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Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age [1]

['Tomoya Nakai', 'Lyon Neuroscience Research Center', 'Crnl', 'Inserm Cnrs', 'University Of Lyon', 'Bron', 'Cléa Girard', 'Léa Longo', 'Hanna Chesnokova', 'Jérôme Prado']

Date: 2023-01 

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.

Hypotheses in Fig 1A were tested using multivariate searchlight decoding across the whole brain [ 25 ], within but also between formats ( Fig 1C ). Within-format decoding involved (i) training cross-participants decoders to classify between adaptation and no-adaptation blocks of either dots or digits and (ii) testing the accuracy of decoders on different participants presented with stimuli in the same format. This was done both within the same age group but also across age groups to evaluate whether neural representations are stable through the first four years of formal education. Finally, the hypothesis that the relation between symbolic and nonsymbolic representations might change with age was evaluated using between-format decoding. Specifically, within each age group (n = 43 for 5-year-olds; n = 46 for 8-year-olds), we tested whether decoders could accurately classify between adaptation and no-adaptation blocks of stimuli presented in a format that differed from the format they were trained on (e.g., dots to digits or digits to dots). This allowed us to evaluate whether any brain regions may represent quantities in an abstract (i.e., format-independent) manner and whether this may change with age.

Pediatric neuroimaging comes with a number of challenges. For example, performance typically increases with age, such that tasks that require an active behavioral response confound developmental changes in activity with differences in performance [ 20 ]. Young children also struggle to lay still in a scanner for long periods of time, increasing motion-related noise in the data [ 21 ]. Therefore, even-related designs that estimate brain activity based on a limited number of trials may lack power and reliability [ 22 ]. To circumvent these issues, we used a block-design adaptation paradigm in which children were passively presented with blocks of nonsymbolic quantities (dot arrays) and Arabic numerals (digits) that were either similar (adaptation) or different (no-adaptation) ( Fig 1B ). Because the repeated presentation of a given stimulus leads to a decrease in activity in the region that processes that stimulus [ 23 ], comparing no-adaptation to adaptation blocks captures a neural adaptation effect in task-relevant regions [ 15 , 24 ].

( A ) Hypotheses regarding the similarity between neural representations of Arabic numerals and nonsymbolic quantities and how it might change with age. ( B ) Dots and digits were passively presented in adaptation and no-adaptation blocks. A target detection task was embedded in the adaptation task to ensure that participants were paying attention. ( C ) A pairwise classifier distinguishing adaptation from no-adaptation blocks of either dots or digits was constructed in each target searchlight sphere. It was subsequently applied to the left-out test samples, which were either of the same format (within-format decoding) or of a different format (between-format decoding).

In the present cross-sectional study, we used functional magnetic resonance imaging (fMRI) to investigate the emergence of the neural representations of Arabic numerals from age 5 to age 8, which corresponds to the first four years of formal education in children. We also aimed to assess the relation between the representations of Arabic numerals and approximate nonsymbolic quantity during that period. Specifically, we made four hypotheses regarding the relation between the representations of Arabic numerals and approximate nonsymbolic quantities in 5- and 8-year-olds. These representations could be (1) always similar; (2) always distinct; (3) similar in 5-year-olds and distinct in 8-year-olds; or (4) distinct in 5-year-olds and similar in 8-year-olds ( Fig 1A ).

A source of difficulty in interpreting the results of previous studies is that they largely focus on educated adults. Educated adults have been exposed to symbolic numbers for many years and have thus acquired extensive experience manipulating symbols without referring to the quantity they represent. Such experience might significantly weaken any preexisting relation between number symbols and nonsymbolic quantity [ 19 ]. In other words, there might still exist a relation between the neural representations of symbolic and approximate nonsymbolic quantity in young children, as would be expected if the ANS scaffolds symbolic numerical skills. However, this relation might disappear with exposure to formal mathematics through elementary school.

However, a growing number of studies have also failed to find an overlapping neural activity for symbolic and nonsymbolic quantity processing [ 12 , 13 ]. For example, two recent reports have shown distinct neural representations of number symbols and nonsymbolic quantities across the largest samples of adult participants to date [ 14 , 15 ]. These studies suggest that quantity may be represented in a format-dependent manner in the brain [ 16 ]. This is consistent with the idea that the emergence of symbolic number knowledge in humans mainly results from cultural practices that have more to do with mastering the logic of counting than mapping symbols onto a perceptual sense of quantity [ 16 – 18 ].

Overall, neuroimaging studies that investigated separately symbolic and nonsymbolic quantity processing have identified similar networks encompassing the IPS and prefrontal cortex in normal adults (for a meta-analysis, see [ 6 ]). This is consistent with a few studies that have also reported shared activation or decodability when quantities are presented to the same individuals in different formats [ 7 – 9 ]. Such shared parietal activity has also been observed in a small group of 6- and 7-year-old children [ 10 ]. Together, these studies support the idea that there is an abstract (i.e., format-independent) representation of numerical quantity in the brain, with similar neuronal populations coding for symbolic and nonsymbolic quantity [ 11 ].

Learning Arabic numerals is a milestone in early elementary education. It is also the first step towards understanding symbolic mathematics, which is fundamental for academic growth in children. Prior studies suggest that brain sensitivity to approximate nonsymbolic quantities precedes the acquisition of number symbols in children [ 1 , 2 ], with early neural processing of approximate nonsymbolic quantities reported around the intraparietal sulcus (IPS) [ 1 – 4 ]. This is consistent with the idea that an early-developing “approximate number system” (ANS) [ 5 ] may scaffold the development of symbolic numerical knowledge. However, very little is known about (i) how neural representations of Arabic numerals emerge in the first years of schooling and (ii) how these representations relate to neural representations of approximate nonsymbolic quantities in children.

Finally, decoding accuracy might depend (to some extent) on the choice of analysis parameters, such as the type of cross-validation procedure and the voxel-level threshold that provides the basis for cluster-level correction [ 29 ]. To evaluate to what extent our results were sensitive to these choices, we performed additional analyses using a different type of cross-validation procedure and a different voxel-level threshold. First, we computed decoding accuracy maps using 10-fold cross-validation instead of LOOCV [ 30 ]. As shown in S11 and S12 Figs, we obtained results that were very similar to our main findings. Notably, we found significant between-format decoding accuracy in the right IPL for 5-year-olds, but not for 8-year-olds. Second, we recalculated the significance of clusters in decoding accuracy maps using a voxel-level threshold of p < 0.001 instead of p < 0.005. Results were again very similar to our main findings. As shown in S13 Fig , we still found (1) greater within-format decoding accuracy in 8-year-olds than in 5-year-olds in frontal, parietal, and occipital brain regions; (2) significant within-format decoding accuracy across groups in the prefrontal and occipital cortex; and most importantly (3) significant between-format decoding in the right IPL for 5-year-olds, but not for 8-year-olds. Altogether, these results indicate that the present findings did not hinge upon a specific cross-validation method or a specific thresholding.

Third, although 5-year-olds and 8-year-olds did not differ with respect to either in-scanner motion (see Materials and methods ) or standardized IQ (see above), it remains possible that differences between groups in terms of motion or general cognitive functioning might have affected our results. To exclude these possibilities, we performed a multiple linear regression analysis (with intercept) using the six head motion parameters and IQ as independent variables, as well as the decoding accuracy of each participant as a dependent variable. The predicted value associated with the independent variables was subtracted from the original decoding accuracy and was used as a new decoding accuracy. The group-level statistical significance was evaluated in the same manner as described above. Again, this analysis revealed similar results, with notably significant between-age decoding accuracy in the bilateral PreCG and higher between-format decoding accuracy for 5-year-olds in the right IPL ( S9 and S10 Figs ). Therefore, differences between children’s in-scanner motion or IQ did not appear to have influenced our results.

Second, because stimuli were passively presented to participants, it is possible that the tasks might have differed in levels of attentional engagement within each age group. For example, a difference in attentional engagement between tasks might have jeopardized our ability to detect similarities between neural responses to adaptation (e.g., in 8-year-olds in which there was no between-format decoding). To examine this possibility, we asked participants to detect a randomly appearing target over the course of the experiment. On average, 5-year-olds detected 75% of targets (SD = 28) in the dot adaptation task, 79% of targets (SD = 25) in the digit adaptation task, and 80% of targets (SD = 22) in the letter adaptation task. Eight-year-olds detected 91% of targets (SD = 14) in the dot adaptation task and 92% of targets (SD = 15) in the digit adaptation task. Target detection rates of three tasks were largely above chance in each group (Wilcoxon signed-rank test, Bonferroni correction for multiple comparisons, adjusted p < 0.001), and there was no difference in target detection rate among the tasks within each age group (between the three tasks in 5-year-olds: Wilcoxon signed-rank test: p > 0.23; between dots and digits adaptation tasks in 8-year-olds: p = 0.44). Therefore, children paid attention to the stimuli in all tasks, and levels of attention did not differ between tasks.

( A ) Letters were passively presented in adaptation and no-adaptation blocks. ( B ) Brain regions in which between-format decoding accuracy was larger across dots and digits compared to between-format decoding accuracy across dots and letters. ( C ) Mean decoding accuracy in the right IPL (defined in Fig 4A ) for all decoding directions (dots to digits, digits to dots, dots to letters, letters to dots, digits to letters, and letters to digits). The underlying data can be found online (see Materials and methods ). Specifically, data supporting panel ( B ) in this figure can be found in files “RawDecAcc_LOOCV_5yo_[Dots2Digits/Digits2Dots/Dots2Letters/Letters2Dots]_[Subjects’ ID].nii” in the “RawDecAcc” folder, while data supporting panel ( C ) can be found in file “BoxPlot_SourceData.npy” in the “GraphSourceData” folder.

The results above suggest the existence of a format-independent neural representation of quantity at age 5. It is important, however, to rule out four other potential explanations for this finding. First, it is possible that this result is not specific to the representation of quantity per se but instead reflects some domain-general similarities in the neural mechanisms associated with repetition-induced adaptation effects in young children. To examine this possibility, 5-year-olds were also presented with adaptation and no-adaptation blocks of letters ( Fig 5A ). Letters are not only perceptually similar to digits; they are also culturally invented symbols that young children learn early in school. Critically, however, letters do not carry any information about numerical quantity. We thus assessed between-format decoding accuracy across dots and letters. Specifically, we tested whether decoders trained to classify between adaptation and no-adaptation blocks of dots could accurately classify between adaptation and no-adaptation blocks of letters, as well as the other way around. Accuracy maps resulting from both analyses (i.e., one using dots as a training set and the other using letters) were then combined in a conjunction analysis. In contrast to the results obtained in the between-format decoding analysis across dots and digits (see above), between-format decoding accuracy across dots and letters was not higher than chance in any cortical region (see S7 Table ). In fact, a whole-brain two-sample permutation test revealed that decoding accuracy between dots and digits was higher than decoding accuracy between dots and letters in the right IPL ( Fig 5B and 5C and S8 Table ). S7 Fig shows the unthresholded between-format accuracy maps across dots and letters. Additional analyses examining within-format decoding for letters and between-format decoding across digits and letters in 5-year-olds are presented in the Supporting information ( S8 Fig and S9 Table ).

( A ) Brain regions in which activity could accurately classify between adaptation versus no-adaptation blocks of quantity presented in one format (dots or digits) based on training with the other format (digits or dots) (conjunction analysis). ( B ) Brain regions in which between-format decoding accuracy was larger in 5-year-olds than in 8-year-olds. IFGtri, triangular part of inferior frontal gyrus; IPL, inferior parietal lobule; MFG, middle frontal gyrus; PreCG, precentral gyrus. ( C-D ) Histogram of mean decoding accuracy across all cortical voxels for ( C ) dots to digits and ( D ) digits to dots directions, plotted for both 5- and 8-year-olds. The underlying data can be found online (see Materials and methods ). Specifically, data supporting panels ( A - B ) can be found in files “RawDecAcc_LOOCV_[5yo/8yo]_[Dots2Digits/Digits2Dots]_[Subjects’ ID].nii” in the “RawDecAcc” folder, while data supporting panels ( C - D ) can be found in files “HistPlot_[Dots2Digits/Digits2Dots]_[5yo/8yo]_SourceData.npy” in the “GraphSourceData” folder.

Although we did not find any region showing this format-independent pattern in 8-year-olds, a region of the right inferior parietal lobule (IPL) (and of the left PreCG) showed such a pattern in 5-year-olds ( Fig 4A and S5 Table ; see S5 Fig for accuracy maps associated with each direction-specific analysis). A direct comparison of accuracy maps between groups showed higher between-format decoding accuracy for 5-year-olds than for 8-year-olds in the right IPL, as well as in regions of the right middle frontal gyrus (MFG) and the triangular part of inferior frontal gyrus (IFGtri) ( Fig 4B and S6 Table ). No region showed higher between-format decoding accuracy for 8-year-olds than for 5-year-olds. Higher between-format decoding accuracy in 5-year-olds can also be seen in histograms across all cortical voxels (p < 0.001; Fig 4C and 4D ). S6 Fig shows the unthresholded between-format accuracy maps for 5-year-olds ( S6A Fig ) and 8-year-olds ( S6B Fig ). Therefore, these results indicate some degree of similarity in the neural representations of symbolic and nonsymbolic quantity in 5-year-olds but not in 8-year-olds.

We then examined whether the neural representations of symbolic and nonsymbolic quantity were similar within each group and whether this similarity depended on the age group. In each age group, we tested whether decoders trained to classify between adaptation and no-adaptation blocks in a given format (i.e., dots or digits) could accurately classify between adaptation and no-adaptation blocks of left-out test samples from the other format (i.e., between-format decoding). Specifically, we reasoned that a brain region in which quantity is represented in a format-independent manner should show significant decoding accuracy both (i) when the classifier is trained with dots and tested on digits and (ii) when the classifier is trained with digits and tested on dots. For each age group, accuracy maps resulting from both analyses (i.e., one using dots as a training set and the other using digits) were combined in a conjunction analysis to identify the regions in which neural representations were format independent.

Second, we evaluated commonalities in neural representations between groups by (i) training decoders to classify between adaptation and no-adaptation blocks in a given age group (i.e., 5-year-olds or 8-year-olds) and (ii) testing whether decoders could accurately classify between adaptation and no-adaptation blocks of the same format but in the other age group (e.g., 8-year-olds or 5-year-olds). For each format, accuracy maps resulting from both analyses (i.e., one using 5-year-olds as a training set and the other using 8-year-olds) were combined in a conjunction analysis to identify the regions in which neural representations were most stable between groups ( Fig 3C and 3D and S3 and S4 Tables ; see S3 Fig for accuracy maps associated with each direction-specific analysis). S4 Fig shows the unthresholded across-groups accuracy maps dots ( S4A Fig ) and digits ( S4B Fig ). Results showed that adaptation versus no-adaptation blocks of dots could be accurately distinguished across groups (i.e., using one group as a training set and the other group as a testing set) in the bilateral precentral gyrus (PreCG) and right superior parietal lobule (SPL). This was only the case in the occipital cortex for adaptation versus no-adaptation blocks of digits. Higher decoding accuracy in dots can also be seen in histograms across all cortical voxels (p < 0.001; Fig 3E and 3F ). Therefore, results of within-format decoding analyses revealed that the neural representations of Arabic numerals, but also of nonsymbolic quantity, clearly expanded from age 5 to age 8.

( A-B ) Brain regions in which within-group decoding accuracy was larger in 8-year-olds than in 5-year-olds for ( A ) dots and ( B ) digits (based on training with the same format). ( C - D ) Brain regions in which activity could accurately classify between adaptation versus no-adaptation blocks of ( C ) dots and ( D ) digits in one group based on training with the same format in the other group (conjunction analysis). IFGtri, triangular part of inferior frontal gyrus; IPS, intraparietal sulcus; PreCG, precentral gyrus; SPL, superior parietal lobule. ( E-F ) Histogram of mean decoding accuracy across all cortical voxels for ( E ) 5- to 8-year-olds and ( F ) 8- to 5-year-olds directions, plotted for both dots and digits. The underlying data can be found online (see Materials and methods ). Specifically, data supporting panels ( A - B) can be found in files “RawDecAcc_LOOCV_[5yo/8yo]_[Dots/Digits]_[Subjects’ ID].nii” in the “RawDecAcc” folder; data supporting panels ( C - D) can be found in files “RawDecAcc_[5to8yo/8to5yo]_[Dots/Digits]_[Subjects’ ID].nii” in the “RawDecAcc” folder; and data supporting panels ( E - F ) can be found in files “HistPlot_[Dots/Digits]_[5to8yo/8to5yo]_SourceData.npy” in the “GraphSourceData” folder.

As can be seen in Fig 2 , there appears to be differences but also similarities in the neural representations of symbolic and nonsymbolic quantity between groups. First, differences between groups were formally assessed by comparing accuracy maps using a whole-brain two-sample permutation test. Although there was no brain region in which either dot or digit decoding accuracy was larger in 5-year-olds than in 8-year-olds, decoding accuracy was larger in 8-year-olds than in 5-year-olds in several brain regions ( Fig 3A and 3B and S1 and S2 Tables ). These notably included the IPS and regions of the occipital cortex for dots, as well as regions of the prefrontal cortex for digits. Higher within-format decoding accuracy in 8-year-olds can also be seen in histograms across all cortical voxels (Wilcoxon signed-rank test, p < 0.001; Fig 2E and 2F ).

( A-B ) For 5-year-olds, brain regions in which activity could accurately classify between adaptation versus no-adaptation blocks of ( A ) dots and ( B ) digits based on training with the same format. ( C-D ) For 8-year-olds, brain regions in which activity could accurately classify between adaptation versus no-adaptation blocks of ( C ) dots and ( D ) digits based on training with the same format. Only statistically significant clusters are shown (sign permutation test, voxel-level p < 0.005, cluster-level p < 0.05 with false discovery rate correction). IPS, intraparietal sulcus; L, left hemisphere; R, right hemisphere. ( E-F ) Histogram of mean decoding accuracy across all cortical voxels for ( E ) dots and ( F ) digits, plotted for both 5- and 8-year-olds. The underlying data can be found online (see Materials and methods ). Specifically, data supporting panels ( A - D ) can be found in files “RawDecAcc_LOOCV_[5yo/8yo]_[Dots/Digits]_[Subjects’ ID].nii” in the “RawDecAcc” folder, while data supporting panels ( E - F ) can be found in files “HistPlot_[Dots/Digits]_[5yo/8yo]_SourceData.npy” in the “GraphSourceData” folder.

Based on multivariate activity from each target searchlight sphere, we trained cross-participant decoders to classify between adaptation and no-adaptation blocks of either dots or digits within each age group. Using leave-one-out cross-validation (LOOCV), we then tested whether the decoders could accurately classify (i.e., above chance level) between adaptation and no-adaptation blocks of left-out test samples from the same format (i.e., within-format decoding). Within each age group, we found several regions in which adaptation and no-adaptation blocks of dots, as well as adaptation and no-adaptation blocks of digits, could be accurately classified. These included regions of the occipital, frontal, and parietal cortices, including the IPS ( Fig 2 ). S1 and S2 Figs show the unthresholded within-format accuracy maps for 5-year-olds (Dots, S1A Fig ; Digits, S1B Fig ) and 8-year-olds (Dots, S2A Fig ; Digits, S2B Fig ).

Measures of mathematical skills included standardized assessments of symbolic and nonsymbolic numerical competence from two age-appropriate batteries, the TEDI-MATH for 5-year-olds [ 27 ] and the ZAREKI-R for 8-year-olds [ 28 ] (see Materials and methods ). For 5-year-olds, measures involved symbolic number comparison and nonsymbolic quantity estimation. For 8-year-olds, measures involved symbolic number comparison and nonsymbolic quantity comparison. For nonsymbolic competence, the average standardized score was 104 in 5-year-olds (SD = 5, range = 85 to 105) and 108 in 8-year-olds (SD = 18, range = 57 to 123). For symbolic competence, the average standardized score was 102 in 5-year-olds (SD = 13, range = 57 to 109) and 107 in 8-year-olds (SD = 7, range = 83 to 111). Therefore, although scores are difficult to compare between groups due to the use of different batteries, average scores of 5- and 8-year-olds were in line with typical age expectation. This also indicates that raw performance was higher for 8- than 5-year-old.

To characterize the samples, children’s intelligence quotient (IQ) and mathematical skills were assessed outside of the scanner using standardized (age-normalized) batteries (see Materials and methods ). Average IQ, as measured by the NEMI-2 [ 26 ], was in the normal range in each age group. Specifically, 5-year-olds had an average IQ of 109 (standard deviation [SD] = 15, range = 76 to 146), while 8-year-olds had an average IQ of 112 (SD = 11, range = 83 to 135). There was no difference in standardized IQ between the two groups (Wilcoxon rank-sum test, p = 0.18).

Discussion

In the present cross-sectional study, we used fMRI to examine the emergence of the neural representations of Arabic numerals through early elementary education. Specifically, we performed a series of within- and between-format searchlight decoding analyses to investigate the relation between the neural representations of Arabic numerals and the neural representations of approximate nonsymbolic quantities from age 5 to age 8. Within-format decoding showed that Arabic numerals and nonsymbolic quantities were represented in distributed cortical regions in both 5-year-olds and 8-year-olds. While there was some similarity between age groups, there was also an expansion of the cortical territory dedicated to these representations. Between-format decoding demonstrated the existence of a format-independent representation of quantity in the right IPL. However, this format invariance was only observed in 5-year-olds, not in 8-year-olds. These results provide support for the symbolic estrangement hypothesis [16,19], which assumes that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal math education.

Cortical representations of symbolic and nonsymbolic quantity expand from age 5 to age 8 A number of previous studies have suggested that neural sensitivity to approximate nonsymbolic numerical quantity can be detected as early as in the first years of life, particularly in the right parietal cortex [1–4]. fMRI evidence has also demonstrated that changes of activity in the parietal and frontal cortices are associated with the development of numerical skills in children [31]. Our findings, however, are novel in that they suggest both stability and changes in the brain system underlying the representation of symbolic and nonsymbolic quantity in children as they are exposed to the first years of formal schooling. On the one hand, we found that the representations of Arabic numerals and nonsymbolic quantities were represented in the bilateral occipital and parietal cortices of both 5- and 8-years-olds. These areas have long been the focus of previous studies investigating neural activity associated with symbolic and nonsymbolic quantity [6,9,13–16]. However, our results suggest the involvement of a more distributed brain system that also includes bilateral regions of the temporal and frontal cortices. Importantly, this finding was only made possible because we used searchlight decoding, allowing for the detection of multivariate representations across the whole brain. This notably contrasts with the majority of previous pediatric neuroimaging studies, which have often investigated whole-brain univariate activity [1–4,32]. Nonetheless, it is interesting to note that our study is not the first to show that the temporal and frontal cortices are involved in the processing of symbolic and nonsymbolic quantity in children. For example, Kovas and colleagues [33] and Kersey and Cantlon [4] found that a distributed system is associated with the processing of nonsymbolic numerosity in children from age 3 to age 10, including the parietal, occipital, temporal, and frontal cortices. Using a searchlight approach, Bulthé and colleagues [12] also reported that nonsymbolic quantity could be decoded across the whole brain. Interestingly, we found here some degree of stability in the neural representation of nonsymbolic quantity. Specifically, decoders trained with brain activity from 5-year-olds accurately classified between activity associated with adaptation versus no-adaptation blocks of dots in 8-year-olds and vice versa. This was notably the case in the right SPL and bilateral PreCG. However, no representational stability was found for the neural representation of Arabic numerals in the parietal, frontal, or temporal cortex between age 5 and age 8, most likely because symbolic numerical skills change massively during that time. On the other hand, we found that the representations of symbolic and nonsymbolic quantity significantly expanded from age 5 to age 8. This was notably the case in the bilateral IPS and occipital cortex for dots, as well as in the prefrontal cortex for digits. Arguably, children are increasingly exposed to symbolic numbers from age 5 to age 8 (which corresponds to the first four years of formal education). This is likely to explain the expansion of territory dedicated to the representation of digits in the prefrontal cortex, as this region has often been found to be involved in symbolic quantity and arithmetic processing in adults [34]. Note, however, that there was also an expansion of the cortical regions representing nonsymbolic quantity, most notably around the IPS. Although nonsymbolic numerosity representations are evolutionarily old and therefore emerge early in children [1–4], this finding is consistent with the idea that the acquisition of symbolic number skills during the first four years of education may still refine the cognitive mechanisms supporting nonsymbolic quantity processing [35].

Cortical representations of symbolic and nonsymbolic quantity become estranged from age 5 to age 8 Between-format decoding revealed that the first four years of formal education had a significant influence on the relation between the brain representations of symbolic and nonsymbolic quantity. Specifically, although we found a region of the right IPL in which quantity was represented in a format-independent manner in 5-year-olds, this format independence was largely absent in 8-year-olds. Between-format decoding accuracy was also significantly higher in 5-year-olds than in 8-year-olds, indicating that the groups statistically differed when compared with each other. This age dependence of the relation between symbolic and nonsymbolic representations is in line with a recent study that reported a correlation between arithmetic skills and representational similarity across symbolic and nonsymbolic numerical processing in elementary school children but not in adolescents [36]. It has long been argued that the acquisition of symbolic numerical skills in humans builds on an evolutionary-old representation of approximate nonsymbolic quantity [5,37]. Neural evidence for this hypothesis comes from a limited number of studies in adults showing format invariance in the brain representation of symbolic and nonsymbolic quantity, particularly in the parietal cortex [7,9]. Yet, a growing number of recent studies, also in adults, have failed to find such format invariance. Some have thus claimed that the link between symbolic and nonsymbolic representations might be more tenuous than previously thought [12–15]. Critically, our findings suggest that the representation of nonsymbolic quantity may still scaffold the acquisition of symbolic numerical skills in young children. It is possible that the inconsistent results observed in the adult literature stem from the fact that adults have had years of experience manipulating numerical symbols, such that their symbolic numerical skills might be integrated into an independent symbolic system [19,38]. More generally, our findings are a reminder that it is difficult to infer the mechanisms underlying the acquisition of numerical skills from studies in adults.

Overlap in the cortical representations of symbolic and nonsymbolic quantity in young children is specific to numerical information Unlike most previous fMRI adaptation studies [3,9,32], our study focuses on multivariate activity patterns during adaptation periods rather than univariate activity associated with a deviant stimulus. Although this makes our design particularly robust and well suited to pediatric neuroimaging, a downside is that we could not evaluate whether decoding was influenced by numerical properties of the stimuli (e.g., distance between quantities). Therefore, it could be argued that the overlap between the neural representations of dots and digits in 5-year-olds is mainly due to domain-general adaptation effects. To rule out this possibility and assess the specificity of the overlap between symbolic and nonsymbolic quantity, we also presented participants with symbolic stimuli that did not involve any quantitative information, i.e., letters. Critically, we did not find significant between-format decoding between dots and letters anywhere in the cortex (and we found higher decoding accuracy between dots and digits than that between dots and letters in the right IPL). This indicated that the overlap between the neural representations of dots and digits in the IPL of 5-year-olds was specific to numbers (Figs 4 and 5).

Cortical representations of digits and letters overlap in young children Interestingly, the lack of overlap between representations of dots and letters was not due to a failure to find shared representations between letters and any other types of stimuli. Indeed, in 5-year-olds, there was significant between-format decoding across letters and digits in both the bilateral fusiform gyrus (FG) and the right PreCG (S8 Fig). This suggests that both of these regions might be involved in representing symbolic information more generally. Consistent with this idea, several studies notably suggest that the FG might include areas dedicated to the identification of both words and numerals from low-level visual features [39–42]. It is also possible that the neural overlap between digits and letters in the right PreCG is due to a common representation of stimuli features, independently of quantity (e.g., visual features).

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