Education enhances the acuity of the nonverbal approximate number system

Children’s Arithmetic Development

In this article, we present the results of an 11-month longitudinal study (beginning when children were 6 years old) focusing on measures of the approximate number sense (ANS) and knowledge of the Arabic numeral system as possible influences on the development of arithmetic skills. Multiple measures of symbolic and nonsymbolic magnitude judgment were shown to define a unitary factor that appears to index the efficiency of an ANS system, which is a strong longitudinal correlate of arithmetic skills. However, path models revealed that knowledge of Arabic numerals at 6 years was a powerful longitudinal predictor of the growth in arithmetic skills, whereas variations in magnitude-comparison ability played no additional role in predicting variations in arithmetic skills. These results suggest that verbal processes concerned with learning the labels for Arabic numerals, and the ability to translate between Arabic numerals and verbal codes, place critical constraints on arithmetic development.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics.

Assessing "economic value": symbolic-number mappings predict risky and riskless valuations

Diminishing marginal utility (DMU) is a basic tenet of economic and psychological models of judgment and choice, but its determinants are little understood. In the research reported here, we tested whether insensitivities in valuations of dollar amounts (e.g., $40, $100) may be due to inexact mappings of symbolic numbers (i.e., "40," "100") onto mental magnitudes. In three studies, we demonstrated that inexact mappings appear to guide valuation and mediate numeracy's relations with riskless valuations (Studies 1 and 1a) and risky choices (Study 2). The results highlight the fundamental notion that individuals' valuations of $100 depend critically on how individuals perceive and map the symbolic quantity "100." This notion has implications for conceptualizations of value, risk aversion, intertemporal choice, and dual-process theories of decision making. Normative implications are also briefly discussed.

The impact of mathematical proficiency on the number-space association

A specific instance of the association between numerical and spatial representations is the SNARC (Spatial Numerical Association of Response Codes) effect. The SNARC effect describes the finding that during binary classification of numbers participants are faster to respond to small/large numbers with the left/right hand respectively. Even though it has been frequently replicated, important inter-individual variability has also been reported. Mathematical proficiency is an obvious candidate source for inter-individual variability in numerical judgments, but studies investigating its influence on the SNARC effect remain scarce. The present experiment included a total of 95 University students, divided into three groups differing significantly in their mathematical proficiency levels. Using group analyses, it appeared that the three groups differed significantly in the strength of their number-space associations in a parity judgment task. This result was further confirmed on an individual level, with higher levels in arithmetic leading to relatively weaker SNARC effects. To explain this negative relationship we propose accounts based on differences in access to qualitatively different numerical representations and also consider more domain general factors, with a focus on inhibition capacities.

Two randomized trials provide no consistent evidence for nonmusical cognitive benefits of brief preschool music enrichment

Young children regularly engage in musical activities, but the effects of early music education on children's cognitive development are unknown. While some studies have found associations between musical training in childhood and later nonmusical cognitive outcomes, few randomized controlled trials (RCTs) have been employed to assess causal effects of music lessons on child cognition and no clear pattern of results has emerged. We conducted two RCTs with preschool children investigating the cognitive effects of a brief series of music classes, as compared to a similar but non-musical form of arts instruction (visual arts classes, Experiment 1) or to a no-treatment control (Experiment 2). Consistent with typical preschool arts enrichment programs, parents attended classes with their children, participating in a variety of developmentally appropriate arts activities. After six weeks of class, we assessed children's skills in four distinct cognitive areas in which older arts-trained students have been reported to excel: spatial-navigational reasoning, visual form analysis, numerical discrimination, and receptive vocabulary. We initially found that children from the music class showed greater spatial-navigational ability than did children from the visual arts class, while children from the visual arts class showed greater visual form analysis ability than children from the music class (Experiment 1). However, a partial replication attempt comparing music training to a no-treatment control failed to confirm these findings (Experiment 2), and the combined results of the two experiments were negative: overall, children provided with music classes performed no better than those with visual arts or no classes on any assessment. Our findings underscore the need for replication in RCTs, and suggest caution in interpreting the positive findings from past studies of cognitive effects of music instruction.

Developmental changes in the association between approximate number representations and addition skills in elementary school children

The approximate number system (ANS) is assumingly related to mathematical learning but evidence supporting this assumption is mixed. The inconsistent findings might be attributed to the fact that different measures have been used to assess the ANS and mathematical skills. Moreover, associations between the performance on a measure of the ANS and mathematical skills may be discontinuous, i.e., stronger for children with lower math scores than for children with higher math scores, and may change with age. The aim of the present study was to examine the development of the ANS and arithmetic skills in elementary school children and to investigate how the relationship between the ANS and arithmetic skills develops. Individual markers of children's ANS (internal Weber fractions and mean reaction times in a non-symbolic numerical comparison task) and addition skills were assessed in their first year of school and 1 year later. Children showed improvements in addition performance and in the internal Weber fractions, whereas mean reaction times in the non-symbolic numerical comparison task did not change significantly. While children's addition performance was associated with the internal Weber fractions in the first year, it was associated with mean reaction times in the non-symbolic numerical comparison task in the second year. These associations were not found to be discontinuous and could not be explained by individual differences in reasoning, processing speed, or inhibitory control. The present study extends previous findings by demonstrating that addition performance is associated with different markers of the ANS in the course of development.

Effects of perceptual variables on numerosity comparison in 5-6-year-olds and adults

Although a critical issue in the debate over the existence of abstract numerical representation, it remains unclear whether and how perceptual variables affect numerosity judgment and how they change across development stages. In this research, we examine the effects of perceptual variables on approximate numerosity comparison in 5–6-year-olds and adults using the identical experimental procedure. In the assessment of the effect of the perceptual variables, we measured precision (i.e., Weber fraction) and accuracy (i.e., point of subjective equality; PSE) of the numerosity comparison. In Study 1, we tested how the manipulation of the cumulative element area would affect approximate numerosity comparison. The results showed that Weber fractions increased and the size of bias enlarged in the large element condition in both adults and 5–6-year-olds. In study 2, we tested how the manipulation of the array area would affect the precision and accuracy of approximate numerosity comparison. The results demonstrated that Weber fractions increased and the size of bias enlarged in the large array condition in both adults and 5–6-year-olds. Overall, our results suggest that the effect of perceptual variables on 5–6-year-olds is qualitatively similar to that on adults. In addition, we also tested whether the performance of approximate comparison correlated with the initial numerical skill in 5–6-year-olds to reveal least relationship between them.

Genetic and environmental contributions to brain activation during calculation

Twin studies have long suggested a genetic influence on inter-individual variations in mathematical abilities, and candidate genes have been identified by genome-wide association studies. However, the localization of the brain regions under genetic influence during number manipulation is still unexplored. Here we investigated fMRI data from a group of 19 MZ (monozygotic) and 13 DZ (dizygotic) adult twin pairs, scanned during a mental calculation task. We examined both the activation and the degree of functional lateralization in regions of interest (ROIs) centered on the main activated peaks. Heritability was first investigated by comparing the respective MZ and DZ correlations. Then, genetic and environmental contributions were jointly estimated by fitting a ACE model classically used in twin studies. We found that a subset of the activated network was under genetic influence, encompassing the bilateral posterior superior parietal lobules (PSPL), the right intraparietal sulcus (IPS) and a left superior frontal region. An additional region of the left inferior parietal cortex (IPC), whose deactivation correlated with a behavioral calculation score, also presented higher similarity between MZ than between DZ twins, thus offering a plausible physiological basis for the observable inheritance of math scores. Finally, the main impact of the shared environment was found in the lateralization of activation within the intraparietal sulcus. These maps of genetic and environmental contributions provide precise candidate phenotypes for further genetic association analyses, and illuminate how genetics and education shape the development of number processing networks.

Non-symbolic halving in an Amazonian indigene group

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS.