Is the ANS linked to mathematics performance?

The relationship between numerical mapping abilities, maths achievement and socioeconomic status in 4- and 5-year-old children

BACKGROUND

Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances.

AIMS

The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance.

SAMPLE

Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds.

METHOD

The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks.

RESULTS

The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks.

CONCLUSION

The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Impaired large numerosity estimation and intact subitizing in developmental dyscalculia

It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.

Visual form perception predicts 3-year longitudinal development of mathematical achievement

Numerous studies have demonstrated an association between approximate number system (ANS) acuity and mathematical performance. Studies have also shown that ANS acuity can predict the longitudinal development of mathematical achievement. Visual form perception in the current investigation was proposed to account for the predictive role of ANS acuity in the development of mathematical achievement. One hundred and eighty-eight school children (100 males, 88 females; mean age = 12.2 ± 0.3 years) participated in the study by completing five tests: numerosity comparison, figure matching, mental rotation, nonverbal matrix reasoning, and choice reaction time. Three years later, they took a mathematical achievement test. We assessed whether the early tests predicted mathematical achievement at the later date. Analysis showed that the ANS acuity measured via numerosity comparison significantly predicted mathematical achievement 3 years later, even when controlling for individual differences in mental rotation, nonverbal matrix reasoning, and choice reaction time, as well as age and gender differences. Hierarchical regression and mediation analyses further showed that the longitudinal predictive role of ANS acuity in mathematical achievement was interpreted by visual form perception measured with a figure-matching test. Together, these results indicate that visual form perception may be the underlying cognitive mechanism that links ANS acuity to mathematical achievement in terms of longitudinal development.

Ontogenetic Origins of Human Integer Representations

Do children learn number words by associating them with perceptual magnitudes? Recent studies argue that approximate numerical magnitudes play a foundational role in the development of integer concepts. Against this, we argue that approximate number representations fail both empirically and in principle to provide the content required of integer concepts. Instead, we suggest that children's understanding of integer concepts proceeds in two phases. In the first phase, children learn small exact number word meanings by associating words with small sets. In the second phase, children learn the meanings of larger number words by mastering the logic of exact counting algorithms, which implement the successor function and Hume's principle (that one-to-one correspondence guarantees exact equality). In neither phase do approximate number representations play a foundational role.