying cognitive demands show that numerical cognition is clearly affected by the lack of a counting system in the Pirahã tribe, suggesting an analog estimation process.