Participants

In total, 104 typically-developing 3- to 10-year-old children (55 girls) and 63 adults (35 women) participated in one of three studies. Age was statistically equivalent between girls and boys (t 1 (102) = 3.32, p = 0.0006, t 2 (102) = 3.43, p = 0.0004), and there were no differences in age variability, reflecting an even distribution of age across-gender groups (F(1,102) = 0.07, p = 0.79, girls’ sd = 1.65, boys’ sd = 1.63). Informed written consent was obtained from adult participants and parents of children, and informed written assent was obtained for children 7 years and older. All protocols were approved by the University of Rochester Research Subjects Review Board.

fMRI paradigms

Study 1

Twenty-six 4- to 10-year-old children (15 girls; girls’ mean age = 6.93 years, boys’ mean age = 7.13 years; range = 4.32–10.80 years) and 20 adults (13 women; women’s mean age = 20.52 years, men’s mean age = 20.98 years; range = 18.9–25.4 years) successfully participated in Study 1. This paradigm consisted of a 20.3-min video containing clips from children’s educational television shows. Clips ranged from 12 to 176 s in length and were edited into a continuous movie. These data have been previously reported15 as the “natural viewing” task.

Study 2

Thirty-five 4- to 8-year-old children (17 girls; girls’ mean age = 6.61 years, boys’ mean age = 6.35 years; range = 4.08–8.67 years) and 23 adults (12 women; women’s mean age = 22.13 years, men’s mean age = 22.65 years; range = 18.44–28.09 years) successfully participated in Study 2. The 11.6-min video contained clips from children’s educational television shows. Clips ranged from 12.5 to 32.4 s in length and were edited into a continuous movie. These data have been previously reported16 as the “natural viewing” task.

Study 3

Forty-three 3- to 5-year-old children (23 girls; girls’ mean age = 4.54 years, boys’ mean age = 4.71 years; range = 3.12–5.96 years) and 20 adults (10 women; women’s mean age = 23.43 years, men’s mean age = 24.17 years; range = 20.15–31.55 years) successfully participated in Study 3. In this study, participants listened to pre-recorded audio tracks of someone counting or saying the alphabet. Short clips from child-friendly cartoons were presented on the screen during the sequences. Audio tracks were removed from the cartoons and were replaced with quieter, child-friendly instrumental music. Cartoon tracks were matched across sequences. Sequences were presented in 70 s blocks of 60 items presented at a rate of one item every 1.1–1.2 s. Fifteen blocks were presented throughout the experimental paradigm and were separated by 4-s of blackscreen. The scan began and ended with 12 s of blackscreen resulting in a total scan time of 19.2 min.

Number Localizer

Eighteen children from Study 1 (11 girls, 7 boys; girls’ mean age = 6.78 years, boys’ mean age = 7.47 years; range = 4.32–10.8 years) completed a traditional fMRI paradigm in which they compared pairs of stimuli (isolated images of faces, numbers, words or shapes) that were presented on the left and right sides of the screen. Participants reported whether they were the same or different by pressing a button only if the two stimuli matched. Half of the pairs presented were “matches”, whereas the other half were “non-matches”. Number comparisons were made across notation (i.e., dot array compared with Arabic numeral), face comparisons were made across a frontal shot and an oblique view, word comparisons were made across a word in all capital letters and the other in all lowercase letters, and shape comparisons were made across two shape images. Stimuli were presented in a blocked design. Each block consisted of three 2-s trials from the same condition, separated by a 2-s intertrial interval. Three blocks of each condition were semi-randomly presented throughout a run with 8 s of fixation between blocks. These data have been previously reported15 as the “traditional functional task”.

fMRI session

Prior to the scanning sessions, children participated in a 30-minute training session in a mock scanner to familiarize them with the scanning environment and to practice remaining motionless. Children who completed the Number Localizer paradigm practiced the task prior to the MRI session. Adults received verbal instructions prior to scanning and did not participate in a training session. During the scan, children’s heads were secured with medical tape, headphones, and foam padding, and adults’ heads were secured with headphones and foam padding.

MR parameters

Whole-brain BOLD imaging was conducted on a 3-Tesla Siemens MAGNETOM Trio scanner with a 12-channel head coil at the Rochester Center for Brain Imaging. High-resolution structural T1 contrast images were acquired using a magnetization prepared rapid gradient echo pulse sequence at the start of each session (repetition time (TR) = 2530 ms, echo time (TE) = 3.44 ms, flip angle = 7, field of view (FOV) = 256 mm, matrix = 256 × 256, 192, 176, or 160 slices depending on head size, 1 × 1 × 1 mm sagittal left-to-right slices). An echo-planar imaging pulse sequence with online motion correction was used for T2*contrast (TR = 2000 ms, TE = 30 ms, flip angle = 90 degrees, FOV = 256 mm, matrix 64 × 64, 30 axial oblique slices, parallel to the AC-PC plane, voxel size = 4 × 4 × 4 mm). The primary paradigms from Studies 1, 2, and 3 were 610 volumes, 348 volumes, and 567 volumes, respectively, and the Number Localizer paradigm was distributed over two to four functional runs of 132 volumes each.

Preprocessing

fMRI data were analyzed in BrainVoyager33 using in-house scripts drawing on the BVQX toolbox. Data from previously published studies were analyzed as originally reported for consistency.15,16 For the Number Localizer and Study 1, which were collected during the same scanning session, the first six TRs of each run were discarded prior to analysis to allow for signal equilibration. For Studies 2 and 3, the first two TRs of each run were discarded. Functional data were registered to high-resolution anatomy images for each participant in native space. Preprocessing consisted of slice scan time corrected (cubic spline interpolation), motion correction with respect to the first volume in the run, and linear trend removal in the temporal domain (cutoff: two cycles within the run). A Gaussian spatial filter with an 8 mm full-width at half-maximum was applied to each volume for Study 1,15 and a 6 mm full-width at half-maximum was applied to each volume for Studies 216 and 3. The functional data from the Number Localizer were not smoothed. Adult and child echo-planar and anatomical volumes were then normalized into Talairach space34 using piecewise affine transformation based on manual identification of anatomical landmarks. Analyses were performed on processed data in Talairach space. Average framewise displacement35,36 was regressed across the brain for each child to control for sudden changes in volume-to-volume head motion.

fMRI data analyses

Neural maturity: neural data were analyzed using an intersubject correlation approach.15,16,17 Between-group intersubject correlations were performed by using the full timecourse of each voxel for each child as a predictor for activation of the corresponding voxel in each adult brain. Functional data from each child were then correlated with that of each adult from the same study to produce paired r-maps. Paired r-maps represent the neural similarity of each child compared with each adult in every voxel of the brain. A single, average brain map was then calculated to represent the neural similarity of each child to all adults. This map is referred to as a map of “neural maturity” because it shows how “adult-like” each child’s neural timecourse appears. To ensure that these similarity maps were not confounded by any adult gender differences prior to averaging, we compared neural maturity calculated to women vs men. For each child, we conducted an Independent Samples t-test to compare neural maturity when calculated to adults of the same vs different gender as the child. This resulted in a map of between-group t values for each child. To determine whether there were any differences that were consistent at the group level, the absolute value of these individual-level between-group t value maps were then subjected to a one-sample t test vs a critical t value of 2.08. The critical value represents the t value at which a difference could be considered significant given the smallest sample of adults (n = 20 for studies 1 and 3; t(18) = 2.08, p = 0.05). If there were a significant difference between neural maturity calculated to adults of the same vs different gender as the child, the one-sample t test should reveal a positive and significant effect, which would indicate that the absolute values of the individual-level between-group t values are significantly above 2.08. Instead, the whole-brain one-sample t test revealed that at the group level, the absolute values of the individual-level between-group t values were significantly below the critical t value of 2.08 (one-sample t test of absolute value of individual-level between-group t values vs critical t value of 2.08: t(102) ≤ −2.62, p ≤ 0.01). In other words, the majority of individual-level between-group t values were less than the critical t value of 2.08 (range of average absolute value of individual-level between-group t values across voxels: 0–1.90). This indicates that overall, the differences between neural maturity when calculated to adults of the same vs different gender were not different, so neural maturity was not biased by the gender of the adult.

Neural similarity

To compare how similar children were to each other, intersubject correlations were calculated across children following the same procedures as for calculating neural maturity. This resulted in two maps for each child: one representing the average neural similarity of a child to children of the same gender and one representing the average neural similarity of a child to children of the different gender. To compare neural similarity within and across gender, these maps were then subtracted from each other (within-gender similarity−across-gender similarity) and these difference maps were subjected to a one-sample t test vs 0.

Number Localizer

Functional data collected during the traditional fMRI paradigm were analyzed using a general linear model (random effects analysis). Experimental events (duration = 10 s) were convolved with a standard dual gamma hemodynamic response function. There were four regressors of interest (corresponding to the four stimulus categories), one regressor for button press, and six regressors of no interest (corresponding to the motion parameters obtained during preprocessing).

Region-of-interest (ROI) analyses

Data were extracted from number network ROIs using MATLAB. Analyses were then conducted using R (version 3.3.1) and R-Studio (version 0.99.902). Independent samples t tests were conducted using the “t test” function assuming equal variance. Tests of equivalence were conducted using the “TOSTtwo.raw” function from the “TOSTER” package (upper and lower bounds set to ±0.667 × standard deviation of the entire group; alpha = 0.05). This function returns two t values (t 1 and t 2 ). For statistical equivalence, both t values must be statistically significant. Statistical equivalence is rejected if either t 1 or t 2 does not reach significance. Levene’s Test of Variance was carried out using the “leveneTest” function in the “car” package. Regression analyses were conducted using the built-in “lm” function.

Assessment of math ability

Math skills were evaluated by administering the TEMA-322 to participants aged 8 and younger. The TEMA-3 tests a variety of math concepts and is standardized for 3–8-year-old children.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.