Disentangling Age and Schooling Effects on Inhibitory Control Development: An fNIRS Investigation

Children show marked improvements in executive functioning (EF) between 4 and 7 years of age. In many societies, this time period coincides with the start of formal school education, in which children are required to follow rules in a structured environment, drawing heavily on EF processes such as inhibitory control. This study aimed to investigate the longitudinal development of two aspects of inhibitory control, namely response inhibition and response monitoring and their neural correlates. Specifically, we examined how their longitudinal development may differ by schooling experience, and their potential significance in predicting academic outcomes. Longitudinal data was collected in two groups of children at their homes. At T1, all children were roughly 4.5 years of age and neither group had attended formal schooling. One year later at T2, one group (P1, n = 40) had completed one full year of schooling while the other group (KG, n = 40) had stayed in kindergarten. Behavioural and brain activation data (measured with functional near-infrared spectroscopy, fNIRS) in response to a Go/No-Go task and measures of academic achievement were collected. We found that P1 children, compared to KG children, showed a greater change over time in activation related to response monitoring in the bilateral frontal cortex. The change in left frontal activation difference showed a small positive association with mathematical ability, suggesting certain functional relevance of response monitoring for academic performance. Overall, the school environment is important in shaping the development of the neural network underlying monitoring of one own’s performance. Research Highlights Using a school cut-off design, we collected longitudinal home assessments of two aspects of inhibitory control, namely response inhibition and response monitoring, and their neural correlates. For response monitoring, P1 children showed a greater difference over time in activation between correct and incorrect responses in the bilateral frontal cortex. The left frontal activation difference in P1 children showed a small association with mathematical ability, suggesting some functional relevance of response monitoring for academic performance. The school environment plays an important role in shaping the development of the neural network underlying monitoring of one own’s performance.

There is accumulating evidence to suggest inhibitory control, the capacity to interrupt a prepotent response and enact an alternative less salient response associated with goal attainment, may play a key role in determining school readiness (Müller et al., 2008) as well as predicting future academic achievement (Blair & Razza, 2007;Duckworth et al., 2019;Gawrilow et al., 2014;McClelland et al., 2014;Smith-Donald et al., 2007;Son et al., 2019). For instance , Bierman et al. (2008) found that, in a sample of typically developing preschool children, tasks of working memory and inhibitory control predicted emerging literacy skills. This finding is in agreement with Blair and Razza (2007), who examined the role of self-regulation in relation to emerging academic abilities in 3-to 5-year-old children. While several aspects of self-regulation predicted certain academic outcomes, inhibitory control made independent contributions to all three measures of academic ability (mathematical knowledge, letter knowledge, and phonemic awareness). The authors suggested that the ability to inhibit distracting or irrelevant information while reading or when faced with a numerical problem may be a contributing factor to success, over and above specific knowledge of problem solutions. For example, inhibitory control may allow children to consider multiple dimensions of a problem, rather than focusing on the most salient or recent aspects.
While inhibitory control prior to starting school may play an important role in predicting future academic success, the school environment itself may play an equally important role in shaping these skills. In school, children are required to follow classroom rules, sit still, and pay attention for a large portion of the lessons while suppressing any distractions that may interfere with their learning (Bierman et al., 2008).
These demands draw heavily on inhibitory processes. Therefore, it is conceivable that the environment of formal schooling may advance the development of inhibitory control, in comparison to kindergartners that tend to be more play-oriented (Morrison et al., 1997).

School cut-off design
To estimate the causal effects of schooling on cognitive development is not trivial, as schooling and development are confounded in time. The cut-off design (for a review, see Morrison et al., 2019) is an effective longitudinal method for examining unique schooling effects by taking advantage of arbitrary school cut-off dates. This method compares children who are similar in age, but due to fixed entry dates, are enrolled into different school years. Previous studies with a cut-off design found causal, beneficial effects of schooling on aspects of literacy Varnhagen et al., 1994) and numeracy (Bisanz et al., 1995;Christian et al., 2000). Recent years have seen a growth in research examining schooling-related effects on more basic cognitive processes, such as EF, given the associations shown between its subcomponents with academic achievement (Morrison et al., 2019). However, the findings here are mixed. For instance, Burrage et al. (2008) assessed inhibition in two groups of 5-year-old children born within 4 months of each other during the fall and spring semesters of the school year. The researchers found no significant difference in performance between children who had attended school and those who had stayed in kinder-

Research Highlights
• Using a modified school cut-off design, we collected longitudinal assessments of two aspects of inhibitory control, namely response inhibition and response monitoring, and their neural correlates. • For response monitoring, P1 children, compared to kindergarten children, showed a greater difference after 1 year of schooling in activation between correct and incorrect responses in the bilateral frontal cortex.
• The left frontal activation difference in P1 children showed a small association with math performance.
• The school environment plays an important role in shaping the development of brain functions underlying the monitoring of one own's performance.
garten. On the other hand, Kim et al. (2021) used a school cut-off design to examine performance on an inhibitory control task in 4-to 7-yearold children. There was a significant difference between first grade children and kindergarten children, with kindergarteners showing greater improvements across the year. However, this result should be interpreted with caution for several reasons. First, based on the data presented, it appears the first-grade children may have been significantly older than the kindergartners at baseline, which was not controlled for in the analyses. Second, initial differences in performance existed between the two groups at the start of the year, with the first graders outperforming the kindergarteners at baseline. Hence, it is unclear whether the kindergarteners improved more from the experience of kindergarten or were just "catching up" in performance with age.

Response inhibition and response monitoring
Despite the growing interest in how schooling may influence various aspects of basic cognition, there have been very few neurodevelopmental investigations. The only longitudinal inquiry into schoolingeffects on neural correlates of inhibitory control was conducted by Brod et al. (2017). Using a cut-off design, fMRI data were collected on 5-and 6-year-old children while they completed a go/no-go task. This study sought to uncover schooling-related effects in response inhibition, and thus focused on activation for successfully inhibited (no-go) and successfully executed (go) trials. While no group differences in activation were found during correct no-go trials, a larger increase in activation in the right superior posterior parietal cortex (PPC), an area associated with sustained attention, was found for correct go trials, only in children who attended school. The authors concluded the increased engagement of the PPC may reflect a direct effect of the schooling experience, where children are required to pay attention for extended periods of time in classrooms.
Although trials with correct responses have traditionally been the focus of analyses in a go/no-go task, a separate literature have highlighted a unique pattern of activation in response to errors. First recognized by ERP researchers (Falkenstein et al., 1991;Gehring et al., 1993), the negative and positive components that arise following an incorrect response to a no-go trial are referred to as the error-related negativity (ERN) and error-related positivity (Pe). These components presumably reflect the functioning of a network of structures, including the anterior cingulate cortex (ACC) and lateral prefrontal cortex (LPFC), and are thought to reflect error detection and/or conflict resolution processes associated with response monitoring (Grammer et al., 2014;Kim et al., 2016).
Interestingly, response monitoring is one of the components of cognitive control that has been linked to academic success (Denervaud, Knebel, et al., 2020;Kim et al., 2016), and its deficits are associated with developmental disorders including attention deficit hyperactivity disorder (Groom et al., 2013). To be successful in school, children must monitor their own progress, detect errors when they occur, and subsequently adapt their own behaviour. In comparison to kindergarten, teachers in school classrooms also provide more directive feedback on the accuracy of children's schoolwork, possibly shaping their sensitivity to errors (Denervaud, Knebel, et al., 2020 (Denervaud, Fornari, et al., 2020;Rubia et al., 2007).

Present study
Based on the review above, several questions remain that the current study aimed to address. First, although Brod et al. (2017) reported that 1 year of formal schooling results in increased engagement of the PPC, it is unknown whether this increase predicts academic achievement.
Previous studies that have investigated the link between response inhibition and academic achievement have been strictly correlational.
Thus, any causal links between the two remain to be demonstrated.  (Blair & Razza, 2007;Gawrilow et al., 2014;McClelland et al., 2014;Smith-Donald et al., 2007;Son et al., 2019), we predicted the schooling-specific increase in parietal activation in the P1 children would be associated with larger improvements in academic achievement. Next, we predicted P1 children would, over time, show stronger response monitoring after committing error (i.e., acting wrongly based on prepotent response), and thus show a stronger change in activation in the frontal cortex in response to error trials. Lastly, based on work by Grammer et al. (2014), we predicted schooling-specific changes in response monitoring in the P1 children would be associated with improvements in academic achievement.

Participants
Participants were recruited through gateway organizations such as before the completion of the task, and three children provided unusable data (two KG children had thick hair that led to poor signal quality, and data from one P1 child was lost due to experimenter error).
Hence, a total of 80 children ( However, due to an error in task programming, the data from the hearts-and-flowers task could not be interpreted. Therefore, we focused on children's performance and brain response on the go/no-go task, and relate these to measures of academic achievement. 2 Given the potential associations between task compliance and inhibitory skills, we compared children who refused to participate versus children who agreed to participate on a broad range of questionnaire variables that were collected as part of the larger project. These questionnaires assessed factors such as child temperament, quality of the parent-child relationship, and SES status. We found a significant group difference in two subscores of the Parenting Stress Index (Abidin et al., 2013). The first subscore measured child hyperactivity (p=.015), with those who did not participate scoring higher on this scale. We also found that children who did not participate were scored as less demanding (p=.014). However, it is important to note that these correlations do not survive correction for multiple comparison. Figure 1)

Response inhibition
Two children (1 P1, 1 KG) were excluded from the response inhibition fNIRS analyses for contributing fewer than six usable correct no-go trials across both timepoints and five children were excluded for providing incomplete data (two children (2 KG) refused to complete the task and data from three children (2 P1, 1 KG) was corrupted). Hence, a total of 73 children contributed longitudinal data for the response inhibition fNIRS analyses. Of these children, 37 were in P1 group and 36 were in KG group.

Response monitoring
Fifteen children (8 P1, 7 KG) were excluded from the response monitoring fNIRS analyses for contributing fewer than six usable incorrect no-go trials across both timepoints, and four children were excluded for providing incomplete data (one KG child refused to complete the task and data from three children (2 P1, 1 KG) was corrupted). A total of 61 children contributed to the response monitoring fNIRS analyses. Of these children, 30 were in P1 group and 31 were in KG group.

Vocabulary
Three children were excluded from the vocabulary analyses (two children (1 P1, 1 KG) refused to do the task and data from one KG child was lost due to experimenter error). Seventy seven children contributed to the final vocabulary analyses. Of these children, 39 were in P1 group and 38 were in KG group.

Numeracy
Six children were excluded from the numeracy analyses (five children (3 P1, 2 KG) refused to complete the task and data from one KG child was lost due to experimenter error). Seventy four children contributed to the final numeracy analyses. Of these children, 37 were in P1 group and 37 were in KG group.

School achievement packs
No children were excluded on either the math or phoneme pack.

Cats-and-dogs task
The cats-and-dogs task (CDT), adapted from Brod et al. (2017), was used to measure response inhibition and response monitoring in

F I G U R E 2 Trial structure of the Cats-and-Dogs Task (CDT)
children-see Figure 2. The task was run in E-prime V.3 software on an HP laptop with a 14-inch screen. During "go" trials, children saw a picture of a dog and were supposed to press a button (spacebar).
During "no-go" trials, children saw a picture of a cat and were supposed to withhold pressing a button. To ensure children understood the rules, the session began with three blocks of practice that progressively allowed less time to response. During the practice, children were reminded of the rules if they made a mistake. Performance on the practice runs was not included in final analyses. After children completed all practice blocks, the test session, consisting of two runs began. The first run was comprised of 59 trials: 44 go trials and 15 no-go trials. Run 2 was compromised of 69 trials: 52 go trials and 17 no-go trials. Pictures of cats and dogs were presented for 500 ms, followed by a fixation cross as jitter that ranged in duration from 2 to 8 s. Responses made during stimuli presentation or during the fixation cross period were recorded.
The order of presentation of go and no-go trials was pseudorandom, with the constraint that no-go trials were preceded equally often by 1, 2, 4, or 5 go trials.

Numeracy task (administered at T1 and T2)
The numeracy screener developed by Nosworthy et al. (2013) was used to assess basic numeracy skills. Children were required to compare pairs of magnitudes ranging from one to nine and judge which was larger. Magnitudes were represented symbolically (56 digit pairs) and non-symbolically (56 pairs of dot arrays). In both the symbolic and non-symbolic conditions, numerical magnitude was counterbalanced for the side of presentation. Dot stimuli were also controlled for area and density. Easier items were presented first, followed by more difficult items. Children were given 1 min to complete each condition. The order of the two conditions were counterbalanced across participants.

Procedure
Data were collected in each participant's home. After arrival, the researcher measured the circumference of the child's head and selected an appropriately sized fNIRS cap. Children were given an iPad to watch cartoons during the set-up. Once the cap was fitted to the child's head, measurements were taken from the inion to the nasion and from the two peri-auricular points to make sure that the cap was centered. After the equipment was safely positioned, the instruction and practices for the CDT started, followed by the actual task. During the task, if children indicated that they made an error, the experimenter reassured the child and encouraged them to continue concentrating on the game. To keep children engaged, each test run contained different sets of picture of cats and dogs. To maintain motivation, children were also rewarded with a sticker after each run.
Once children completed the CDT, they were provided the iPad to watch cartoons while the researchers removed the cap. After a short break, testing proceeded with the vocabulary task, followed by the numeracy task. At T2, children were additionally tested on the phonemes pack and math pack. The order of the academic performance tasks presented was counterbalanced across participants. Children were rewarded with stickers after completing each task, regardless of their performance. All children were remunerated with £10 and a toy upon completion of each time point measurement. As part of the overall procedure for the project, children also completed tasks on visual working memory, counterfactual reasoning, and associative memory, while parents filled in questionnaires collecting data on demographics, child behaviour, and life stress (data not included here, see details in McKay et al., 2021).

Behavioural analyses
Accuracy was calculated separately for each trial type (go and no-go) and test run (run 1 and run 2) and timepoint (T1 and T2). The following formula was used to calculate accuracy and reaction time at each timepoint to account for the different number of trials included in each run.
Weighted average: ((run 1 score * run 1 number of trials) + (run 2 score * run 2 number of trials)) Total number of trials After computing the weighted averages, a corrected measure of accuracy (against response biases) was calculated for each subject, by subtracting no-go incorrect responses from go correct responses (Go correct -NoGo incorrect ), separately at each timepoint.

Outlier correction
All behavioural data were screened for outliers. To correct for longitudinal outliers, we used the Mahalanobis distance (MD) method.
Further, we screened for outliers that were ±3 SDs from the mean at each timepoint. Three outliers were identified: two P1 children were removed from the phonemes pack analyses and one KG child was removed from the math pack analyses. No other outliers were identified.

fNIRS group analyses
Oxygenated haemoglobin (HbO) and deoxygenated haemoglobin (HbR) beta values were extracted for each run (run 1 and run 2) and each condition (cue onset of correct go trials, cue onset of correct nogo trials, cue onset of incorrect go trials, cue onset of incorrect no-go trials, response at go trials, response at no-go trials). A weighted average was then calculated to account for the different number of trials included in each test run to produce one beta estimate per subject, per condition, per chromophore, and per timepoint.

Response inhibition analyses
For the response inhibition analyses, we focused on HbO and HbR beta estimates for cue onset on correct no-go trials versus correct go trials.
These beta values captured activation right after the onset of the stimulus. At T1, the mean number of correct trials included for P1s were 60 ± 4 go trials and 16 ± 1 no-go trials. The mean number of correct trials included for KGs were 66 ± 3 go trials and 18 ± 2 no-go trials. At T2, the mean number of correct trials included for P1s were 69 ± 4 go trials and 19 ± 1 no-go trials. The mean number of correct trials included for KGs were 75 ± 4 go trials and 18 ± 1 no-go trials.

Response monitoring analyses
In the pre-registration, we initially only planned for analysis of response inhibition, focusing on correct responses on no go trials. However, based on consideration from the literature, we also investigated activation relating to response monitoring, namely contrasting erroneous responses on no-go trials against correct response on go trials. In both trial types a motor response was conducted, followed by no explicit feedback. Therefore, the post-processing of the erroneous response in the case of no-go trials is assumed to involve the selfdetection of error and conflict, which should lead to more monitoring and careful responding in subsequent trials, consequently overall better performance on the task. Thus, for the response monitoring analyses, we focused on HbO and HbR betas estimates for response on go trials and response on no-go trials. These beta values captured activation at the onset of the child's button press. At T1, the mean number of trials included for P1s were 61 ± 4 correct go trials and 12 ± 1 incorrect no-go trials. The mean number of trials included for KGs were 65 ± 4 correct go trials and 10 ± 1 incorrect no-go trials. At T2, the mean number of trials included for P1s were 69 ± 4 correct go trials and 9 ± 1 incorrect no-go trials. The mean number of trials included for KGs were 74 ± 4 correct go trials and 12 ± 1 incorrect no-go trials.

Modelling framework
Univariate latent change score (LCS) models (Kievit et al., 2018;McArdle & Hamagami, 2004) were used to investigate the degree of longitudinal change in behavioral performance and brain activation.
All univariate models were set up as multi-group models, allowing the same model to be fitted for each group (P1 vs. KG) and later on parameter comparisons. Individual growth is captured by T1 (i.e., the intercept of X1_T1- Figure 3) and the latent change score factor (ΔX1), modelled as the difference between the initial observation and subsequent observation. Average group change across time is captured by the mean of the latent change score factor (μ ΔX1 ), and between-person differences in change are captured by the variance (σ2 ΔX1

School achievement packs
Univariate models could not be fitted to the school achievement packs as they were only administered at T2. Thus, simple t-tests were conducted to compare performance between P1 and KG children on these measures. As expected, we found that P1 children (

fNIRS results
fNIRS data were comprised of HbO and HbR beta values for each of the 14 channels. To reduce data dimension and focus subsequent analyses on effects that had a difference between HbO and HbR, an initial repeated measure ANOVA including chromophore (HbO, HbR) as a factor was run for each channel, using the Benjamini-Hochberg method to correct for multiple comparisons. For the response inhibition analyses, a repeated measures ANOVA with a within-subject factor of trial type (go correct, no-go correct) and chromophore (HbO, HbR) and a between-subjects factor of group (P1, KG) was run for each of the 14 channels. For the response monitoring analyses, a repeated measures ANOVA with a within-subject factor of trial type (go correct, no-go incorrect) and chromophore (HbO, HbR) and a betweensubjects factor of group (P1, KG) was run for each of the 14 channels.
We focused on significant interactions involving chromophore as a factor, and followed up with post-hoc analyses conducted on the HbO estimates.

Response inhibition analyses
Only channels that showed a significant interaction involving chromophore and that survived the Benjamini-Hochberg correction are reported. The interaction between trial type and chromophore was significant in channels overlying the right middle frontal tests revealed that HbO activation for go correct trials was greater than activation for no-go correct trials (see Table 2). The remaining three-and four-way interactions between group, trial type, time, and chromophore were either not significant or did not survive the Benjamini-Hochberg correction.

Response monitoring analyses
Only channels that showed a significant interaction with chromophore and that survived the Benjamini-Hochberg correction are reported. The interaction between trial type and chromophore was significant in channels overlying the right middle frontal gyrus  Table 3.
Importantly, in the bilateral middle frontal gyrus and bilateral inferior frontal gyrus, P1 children showed greater negative activation for response at incorrect no-go trials than for correct go trials at both T1 and at T2. This was not the case for KG children, who only showed a difference in activation between these trials at T1. Therefore, the ANOVA revealed that the difference in activation between correct go trials and incorrect no-go trials across time differentiated P1 children from KG children. To relate these neural differences in response monitoring to behavior using the bivariate LCS models, an average difference in activation (go correct activation-no-go incorrect activation) was computed across channels of nearby regions that showed the significant four-way interaction with similar patterns. Specifically, this led to two clusters covering the right frontal cortex (averaging channels 1, 2, and 3; see Figure 5a) and the left frontal cortex (averaging channels 5 and 7; see Figure 5b).

TA B L E 2
Response inhibition analysis: Channels showing significant interactions between trial type (go correct and no-go correct) and

F I G U R E 5
The difference in activation between go correct and no-go incorrect trials (response monitoring contrast) in the (a) right frontal cluster (

Bivariate LCS modelling
As the first step, we tested the longitudinal coupling between activation difference in the two frontal clusters and corrected accuracy on the CDT task for both groups. This is mainly to verify the functional relevance of the two frontal clusters of response monitoring activation for overall task performance.

Right frontal cluster and CDT corrected accuracy
Parameter estimates are shown in Table 4. For KG Children, corrected accuracy at T1 was positively correlated with the difference in activation in the right frontal cluster at T1. Namely, children who showed more difference in activation related to response monitoring had better performance. Constraining the baseline correlation at T1 to be 0 in KG children led to a significant drop in model fit, Δx 2 = 10.707, Δdf = 1, p = 0.001. No other cross-domain parameters were significant.
For P1 children, corrected accuracy at T1 negatively predicted the change in the difference in activation in the right frontal cluster from T1 to T2. Thus, children with better performance at T1 showed less change in activation over time. However, constraining the coupling pathway to be 0 did not lead to a significant drop in model fit

4.2.2
Left frontal cluster and CDT corrected accuracy For KG children, better corrected accuracy at T1 was correlated with higher difference in activation in the left frontal at T1. Constraining the baseline correlation at T1 to be 0 in KG children led to a significant drop in model fit, Δx 2 = 5.028, Δdf = 1, p = 0.025. Furthermore, higher corrected accuracy at T1 predicted more change in the difference in activation in the left frontal. To follow-up on this, the coupling pathway was constrained to be 0 in KG children, which led to a significant drop in model fit Δx 2 = 4.492, Δdf = 1, p = 0.034.
For P1 children, similar to KG children, better corrected accuracy at T1 was correlated with higher difference in activation in the left frontal at T1. Constraining the baseline correlation at T1 to be 0 in P1 children lead to a significant drop in model fit, Δx 2 = 5.536, Δdf = 1, p = 0.019.
No other cross-domain pathways were significant.
Taken together, in KG and P1 children, higher response monitoring activation difference in the left frontal cluster (additionally right frontal cluster for KG) was related to better overall performance in the inhibitory control task.

Academic achievement in P1 children
To address our second research question, we tested to what extent the schooling-specific response monitoring activation changes in the two frontal clusters could predict academic achievement. The longitudinal coupling between the activation difference with performance on the academic tasks was examined. Here, we focused on bivariate relationships of P1 children (since they were the only group that attended school and showed a greater response monitoring activation difference across time). Bivariate relationships for KG children are shown in Supplementary Material (Table S1).

Right/left frontal cluster and academic achievement
Bivariate longitudinal models were fitted for the response monitoring activation in the right frontal (or left frontal, respectively) and (1) vocabulary scores (2) math pack, and (3) phonemes pack. The longitudinal change in activation in the left frontal cluster was positively correlated with math pack scores at T2 (p = 0.04). To follow-up on this finding, the coupling pathway was constrained to be 0, which led to a trend in drop of model fit Δx 2 = 3.488, Δdf = 1, p = 0.062. No other crossdomain parameters were found to be significant in all other models.

DISCUSSION
The present study sought to examine to what extent 1 year of formal schooling shapes the development of neural processes underlying response inhibition and response monitoring, as well as establish whether these effects, if significant, were related to academic achievement. First, we found that P1 children and KG children started out with similar corrected accuracy on the go/no-go task. Although P1 children, but not KG children, showed significant improvement on task accuracy over time, the magnitude of change between the two groups was statistically comparable. In terms of brain activation, no significant differences in response inhibition were found between the two groups of children. However, for response monitoring, after 1 year of schooling P1 children showed a greater activation difference than KG children.
Functionally, this activation difference was associated with better performance on the go/no-go task. When relating to broader measures of academic achievement, we found a small association between response monitoring and math performance. Each of these aspects of results are discussed in the following.
While we hypothesized that P1 children would show greater improvement than KG children across the year, our findings are in line with Brod et al. (2017) who also reported no group differences in response inhibition behaviour across the year. However, unlike Brod et al. (2017) and in contrary to our hypothesis, we also did not find any group difference in neural activation related to response inhibition (or parietal activation during go trials as in Brod et al., 2017).
Several methodological differences exist that may account for this inconsistency. First, children in the current study were between 1 to 2 years younger than the children in the Brod et al. (2017) study, due to national differences in school entry age. It is conceivable that the first year of schooling may be set up to be less demanding and formally structured where children start school at a younger age. Thus, the increase in parietal activation resulting from a schooling environment may only appear if there is a sufficiently large change in terms of demand and expectations transitioning from kindergartens to classrooms. Second, the current study and that of Brod et al. (2017) employed different modalities to record brain activation. The fNIRS channel-based analyses employed here may not have been as sensitive as the fMRI analyses conducted by Brod et al. (2017) to detect changes in activation in small clusters of voxels (as reported in that study). A potential way to improve upon this would be to conduct more targeted analyses. For instance, novel image reconstruction uses a head model to generate functional images of the fNIRS data, transforming surface level channel-based data into a volumetric representation within the brain (Forbes et al., 2021). This would allow for greater comparability with fMRI investigations.
Another Specifically, this study included a sample size of 53 at 5-months, 40 at 8-months, and 45 at 12-months. Thus, the authors concluded that at these group sizes, the inferences drawn from group level channelbased analysis are unlikely to be significantly affected by variability in array position and shifting head sizes.
Finally, Brod et al. (2017) employed a traditional school cut-off design, in which children whose birthdates fell shortly before and shortly after an arbitrary cut-off date were compared, resulting in group assignment that is to some extent random ( sures. This included a colour change-detection task (assessing visual working memory) and a grid memory task (assessing associative memory). No group differences in performance were found on any of these measures. Finally, and most interestingly, we also administered a battery of questionnaire to the parents of the children assess here measuring child temperament, quality of the parent-child relationship, and a range of environmental factors including SES, level of disorganisation in the home, and number of daily hassles experienced by parents. Critically, no differences between P1 and KG children emerged in any of these parent-reported measures. In sum, parental belief concerning the child's school readiness is not systematically reflected in quantitative measures of cognitive function, academic performance, and temperament. Descriptive statistics and statistical test results for these comparisons can be found in Supplementary Materials (Table S2 and S3).
Our second major finding concerns the activation related to response monitoring, in which we found that P1 children, but not KG children, showed a greater difference after 1 year of schooling.
As the response monitoring contrast was not part of the study preregistration, it was important for us to first establish the functional relevance of the two frontal clusters (left and right middle/inferior frontal gyrus) that emerged from this contrast. Therefore, we tested the coupling between the difference in activation with performance on the CDT task, and found that a greater response monitoring activation difference in the left frontal cluster was related to better performance in the inhibitory control task in both groups. For KG children, a similar relationship was also found for the right frontal cluster. This is in line with previous research reporting that a greater difference in activation between correct go and incorrect no-go trials reflects more efficient response monitoring (Grammer et al., 2014;Torpey et al., 2012), which may support better task performance. Previous adult fMRI stud- this interpretation seems likely as children occasionally showed a reaction reflecting conflict after making an incorrect button press in a no-go trial. Children would either verbally indicated that they made a mistake (e.g., saying "oh no") or show behavior of having committed an error (e.g., clasping hands over mouth, pulling hand away from keyboard).
Most importantly, in the two frontal clusters identified from the response monitoring contrast, P1 children showed a greater difference in activation across time than KG children. We posit that, across the first school year, P1 children show stronger response monitoring due to the nature of the schooling environment. In school, emphasis is placed on instructional learning where children are provided with opportunities to engage in schoolwork and gain insights into their own performance based on teacher feedback (Denervaud, Knebel, et al., 2020).
As this instructional learning takes hold, children learn to value correct answers and avoid errors (Denervaud, Knebel, et al., 2020). In contrast, the kindergarten environment introduces learning through more play-initiated activities (Morrison et al., 1997). While free play orientation may benefit children in many ways, it likely does not encourage the identification of errors on academic tasks as effectively as formal schooling (Denervaud, Knebel, et al., 2020).
Third, as the next step to determine whether the larger activation difference in response monitoring in the P1 children could predict academic performance, we investigated the longitudinal coupling between these variables. We found borderline significant positive correlations between the change in activation in the left frontal cluster with performance on the math pack. This is in line with Kim et al. (2016) who found that stronger math skills (as well as reading skills) predicted stronger ERP component related to response monitoring. Further support for our finding stem from previous adult EEG research that found a larger ERN was significantly correlated with better academic performance (Hirsh & Inzlicht, 2010). Given that monitoring one's own performance is a key aspect of self-regulation, the authors interpreted that individuals with a greater ability to monitor tend to engage in self-regulatory behaviours that are important for academic success (Pintrich & De Groot, 1990). It is however important to note that the change-change association between the left frontal cluster activation and math performance did not survive the formal model comparison. Therefore, the result needs to be interpreted with caution and stands for replication test. Future studies need to be better powered in terms of sample size. Hertzog et al. (2006)  the two studies that did find a positive effect either had higher program standards or a curriculum that emphasised greater vocabulary instruction. A potential reason for this discrepancy in findings might be related to SES. Wright and Neuman (2014) found that children from lower income schools (i.e., schools where more than 50% of students received free and reduced lunch) encounter less opportunity for vocabulary learning than children from higher income schools (i.e., schools where fewer than 25% of students received free and reduced lunch). Specifically, the authors found that teachers from economically disadvantaged schools were less likely to discuss word meanings with children and also explained fewer challenging words.
Consequently, children from lower income schools received only 60% of the vocabulary instruction provided to their more economically advantaged peers. This is important, as several studies have demonstrated that instruction aids children's vocabulary acquisition (Biemiller & Boote, 2006;Kim, 2017). In the current study, parental education and income was above the national average, and thus, it is likely children were enrolled into economically advantaged schools that provided a greater degree of instructional learning, leading to an improvement in vocabulary beyond children attending kindergarten.
Finally, it is worth mentioning that, for KG children only, those who began the study with better performance on the CDT task showed a greater increase in response monitoring activation across the year. We did not predict this result but it seems interesting, given that the KG children, at the mean level, did not show a significant change in activation difference across time. One interpretation for this finding relates to the interplay between children's individual characteristics and the schooling/kindergarten environment. We posit that the schooling environment may have facilitated all school children, regardless of their starting point, to become more sensitive to task accuracy and error, leading to a mean change in brain activation across the year associated with stronger response monitoring. On the other hand, for the reasons highlighted above, kindergarten children may encounter less explicit instruction. Only those who are already advanced at the start, presumably by eliciting more advanced interaction with adult caregivers, show a change in brain activation associated with more efficient response monitoring. Future studies should test this postulation by getting more direct measurement of social/instructional environment of children.
The current study uniquely contributes to the current special issue on the development of self-regulation, cognitive control, and executive function, by being the first study to use a cut-off design to assess the impact of 1 year of schooling on both response inhibition and response monitoring and to relate these differences to measures of academic achievement. Our findings highlight the causal roles of the school environment in shaping the development of brain functions underlying EF, particularly in the monitoring of one own's error. Such schoolingspecific neurocognitive changes can predict specific aspect of academic performance across the first school year and may indicate how adaptive children are in adjusting to the new formal schooling environment.
At the methodological level, our study demonstrated the feasibility of collecting good quality neural data using fNIRS from children in their homes. Future studies may explore to what extent such neural measures can be utilized to identify children who are potentially struggling during the critical transitional period from kindergarten to first grade.

ACKNOWLEDGMENTS
We would like to thank all the children and their parents who par- Open Access funding enabled and organized by Projekt DEAL.

CONFLICT OF INTEREST
No potential conflict of interest is reported by the authors.

ETHICAL APPROVAL STATEMENT
This research was approved by the General University Ethics Panel (GUEP 375 and 375A) at the University of Stirling.

DATA AVAILABILITY STATEMENT
All group-level data and analysis scripts have been made publicly available via the Open Science Framework and can be accessed at https:// osf.io/nyjqe/. Further information regarding the fNIRS pre-processing and analysis are available upon request.