Neural evidence for procedural automatization during cognitive development: Intraparietal response to changes in very-small addition problem-size increases with age.

Cognitive development is often thought to depend on qualitative changes in problem-solving strategies, with early developing algorithmic procedures (e.g., counting when adding numbers) considered being replaced by retrieval of associations (e.g., between operands and answers of addition problems) in adults. However, algorithmic procedures might also become automatized with practice. In a large cross-sectional fMRI study from age 8 to adulthood (n = 128), we evaluate this hypothesis by measuring neural changes associated with age-related reductions in a behavioral hallmark of mental addition, the problem-size effect (an increase in solving time as problem sum increases). We found that age-related decreases in problem-size effect were paralleled by age-related increases of activity in a region of the intraparietal sulcus that already supported the problem-size effect in 8- to 9-year-olds, at an age the effect is at least partly due to explicit counting. This developmental effect, which was also observed in the basal ganglia and prefrontal cortex, was restricted to problems with operands ≤ 4. These findings are consistent with a model positing that very-small arithmetic problems-and not larger problems-might rely on an automatization of counting procedures rather than a shift towards retrieval, and suggest a neural automatization of procedural knowledge during cognitive development.

Task-independent neural bases of peer presence effect on cognition in children and adults.

There is ample behavioral evidence that others' mere presence can affect any behavior in human and non-human animals, generally facilitating the expression of mastered responses while impairing the acquisition of novel ones. Much less is known about i) how the brain orchestrates the modulation of such a wide array of behaviors by others' presence and ii) when these neural underpinnings mature during development. To address these issues, fMRI data were collected in children and adults alternately observed and unobserved by a familiar peer. Subjects performed a numerosity comparison task and a phonological comparison task. While the former involves number-processing brain areas, the latter involves language-processing areas. Consistent with previous behavioral findings, adults' and children's performance improved in both tasks when observed by a peer. Across all participants, task-specific brain regions showed no reliable change in activity under peer observation. Rather, we found task-independent changes in domain-general brain regions typically involved in mentalizing, reward, and attention. Bayesian analyses singled out the attention network as the exception to the close child-adult resemblance of peer observation neural substrates. These findings suggest that i) social facilitation of some human education-related skills is primarily orchestrated by domain-general brain networks, rather than by task-selective substrates, and ii) apart from attention, peer presence neural processing is largely mature in children.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age.

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats.

Humans differ from other animal species in their unique ability to use symbols to represent numerical information. This ability is thought to emerge from the "neural recycling" of mechanisms supporting nonsymbolic magnitudes in the intraparietal sulcus (IPS), a hypothesis that has been applied to both absolute magnitudes (e.g., whole numbers) and relative magnitudes (e.g., fractions). Yet, evidence for the neuronal recycling hypothesis is inconsistent for absolute magnitudes and scarce for relative magnitudes. Here, we investigated to what extent the neural representations of absolute and relative magnitudes in symbolic and nonsymbolic formats overlap in the IPS. In a functional magnetic resonance imaging (fMRI) adaptation design, 48 adult participants were sequentially presented with lines, whole numbers, line ratios, and fractions that varied (vs. not varied) in magnitudes. Univariate analyses showed that the extent to which IPS mechanisms associated with whole numbers relied on mechanisms associated with lines depended upon participants' arithmetic fluency. Multivariate analyses revealed that the right IPS encoded differences in format (nonsymbolic vs. symbolic) across both absolute and relative magnitudes. Therefore, IPS activity associated with magnitude processing may depend on the presentation format (nonsymbolic vs. symbolic) more than it depends on the type of magnitude (absolute vs. relative), at least for most adult participants.

Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals.

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

Nurturing the reading brain: home literacy practices are associated with children's neural response to printed words through vocabulary skills.

Previous studies indicate that children are exposed to different literacy experiences at home. Although these disparities have been shown to affect children's literacy skills, it remains unclear whether and how home literacy practices influence brain activity underlying word-level reading. In the present study, we asked parents of French children from various socioeconomic backgrounds (n = 66; 8.46 ± 0.36 years, range 7.52-9.22; 20 girls) to report the frequency of home literacy practices. Neural adaptation to the repetition of printed words was then measured using functional magnetic resonance imaging (fMRI) in a subset of these children (n = 44; 8.49 ± 0.33 years, range 8.02-9.14; 13 girls), thereby assessing how sensitive was the brain to the repeated presentation of these words. We found that more frequent home literacy practices were associated with enhanced word adaptation in the left posterior inferior frontal sulcus (r = 0.32). We also found that the frequency of home literacy practices was associated with children's vocabulary skill (r = 0.25), which itself influenced the relation between home literacy practices and neural adaptation to words. Finally, none of these effects were observed in a digit adaptation task, highlighting their specificity to word recognition. These findings are consistent with a model positing that home literacy experiences may improve children's vocabulary skill, which in turn may influence the neural mechanisms supporting word-level reading.

The relation between home numeracy practices and a variety of math skills in elementary school children.

A growing number of studies suggest that the frequency of numeracy experiences that parents provide at home may relate to children's mathematical development. However, the relation between home numeracy practices and children's numerical skills is complex and might depend upon both the type and difficulty of activities, as well as the type of math skills. Studies have also argued that this relation may be driven by factors that are not systematically controlled for in the literature, including socio-economic status (SES), parental math skills and children's IQ. Finally, as most prior studies have focused on preschoolers, it remains unclear to what extent there remains a relation between the home numeracy environment and math skills when children are in elementary school. In the present study, we tested an extensive range of math skills in 66 8-year-olds, including non-symbolic quantity processing, symbolic number understanding, transcoding, counting, and mental arithmetic. We also asked parents to complete a questionnaire about their SES, academic expectations, academic attitudes, and the numeracy practices that they provide at home. Finally, we measured their arithmetic fluency as a proxy for parental math skills. Over and above differences in socio-economic status, parental arithmetic fluency, child's IQ, and time spent with the child, we found a positive relation between the frequency of formal numeracy practices that were at or above grade level and two separate measures of mental arithmetic. We further found that the frequency of these advanced formal numeracy practices was related to parents' academic expectations. Therefore, our study shows that home numeracy experiences predict arithmetic skills in elementary school children, but only when those activities are formal and sufficiently challenging for children.

Learning to run the number line: the development of attentional shifts during single-digit arithmetic.

Solving single-digit subtraction and addition problems is associated with left and right shifts of attention in adults. Here, we explored the development of these spatial shifts in children from the third to fifth grade. In two experiments, children solved single-digit addition (Experiments 1 and 2), subtraction (Experiment 1), and multiplication (Experiment 2) problems in which operands and the arithmetic sign were shown sequentially. Although the first operand and the arithmetic sign were presented on the center of a screen, the second operand was presented either in the left or the right visual field. In Experiment 1, we found that subtraction problems were increasingly associated with a leftward bias by the fifth grade, such that problem solving was facilitated when the second operand was in the left visual field. In Experiment 2, we found that children can also associate addition problems with the right side of space by the fourth grade. No developmental increase in either leftward or rightward bias was observed for multiplication problems. These attentional shifts might be due to the increasing reliance on calculation procedures that involve mental movements to the left or right of a sequential representation of numbers during subtraction and addition.