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# Mind wandering and its relationship with sustained attention and executive functions in preschoolers

Camilla Ziane, Claire Wardak, Suliann Ben Hamed

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## To cite this version:

Camilla Ziane, Claire Wardak, Suliann Ben Hamed. Mind wandering and its relationship with sustained attention and executive functions in preschoolers. Journal of Experimental Child Psychology, 2025, 262, pp.106372. 10.1016/j.jecp.2025.106372. hal-05298832

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# MIND WANDERING AND ITS RELATIONSHIP WITH SUSTAINED ATTENTION AND EXECUTIVE FUNCTIONS IN PRESCHOOLERS

Camilla Ziane¹, Claire Wardak*², Suliann Ben Hamed*¹

1. Institut des Sciences Cognitives Marc Jeannerod, CNRS UMR 5229, Université Claude Bernard Lyon I, Bron, 69500 France

2. Université de Tours, INSERM, Imaging Brain & Neuropsychiatry iBraiN U1253, 37032, Tours, France.

**Corresponding authors:** Camilla Ziane, [camilla.ziane14@gmail.com](mailto:camilla.ziane14@gmail.com); Suliann Ben Hamed, [benhamed@isc.cnrs.fr](mailto:benhamed@isc.cnrs.fr)

## Acknowledgments

This work was funded by the Agence Nationale de la recherche to S.B.H. (ANR-11-LABX-0042, ANR—IDEX-0007) as well as by a funding from the Université Lyon 1 Claude Bernard and the Région AuRA, through the PackAmbition funding instrument. We thank neuropsychologists Laura Bon and Violette Bigot for their investment in the selection of neuropsychological tests and their help on the tests scoring. We thank Sonia Fortas and Léon Jouhaux, preschool directors for their assistance in this project.

## Author contribution

Conceptualization: C. Z., C. W., S.B.H.; Data Curation: C.Z., S.B.H.; Formal Analysis: C.Z., S.B.H.; Funding Acquisition: S.B.H.; Investigation: C.Z., S.B.H., C.W.; Methodology: C.Z., S.B.H.; Project Administration: S.B.H.; Resources: S.B.H.; Software: S.B.H.; Supervision: S.B.H., C.W.; Validation: S.B.H., C.W.; Visualization: C.Z., S.B.H.; Writing—Original Draft Preparation: C. Z., C. W., S.B.H.; Writing—Review & Editing: C. Z., C. W., S.B.H.

<footnote>* These two authors are co-last authors and equally contributed to the work</footnote>
MIND WANDERING AND ITS RELATIONSHIP WITH SUSTAINED
ATTENTION AND EXECUTIVE FUNCTIONS IN PRESCHOOLERS

ABSTRACT (222)

Mind wandering (MW) is a phenomenon that has been largely described in adults, during which thoughts do not stay on the current tasks or goals. Considering its negative impact on educational outcomes, measuring and understanding MW in children is essential. MW has been associated with attentional and executive performance in children above 8 years old. Given the huge changes in attention and executive functions organization before 6 years old, our study aimed at exploring how mind wandering interacts with these processes in preschoolers.

Sixty children aged 4 to 6 years old were asked to evaluate their mind wandering propensity in the classroom using an adapted daydreaming questionnaire. They were also administered neuropsychological tests and questionnaires evaluating sustained attention, processing speed, cognitive flexibility, inhibition and a selection of individual traits.

Preschoolers' self-evaluation strongly correlated with their teacher's evaluation, showing the feasibility of assessing MW in young children. The MW scores also correlated with the children's performance in several tests assessing sustained attention, processing speed, cognitive flexibility and inhibition, as well as some individual traits. A latent variable modeling revealed that MW is best modeled by a latent factor independent from attention, speed and inhibition, but highly correlated with attention.

Our results thus reveal the central role of attention in child development, suggesting that mind wandering in preschoolers could be linked to attention immaturity.
## KEYWORDS

Exploratory Factor Analysis; Structural Equation Modeling; preschoolers; sustained attention; inhibition; daydreaming; mind wandering

## ABBREVIATIONS

ASEBA: Achenbach System of Empirically Based Assessment; DDFS: Daydream Frequency Scale auto-evaluated by children; DDFS-t: Daydream Frequency Scale evaluated by teacher; EF: executive functions; EFA: Exploratory Factor Analysis; Go/NoGo_FA: number of false alarms in Go/NoGo task; Go/NoGo_T: completion time for the Go/NoGo task; Go/NoGo_TE: total number of errors in Go/NoGo task; MW: Mind wandering; MWQ: Mind Wandering Questionnaire; PFC: prefrontal cortex; PT: processing time; PDTP: Picture Deletion Task for Preschoolers; SA: sustained attention score from the PDTP; SEM: Structural Equation Modeling; TMTA: Trail Making Test version A; TMTB: Trail Making Test version B; TMTAE: error rate in TMTA; TMTBE: error rate in TMTB; TMTB-TMTA: difference in completion time between TMTB and TMTA; SIE: Stroop Test interference index for error rates between ST3 and ST4; ST1: Stroop Test version 1 (ST1T: time; ST1E: error); ST2: Stroop Test version 2 (ST2T: time; ST2E: error); ST3: Stroop Test version 3 (ST3T: time; ST3E: error); ST4: Stroop Test version 4 (ST4T: time; ST4E: error); WSR: Weiss Symptom Record; Zazzo: Zazzo cancellation test (Zazzo_E1: efficiency for sheet 1; Zazzo_E2: efficiency for sheet 2; Zazzo_T1: time to complete sheet 1; Zazzo_T2: time to complete sheet 2).
## INTRODUCTION

Mind wandering (MW) refers to a mental state in which thoughts spontaneously stray from their current goals, turning towards task-unrelated thoughts, distraction or daydreaming episodes (Smallwood and Schooler 2006). Adults are estimated to spend between 30 and 50 % of their wake time daydreaming (Killingsworth and Gilbert 2010). This complex phenomenon can impact various aspects of cognition and behavior (Mooneyham and Schooler 2013), enhancing creativity (Preiss 2022), or decreasing performance in demanding cognitive tasks (Smallwood, Fishman, and Schooler 2007, Smallwood, McSpadden, and Schooler 2007) and in tasks requiring sustained attention and prolonged focus (Smallwood et al. 2008, Salley and Dixon 2007).

The interaction between mind wandering, executive functions (EF), and sustained attention is complex and context-dependent (Smallwood and Schooler 2006, Seli et al. 2016). It has been proposed that MW arises from a failure in executive control (either by not maintaining goal-oriented processes towards the current task or by failing to inhibit interfering thoughts), from a shift of attention away from external representations towards internal goals, and competes with the current task for working memory and attentional resources (McVay and Kane 2010a, Smallwood and Schooler 2006, Smallwood, Ruby, and Singer 2013). This interaction between MW, EF and attention can also be observed at the cerebral level. A fMRI meta-analysis (Fox et al. 2015) revealed that MW mainly recruited the Default Mode Network, which is activated during resting state, episodic memory recall and internal processing (Andrews-Hanna 2012), and the frontoparietal control network, which is involved in cognitive control and goal-directed cognition (Niendam et al. 2012, Vincent et al. 2008).

The influence of MW in an educational context has been the focus of many studies in particular in undergraduate students, showing around 10 to 50% of MW during lectures and a negative influence of MW on comprehension, retention, and academic performance (e.g. Lindquist and McLean 2011, Pachai et al. 2016, Smallwood, Fishman, and Schooler 2007, Szpunar, Moulton, and Schacter 2013). Surprisingly, only a few studies have evaluated MW in children, above 6 years old, either by probing for task-unrelated thoughts during a task (Cherry, McCormack, and Graham 2022, Keulers and Jonkman 2019, Teague et al. 2025, Ye et al. 2014, Zhang et al. 2015), or using dedicated questionnaires (Cao et al. 2022, Mrazek et al. 2013). MW has been shown to occupy from 20-25% to approximately 35% of nine- to eleven-year-old children's time, and to be negatively correlated with sustained attention performance and significantly linked to inhibition processes (Keulers and Jonkman 2019, Zhang et al. 2015). In six- to eleven-year-olds, a mean proportion of 25% of MW is described, predicting memory retention performance (Cherry, McCormack, and Graham 2022). However little is known about MW in preschool children.

Infants, from their earliest months, exhibit attention primarily directed toward salient sensory stimuli and social interactions with caregivers (Ruff and Rothbart 2001). This early attentional orienting has been correlated with executive functioning at 3 years of age (Kraybill, Kim-Spoon, and Bell 2019). Throughout preschool years, a gradual progression in sustained attention is observed, enhancing their ability to concentrate on prolonged tasks (Posner and Rothbart 2007). Sustained attention is a pivotal skill in the cognitive development of young children (Salley and Dixon 2007) and has been identified as a significant predictor of later school success (McClelland, Acock, and Morrison 2006). The development of attention in children has been closely linked to the maturation of the prefrontal cortex (PFC) (Crone and Dahl 2012, Luna, Padmanabhan, and O'Hearn 2010), followed by the establishment of interactions between the PFC and other brain regions, such as the superior parietal cortex (Crone and Ridderinkhof 2011). To better understand the evolution of the organization of attention and functioning, one of the most common approaches has been to use latent factor analysis. By combining
scores from multiple tests, studies have tried to describe the core structure of attentional processes. Studies in adults have converged towards four-factor models, with three factors that can be described as attentional, and another factor more related to encoding in working memory (e.g. Mirsky et al. 1991, Robertson et al. 1997). In children above 6 years old, the same kind of organization has been observed (Mirsky et al. 1991, Manly et al. 2001), suggesting that while these attentional processes may not be mature yet (Klenberg, Korkman, and Lahti-Nuuttila 2001), they already exist after age six. In preschoolers (3-6 years old), Steele et al. (2012) described a two-factor model (executive attention, sustained selective attention) while Breckenridge et al. (2013) found a two-factor model in three to four and half years old (sustained attention, selection/response) but a three-factor model in four and a half to six years old (sustained attention, selective attention, attentional control). These results thus suggest that the three to six years period is crucial for the development of attentional organization.

The development of executive functions is proposed to occur in successive phases (Garon, Bryson, and Smith 2008, Zesiger 2009), starting before three years old. It may be linked to the maturation of PFC (Crone et al. 2006, Heyder, Suchan, and Daum 2004, Kagan and Baird 2004), possibly through a first maturation phase from zero to six years, and a second from eight to sixteen years (Thatcher 1991). The main model for executive functions proposed in adults is a three-factor model. Miyake et al. (2000) identified three distinct but correlated executive factors (inhibition, switching, updating), coordinated by a shared central inhibitory or attentional system. While the three-factor model is well suited for adults and even school-aged children (Friedman and Miyake 2004, Lehto et al. 2003), it seems that in younger preschoolers (three to six years old), a model with a unique latent factor is more appropriate (Wiebe, Espy, and Charak 2008, Wiebe et al. 2011, Hughes et al. 2009, Fuhs and Day 2011).

Considering the huge changes in attention and executive functions organization before 6 years old, our study aimed at exploring how mind wandering interacts with these processes in preschoolers. Our first objective was to evaluate mind wandering in four to six years old children. We thus adapted a daydreaming questionnaire to ask the children to self-evaluate their MW in the classroom and correlated their report with MW evaluated by their teachers. We replicated this MW self-evaluation in preschoolers in a second group of children, assessing test-retest and inter-rater reliability. Our second objective was to explore how MW evolved during the four to six years period and how it related to sustained attention and some EF (in particular inhibition and flexibility that have been linked to MW). Third, as MW has been associated with some individual traits and neurodevelopmental disorders (e.g. Alali-Morlevy and Goldfarb 2021, Pereira, Gurguryan, and Ristic 2020, Seli et al. 2019), we also evaluated how MW was linked to some developmental and emotional difficulties as assessed from everyday life situations. Our last objective was to test how MW fitted in a functional model encompassing sustained attention and the EF assessed in the current study. Based on what has been described in previous studies, we tested several models, ranging from a unique latent variable modeling to separate latent variables modeling.

# MATERIAL AND METHODS

## Participants

Our main group of children consisted of sixty participants distributed across three age groups and supported the main results of the current paper. The first group included twenty four-year-old children (mean age 55.5 ± 3.5 months), the second twenty five-year-old children (mean age 64.4 ± 3.1 months), and the third group twenty six-year-old children (mean age 76.5 ± 3.3 months), with an equal number of girls and boys in all groups. Three supplementary children (two four-year-olds and one five-year-old) were excluded as they did not pass the comprehension checks for mind wandering testing (see
below). A second group of children consisted of forty-five participants distributed across three age
groups and supported the assessment of inter-rater reliability and test-retest reliability. The first group
included fifteen four-year-old children (mean age 52.9± 3.3 months, eight girls), the second fifteen
five-year-old children (mean age 66.5 ± 5.3 months, six girls), and the third group fifteen six-year-old
children (mean age 77.3 ± 3.0 months, seven girls). No child was excluded from this cohort. This second
group of forty-five participants was only tested specifically on the MW self-report and teacher
questionnaire measures, more than twelve-months after the completion of the first test.

Participants were recruited from two local schools in Lyon, France. Ethical and administrative approval
was obtained from the local school administration. The project was then presented to the teachers
and the parents. All legal representatives received written information and gave written consent for
their child's participation. All children were orally informed of the goal of the study, how it would
proceed, and that they could stop at any time without any consequences. They gave oral consent to
participate in the study. The study conformed with the Declaration of Helsinki (World Medical
Association, 2013) and the European General Data Protection Regulation.

Tests and questionnaires

Tests and questionnaires are described in detail in **Supplementary Information SI1**. Briefly, to assess **mind wandering** in the current study, we developed a questionnaire adapted from the Daydream Frequency Scale (DDFS, Stawarczyk et al. 2012 ; see **Supplementary Information SI2**). It consisted of a self-assessment of mind wandering with a single straightforward question directly asked to the child: "Where do you see yourself in the classroom?" Two arrows presented the possible visual choices: one depicted a pupil in a classroom, attentive to the teacher's words, while the other showed the same pupil, still in the classroom, with multiple thoughts represented by various icons in a speech bubble: a cat, parents, home, candies, outdoor games – unrelated to the subject being taught. The child had to choose one of five levels under each picture along a gradient of green, going from "Never" corresponding to the lightest green, to "Almost Never," "Sometimes," "Frequently," and "Always" for the darkest green. The questionnaire was presented orally by the experimenter who explained the scoring and read the words to the child. A precise scenario was followed by the experimenter, with several steps and comprehension checks, to make sure the child understood the different notions by reformulating the situation, giving examples, until the experimenter ensured that the child could confidently point to his/her answer (see **Supplementary Information SI1** and **SI3** for more details). Formulation of the sentences and examples were adapted for the youngest children with more direct and shorter sentences. Three children (see Participants) did not pass the comprehension check for the circle scale (see **Supplementary Information SI3**) and were excluded. To enhance identification with the cartoon, we provided separate versions for boys and girls. The scale went from 1 to 5, where 1 corresponded to "Never" and 5 corresponded to "Always". These scores were subsequently transformed into percentages as follows for a more intuitive understanding of the scale: 1 = 0%, 2 = 25%, 3 = 50%, 4 = 75%, 5 = 100%. The highest values thus corresponded to the highest levels of mind wandering behavior. In order to evaluate the children's response to our adapted DDFS, we asked the teachers to fill out both the classical DDFS (which is a self-report questionnaire in older participants; validated French version, Stawarczyk et al. 2012) and the Mind Wandering Questionnaire (MWQ, Mrazek et al. 2013; back-translated in French after agreement from M. Mrazek) for all children. To ensure that the teachers' evaluations were based on the same cues for all the teachers, and that they evaluated MW and not inattention in their pupils, a training session was organized with neuropsychologists several months before data collection to explain the concepts of MW and inattention (see **Supplementary Information SI1**). The same teachers were involved in evaluating
Mind-Wandering ratings in the first group (initial test group) and in the second group of children (test-retest group). As the two experiments were more than twelve months apart, a short reminder on the difference between inattention and mind-wandering was provided to them.

To assess **sustained attention** in our participants, we used the Picture Deletion Task for Preschoolers (PDTP; Corkum et al., 1995) and Zazzo cancellation test (Zazzo 1964) (see **Supplementary Information SI1**). **Processing time**, reflecting both perception of visual geometric shapes and motor skills (see **Supplementary Information SI1**), was assessed with a fourth sheet included in the Picture Deletion Task for Preschoolers (PDTP; Corkum, Byrne, and Ellsworth 1995) as well as the Trail Making Test (TMT; Amieva et al. 2009). The classical TMT is not suitable for children aged 4 to 6 years as it requires basic skills such as number and letter recognition and literacy. For the current study, we thus adapted a version tailored to their age (**Supplementary Information SI4 and SI5**). This adapted TMT served both to assess processing time as stated above, but also cognitive **flexibility**. To assess **inhibitory functions**, we used a Stroop Test, which evaluates participants' inhibition, cognitive control and attention skills (Stroop 1935; Troyer, Leach, and Strauss 2006), and a Go/No-Go task (e.g. Swick, Ashley, and Turken 2011). We designed a children's Stroop in which the word and letter content was absent (see **Supplementary Information SI1 and SI6**), inspired by several bodies of work (Baron 2004, Monette and Bigras 2010, Okuzumi et al. 2015), and a Go/NoGo task based on colors (Durston et al. 2002, Kawashima et al. 1996, Konishi et al. 1998). Last, in order to assess the possible link with learning or emotional disorders in participants, we used a portion of the Weiss Symptom Record (WSR, Weiss 2010) and of the Achenbach System of Empirically Based Assessment (ASEBA, Achenbach and Rescorla 2000) questionnaires (see **Supplementary Information SI1**). The behavioral results for our adapted tests, TMT and Stroop, are presented in **Supplementary Results R1** and **Supplementary Figure S1**.

## Testing conditions

All tests were performed by a unique experimenter in the classroom setting, in the presence of the teacher, with the selected children seated at their usual desk. The familiar environment allowed the children to feel comfortable and helped alleviate stress. Testing was performed individually, so that there was no interference from peers. Tests were performed in the morning before the beginning of the daily school activities. For each child, testing was spread across two to three morning sessions, each session lasting between 30 and 40 minutes, with regular breaks, thus preventing fatigue and loss of concentration. Each class was assigned a single teacher, ensuring continuity and allowing for a strong teacher-child relationship to develop. Testing was performed five to six months after the start of the school year, so that teachers had already built an accurate representation of the children's behavior and abilities and a relation of trust had developed between the teachers and the children. In addition, this time lapse allowed the children to become fully accustomed to the classroom environment.

A second testing phase was organized two years later to assess the reliability of the mind wandering auto-evaluation. A secondary group of children (not included in the first phase) was tested in the same classroom conditions, only for the mind wandering auto-evaluation scale, as well as for the DDFS by the teacher. The original experimenter and a new experimenter tested the children with a cross-over design: they each tested half of the children first, and then retested the second half of the children two weeks later. This aimed to evaluate test-retest and inter-rater reliability. The teachers of the children also filled the DDFS questionnaire. This phase occurred nine months after the start of the school year.
# Statistical analyses

All statistical analyses and figures were performed with R (v4.4.1; R Core Team 2024; see **Supplementary Information SI7** for complete reporting on the packages used) and Matlab (MATLAB version: 9.13.0 R2022b, Natick, Massachusetts: The MathWorks Inc.; 2022). To compare scores or response times in different tests or between different age groups, we used the following non-parametric tests: Wilcoxon tests when comparing two conditions and Kruskal-Wallis tests when comparing three or more categories, followed by Dunn post-hoc pairwise comparisons adjusted for multiple comparisons. We tested the effect of sex by performing non-parametric two-way ANOVAs with age groups and sex as categorical factors (David Stern, 2023, https://www.mathworks.com/matlabcentral/fileexchange/44308-randanova2). We reported the p values or the adjusted p values when multiple comparisons were performed. To evaluate age as a continuous factor, or to correlate scores, response times or questionnaire outcomes between themselves, we first performed a Spearman correlation, and we reported the p value and the correlation coefficient (r). We then tested a linear fit or a second order polynomial fit to the data and reported the adjusted R². Inter-rater and test-retest reliability were evaluated using a weighted Cohen's kappa which accounts for the ordinal nature of the categories.

# Modeling

## Exploratory factor analysis

We applied an exploratory factor analysis (EFA) in order to identify the factor loadings of several indicators and what indicators grouped together. Considering the high degree of correlation between our indicators (see **Results** and **Supplementary Results R3, R4 and R5**), we used an oblique rotation (oblimin). We fixed the factor loading threshold at 0.7 based on the size of our population (N=60) (Stevens 2002). The results from this EFA, together with prior hypotheses from the literature, allowed us next to design models to fit on our data using structural equation modeling.

## Structural equation modeling

We used structural equation modeling to test whether mind wandering, attention, processing speed, flexibility and inhibition segregated into different latent variables or not and how they related to each other. We tested several models. Unless stated otherwise, we tested non-directional relationships between latent variables. Some yielded bad fit to the data and others yielded good fit to the data. While we discuss both types of models, we only present the good fitting models. For these, solid paths represent statistically significant paths (p< 0.05) and dotted lines represent statistically nonsignificant paths or high multicollinearity between predictors and indicators. The chi-square values, degrees of freedom, and chi-square significance are reported. The chi-square assesses overall fit and discrepancy between the covariance matrix implied by the model and the observed covariance matrix. A nonsignificant chi-square value, indicating that the model is not statistically different from a general population model, is preferred. However, this measure is very sensitive to sample size and degrees of freedom, and is based on assumptions that are rarely met in practice (Schermelleh-Engel, Moosbrugger, and Müller 2003). Thus other measures have to be used to decide on goodness of fit. These are the confirmatory fit indices (CFI; with a CFI above 0.9 models are considered acceptable; with a CFI above 0.95, or higher, models are considered a good fit; Hu and Bentler 1999) and the standardized root mean square residual (SRMR, with values below 0.08 considered as indicating a good fit, Hu and Bentler 1999). Any models that have poor model fit indicate that the model does not sufficiently approach the observed covariance matrix.
## Mind wandering can be auto-evaluated by preschoolers

To assess the validity of children's responses to the adapted DDFS auto-questionnaire, we performed a correlation between DDFS scores and the scores of the MWQ (Mind Wandering Questionnaire) completed by the teachers. As shown in **Figure 1A**, the two scores were significantly highly correlated (r=0.889, p<1e-20; linear regression: r²adj=0.787; polynomial regression: r²adj=0.785), showing that teachers and preschoolers evaluated similarly their level of mind wandering in the classroom. We also observed a significant correlation between DDFS and DDFS-t (filled out by teachers) scores (r=0.907, p<1e-22; linear regression: r²adj=0.820; polynomial regression: r²adj=0.819; **Figure 1B**). As observed in other studies in other age groups (e.g. Kawagoe, Onoda, and Yamaguchi 2020) there was a significant correlation between DDFS-t and MWQ scores (r=0.973, p<1e-38; linear regression: r²adj=0.946; polynomial regression: r²adj=0.948; **Supplementary Figure S2**).

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Auto evaluation DDFS (in %) as a function of (A) MWQ scores (in %) and (B) DDFS-t scores (in %). Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>

## Reliability of Mind wandering auto-evaluation in preschoolers

To assess the reliability of preschoolers' self-evaluation of mind wandering, we examined both inter-rater and test-retest consistency of DDFS scores across two different testing sessions and two independent experimenters, on an independent group of forty-five participants. As shown in Figure 2A and 2B, we reproduced the observations reported in **Figure 1B**. Indeed, we observed a significant correlation between DDFS and DDFS-t (filled out by teachers) scores both in the first testing session (r=0.771, p<1e-22; linear regression: r²adj=0.620; polynomial regression: r²adj=0.618; **Figure 2A**), and the second testing session (r=0.787, p<1e-22; linear regression: r²adj=0.595; polynomial regression: r²adj=0.588; **Figure 2B**). Test-retest reliability across sessions was highly significant (r=0.915, p<1e-22; linear regression: r²adj=0.838; polynomial regression: r²adj=0.842; **Figure 2C**). Agreement between the two ratings was almost perfect (weighted Cohen's kappa, κ = 0.90, 95% CI [0.84, 0.97]). This indicated a consistent self-report across time. Inter-rater reliability was also highly significant (r=0.899, p<1e-22; linear regression: r²adj=0.809; polynomial regression: r²adj=0.807; **Figure 2D**). Inter-rater agreement was almost perfect (weighted Cohen's kappa, κ = 0.90, 95% CI [0.84, 0.97]). These results indicate that preschoolers' self-evaluation of mind wandering is both stable over time and consistent across different raters.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Reliability of auto evaluation DDFS in an independent participant group. (A) Auto evaluation DDFS (in %) as a function of DDFS-t scores (in %), as in Figure 1B. (B) Auto evaluation DDFS (in %) during re-test as a function of DDFS-t scores (in %). (C) Auto evaluation DDFS (in %) during re-test as a function of DDFS scores during initial test (in %). (D) Auto evaluation DDFS (in %) by second tester as a function of DDFS scores by first tester (in %). Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>

Mind wandering decreases with age

We analyzed the effect of age on the scores of the self-assessed DDFS questionnaire. When considering three age groups, we obtained a significant effect of age groups (Kruskal-Wallis, p<1e-4), with the score of mind wandering (reflecting the propensity to mind wandering) decreasing with age (mean ± s.e.: four-year-olds: 4±0.15, five-year-olds: 3.8±0.16, six-year-olds: 3±0.13). Post-hoc Dunn comparisons showed that the six-year-old group was significantly different from the two other groups (four- vs six-year-olds: p<1e-4; five- vs six-year-olds: p<0.001; four- vs five-year-olds: p<0.05; Figure 3A). Sex had no effect on the DDFS scores (two-way ANOVA, main effect of age: p<1e-4, no effect of sex nor interaction). This decrease of DDFS scores with age was confirmed by a correlation analysis between the mind wandering scores and age in months (r=-0.498, p<1e-4; linear regression: r²<0.236; polynomial regression: r²<0.228; Figure 3B).

<figure><img src="image_6.png" /><figcaption>**Figure 3.** (A) Auto evaluation DDFS (in %) as a function of age groups. Violin plots: density curves of data distribution; individual data points; blue (red) point: mean (median). \*\*: p<0.01, \*\*\*: p<0.001. (B) Auto evaluation DDFS (in %) as a function of age (in months). Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>
As the DDFS scores were highly correlated to the other mind wandering questionnaire scores (MWQ and DDFS-t, see previous section, **Figure 1** and **Figure S2**), we found exactly the same relationship between MWQ and DDFS-t scores and age as described for DDFS (**supplementary Results R2, Figure S3**). In parallel, sustained attention and executive functions improved with age (**supplementary Results R2, Figure S4**).

## Wind wandering correlates with attentional functions, executive functions and measures of developmental and emotional difficulties

All the evaluated parameters were significantly correlated with age. However, we hypothesized that they might still be interrelated independently of age. To test this, we examined the relationship between mind wandering scores and attentional and executive parameters while controlling for age, using a stepwise multiple regression approach. We chose robust regression over ordinary least squares to reduce the potential impact of extreme values. We chose to focus on DDFS-t, which was correlated with DDFS, but provided a more fine-grained assessment of mind wandering. First, we tested how DDFS-t scores were correlated to attentional parameters, then to processing time parameters, then to flexibility parameters, then to inhibition parameters. Finally we kept all parameters with a significant or marginal impact on DDFS-t scores to conduct a global multilinear regression analysis. The same approach was also used for MWQ and PDTP attentional scores (**Supplementary Results R3 and R4, Figure S5**).

For attention, we tested scores from the PDTP and Zazzo tests (SA: PDTP combined sustained attentional score, Zazzo\_E1 and \_E2: efficiency on sheets 1 and 2). We observed a significant multilinear regression (pseudo r²<sub>adj</sub>=0.935, likelihood ratio test, p<1e-15) between DDFS-t scores and attentional parameters, with a significant impact of SA (p<0.0001) and Zazzo\_E2 (p<0.05). For processing time, we tested processing time (PT) measured in PDTP and execution times of TMTA and TMTB. We observed a significant multilinear regression (pseudo r²<sub>adj</sub>=0.672, p<1e-12) between DDFS-t scores and processing time parameters, with a marginally significant effect of TMTA only (p=0.088). For flexibility, we tested several parameters extracted from the TMT test (TMTB – TMTA time, number of errors in TMTA and TMTB). We observed a significant multilinear regression (pseudo r²<sub>adj</sub>=0.427, p<1e-6) between DDFS-t scores and flexibility parameters, with a significant effect of TMTB-TMTA time only (p<0.0005). For inhibition, we tested several parameters extracted from the Stroop and Go/NoGo tests (Stroop: ST4E number of errors for ST4, SIE Stroop interference index for error rates between ST3 and ST4; Go/NoGo: number of FA false alarms and of TE total errors). We observed a significant multilinear regression (pseudo r²<sub>adj</sub>=0.806, p<1e-15) between DDFS-t scores and inhibition parameters, with a significant effect of both Go/NoGo parameters (FA: p<0.0001, TE: p<1e-15). The global multilinear regression analysis thus included the following parameters: SA, Zazzo\_E2, PT, TMTB-TMTA, ST4E, Go/NoGo\_FA, and Go/NoGo\_TE. This analysis was significant (r²<sub>adj</sub>=0.924, p<1e-15), revealing a significant effect of SA (p<1e-15) and TMTB-TMTA time (p=0.026) and marginally significant effect of PT (p=0.078), but not inhibition parameters, on DDFS-t scores. These relationships are illustrated in **Figure 4**.

As some socio-emotional difficulties are usually reported as associated with attentional troubles (see also **Supplementary Results R3, Figure S6**), we tested the association between mind wandering and some of these difficulties evaluated thanks to WSR and ASEBA questionnaires. We found that mind wandering was positively correlated with anxiety, sadness, and sleep problems (see **Supplementary Results R5, Figure S6**).
<figure><img src="image_7.png" /><figcaption>**Figure 4.** (A) Sustained attention SA performance (in %) as a function of DDFS-t scores (in %). (B) Processing time PT (in %) as a function of DDFS-t scores (in %). (C) TMTB-TMTA time (in s) as a function of DDFS-t scores (in %). (D) ST4E (in %) as a function of DDFS-t scores (in %). Note that while the linear and polynomial regressions between ST4E and DDFS-t are significant when tested alone, ST4E effect is not significant when tested in the multilinear regression analyses. (E) Go/NoGo false alarms (in absolute number) as a function of DDFS-t scores (in %). (F) Go/NoGo total errors (in absolute number) as a function of DDFS-t scores (in %). For all panels: Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>

Mind wandering is independent from attention and inhibition in a model of latent functions

Exploratory factor analysis

In older children and adults, sustained attention, processing speed, flexibility and inhibitory functions
are considered independent though inter-related functions. In preschoolers, some studies have
described less differentiation between functions. As our multilinear regression analysis revealed
mainly a functional relationship between MW and sustained attention, we questioned how this
relationship fitted within a larger model of cognitive organization. With the goal of describing the
functional relationship between MW and all the cognitive functions assessed in the current study, we
decided to run an exploratory factor analysis (EFA). As a first step toward a Structural Equation
Modeling (SEM), we chose a minimum of 3 parameters describing each a priori defined function (based
on the use of each test in the literature). We thus chose the following variables: for mind wandering
DDFS, DDFS-t, and MWQ scores; for attention SA, Zazzo_E1, Zazzo_E2; for processing speed PT,
Zazzo_T1, Zazzo_T2, and Go/NoGo_T; for flexibility TMTAE, TMTBE, TMTB-TMTA time; and for
inhibition ST3E, ST4E, Go/NoGo_FA, Go/NoGo_TE. We used principal axis factoring with an oblimin
rotation with a maximal number of factors of 10 (correlations are described in **Supplementary Table
ST1**). Four factors were sufficient to explain a proportion of 0.9 of the total variance. A first factor
grouped DDFS, DDFS-t, and MWQ at one extreme and SA, Zazzo_E1, and Zazzo_E2 at the other
extreme. A second factor grouped all the timing measures that we a priori described under the
processing speed label (PT, Zazzo_T1, Zazzo_T2, Go/NoGo_T). A third factor grouped errors from the TMT and Stroop tests (TMTAE, TMTBE, ST3E, ST4E) that we a priori described as either reflecting flexibility or inhibition. A fourth factor corresponded to the Go/NoGo_FA. Two parameters did not load efficiently on these factors: TMTB-TMTA time, which loaded mostly (0.51) on the processing time factor, and Go/NoGo_TE, which loaded mostly (0.50) with Go/NoGo_FA. Factor loadings are described in **Supplementary Table ST2**.

Structural equation modeling

In order to further investigate the relationship between mind wandering, attention, processing speed, flexibility and inhibition in preschoolers, we applied structural equation modeling. Such latent analyses require multiple indicators per factor. Based on EFA, we settled on the following indicators: for the factor "Mind Wandering" DDFS, DDFS-t and MWQ; for the factor "Attention" SA, Zazzo_E1 and Zazzo_E2; for the factor "Speed" the three highest loadings in the EFA, i.e. PT, Zazzo_T1 and Zazzo_T2; then based on the EFA we grouped TMTAE, ST3E and ST4E under a factor labelled "Flexibility"; finally we kept only Go/NoGo_FA for the factor "Inhibition" (less than three indicators per factor can be used if the loading if very strong, as it is the case in our results where the inhibition latent variable is entirely described by Go/NoGo_FA). In all our models, "Age" (in months) was considered as an exogenous variable.

In a first step, we investigated a structural model testing the relationship between Age, Attention, Speed, Flexibility and Inhibition without considering Mind Wandering. Based on the literature, we tested the following models: 1) a unitary model postulating the cognitive functions considered as best modeled as a unique latent variable in preschoolers (e.g. Wiebe et al. 2008); 2) a model proposing the existence of an attentional latent variable and a unique EF latent variable (e.g. Steele et al. 2012); and 3) a model proposing, as in older children (e.g. Friedman and Miyake 2004), that all the functions considered represent separate but correlated latent variables. Moreover, as the definition of processing speed as a cognitive function has been discussed, we tested two additional models: 4) a model considering processing speed as included in the attentional functions (e.g. Robertson et al. 1997); 5) a model in which speed is considered as an exogenous factor influencing all the variables (e.g. Huizinga et al. 2006). Model 1 resulted in a poor fit of the data ($\chi^2(44) = 590.0, p<1e-4, SRMR = 0.21, CFI = 0.76$), as did Model 2 ($\chi^2(42) = 302.2, p<1e-4, SRMR = 0.2, CFI = 0.5$). In contrast, Model 3 testing the existence of four latent variables defined by Attention, Speed, Flexibility and Inhibition resulted in a good fit of the data ($\chi^2(36) = 82.7, p<1e-4, SRMR = 0.04, CFI = 0.96$, **Supplementary Figure S7**). All indicators had very strong loadings on the latent variables. Age was correlated to all four variables. Attention and Speed were influencing each other much more than any variables, especially Flexibility. Models 4 and 5 yielded less good fits of the data (Model 4: $\chi^2(40) = 398.2, p<1e-4, SRMR = 0.11, CFI = 0.67$; Model 4: $\chi^2(39) = 111.9, p<1e-4, SRMR = 0.13, CFI = 0.93$).
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Structural equation model showing latent variables for attention (Att), mind wandering (MW), processing speed (Spd), flexibility (Flx) and inhibition (Inh). Standardized regression weights and covariance estimates are presented on the corresponding links. Continuous arrows indicate significant links.</figcaption></figure>

In a second step, we investigated how the introduction of the mind wandering indicators impacted this latter model. Based on the EFA, we tested two models: A) a model in which mind wandering indicators were grouped with attention indicators (as they loaded on the same factor but on the opposite extremes); and B) a model in which mind wandering was considered as a separable latent variable. Model A yielded a good fit of the data but did not reach statistical thresholds for model acceptance ($\chi^2(69) = 172, p<1e-4$, SRMR = 0.03, CFI = 0.93), whereas Model B resulted in a better fit of the data ($\chi^2(64) = 127.2, p<1e-4$, SRMR = 0.03, CFI = 0.96, **Figure 5**). This thus suggests that in preschoolers, attention, mind wandering, processing speed, flexibility and inhibition are implemented by distinct though interacting cognitive functions. All indicators had very strong loadings on the latent factors. Age mainly influenced attention and mind wandering. As already observed with the EFA, attention and mind wandering were very highly correlated, while flexibility and inhibition were less correlated to the other variables.

To explore even further the link between attention and mind wandering, we compared models (considering only attention and mind wandering indicators) with bidirectional relationship or unilateral relationships between the two variables. While all models yielded excellent fits of the data, the best one was the one in which mind wandering unilaterally influenced attention ($\chi^2(13) = 19.4, p=0.11$, SRMR = 0.01, CFI = 0.99).
## Mind Wandering in preschoolers

In this study, we demonstrated that a newly constructed scale, modeled after the Daydream Frequency Scale (DDFS, Stawarczyk et al. 2012), could be used to measure Mind Wandering (MW) in children between the ages of four and six years. The scale was tailored to the cognitive and language capacities of the children. Our results showed a robust association between its scores and those of the two other mind wandering scales completed by the teachers of the children. In addition, these results showed a strong inter-rater and test-retest stability, as assessed by a specific replication experiment addressing these two points. This indicates that preschoolers' self-reports of mind wandering are not only meaningfully related to teacher observations but are also reproducible over time and consistent across evaluators. Together, these findings suggest empirical validity and reliability of the proposed mind wandering scale.

As MW has been observed in all the populations studied to date (i.e. over six years before the current study), we had no assumption about an absence of MW in preschoolers. The challenge in this population pertained to the ability to estimate the degree of MW. Indeed, the ability to report MW requires the capacity to form judgments about one's own mental activity (metacognition; e.g. Veenman, Van Hout-Wolters, and Afflerbach 2006). Several studies have suggested that this ability emerges around four or five years old (Flavell, Green, and Flavell 1993, Flavell 2000, Wellman and Liu 2004), but only fully mature around eight years of age (Flavell, Green, and Flavell 1993, Flavell 2000). However, other authors have suggested that metacognitive abilities in preschoolers may have been underestimated due to difficulties in verbalization and load on working memory, and would be more easily observed in natural settings (see for review Misailidi 2010, Whitebread et al. 2009). Our successful assessment of MW in preschoolers may thus be the result of a combination of facilitating factors: 1) the assessment was done in the familiar environment of the classroom; 2) verbal responses were not required (children had to point towards their auto-assessed level of MW, after the experimenter had confirmed their understanding of the task); and 3) unlike the experiments of Flavell's team (e.g. 1993, 2000) in which children had to evaluate their own or someone else's stream of thoughts during a particular experimental period, children had to evaluate their general tendency toward MW in the classroom. Although their assessment was highly correlated with that of their teacher, we cannot ensure whether they based their auto-evaluation on a specific memory, a specific period in time or whether they indeed assessed their overall behavior in the classroom.

While the correlation between the teachers' and children's evaluations was robust, several considerations have to be kept in mind. MW has been defined as a mental state in which thoughts are no longer focused on the current task but turn towards internal goals (Smallwood and Schooler 2006, Smallwood and Schooler 2015), automatically or voluntarily (Seli, Carriere, and Smilek 2015). The reason why questionnaires or thought sampling protocols have been developed is precisely because it is difficult for an external observer to characterize the mind wandering episodes of someone else (Smallwood and Schooler 2015). We would like to argue that this limitation does not apply to preschoolers, as they are prompt to distractibility, and have a low level of self-regulation (Rothbart, Posner, and Kieras 2006; Rothbart, Sheese, and Posner 2007). As a result, they exhibit a wide range of behaviors that could reflect their mental states or focus of interest. Some authors have proposed that, in preschoolers, self-regulation and metacognition abilities can be evaluated through observation (Whitebread et al. 2009). This would account for the precise assessment of preschoolers MW by their teachers, as well as for the high correlation between these MW scores and the teachers' assessment of the kids' anxiety and sadness. This however also raises the question of the difference between mind
wandering and distractibility, as least in young children, even if in the present study the teachers were briefed in order to distinguish the concepts of mind wandering and inattention. While many authors suggest that MW is functionally distinct from external distraction (though correlated to it, e.g. Unsworth and McMillan 2014), other authors propose that both MW and distractibility reflect lapses of attention and thus a failure of executive attention (McVay and Kane 2010b).

The estimation of the degree of MW is very variable across studies (e.g. Killingsworth and Gilbert 2010, Lindquist and McLean 2011, Keulers and Jonkman 2019, Cherry, McCormack, and Graham 2022), probably depending on the nature of the assessment (questionnaire or sampling) and the context (laboratory or classroom), and the relationship between MW and age has not been systematically explored. This is discussed in **Supplementary Discussion D1**. Many studies have tried to model latent functions to describe executive or attentional functions, and their development. Our study focused on MW and did not aim at confirming or disclaiming previous models. How our observations relate to previous literature on this topic is discussed in **Supplementary Discussion D2**.

**Mind wandering is an independent function strongly related to attention**

While several hypotheses have been proposed to account for mind wandering, Smallwood et al. (2013) mainly propose an involvement of sustained attention and/or executive/attention/cognitive control. In order to address this point in preschoolers, we performed a series of analyses informing on how mind wandering articulated with sustained attention. The regression analyses were used to explore associative patterns between MW and individual cognitive domains. We observed that our MW scores significantly correlated with all our other measures (attention, processing speed, flexibility and inhibition), showing that less MW was associated with better performance (Randall, Oswald, and Beier 2014), even if the correlation with attention was the strongest. While these findings showed strong linear relationships, particularly between MW and attention measures, but they did not account for shared variance or measurement error across constructs. The EFA served as a data-driven step to investigate how observed variables clustered together. It thus provided a first approximation of the underlying factor structure without assuming predefined relationships. EFA indicated that MW and attention indicators loaded on the same factor, but at opposite ends—suggesting a close yet distinct relationship. While regression and EFA both suggested a close relationship between mind wandering and attention, only SEM allowed us to test whether these constructs should be modeled as distinct latent variables while accounting for measurement error. Our SEM modeling showing a very strong link between attention and MW. However, attention and MW were still best modeled as independent factors, as observed by Kane et al. (2016) in adults. The specific relationship between MW and attention could be modeled with very good fits either by a bidirectional link, or unidirectional links, the best model being MW influencing attention. This result is surprising as theories about MW usually propose that MW is the result of an executive or attentional control failure, thus favoring a theoretical unilateral link from attention towards MW (Unworth et al. 2012). One hypothesis is that, considering the large amount of MW described in preschoolers, MW is a limiting factor for all cognitive abilities in young children, and that this functional relationship shifts with age and the development of attentional abilities.

The link between MW and inhibition or flexibility, described in adults (Unsworth, Robison, and Miller 2021, Kane et al. 2016) and children (Keulers and Jonkman 2019), was weak in our model. One should note, however, that further exploring the link between MW and other attentional and executive functions would require an evaluation of MW during the execution of a task, with thought probes (Marcusson-Clavertz et al. 2022, Robison, Miller, and Unsworth 2020), which seems unrealistic in preschoolers with regards to their metacognitive abilities (Flavell 2000). Another approach to better
understand the functional relationships between MW, attention and EF in preschoolers would be to use neurophysiological or neuroimaging techniques, in particular to assess the functioning of the Default Mode Network (DMN), frontal, and parietal regions (Fox et al. 2015). Interestingly, in preschoolers, Quiñones-Camacho et al. (2019) have demonstrated that performance in cognitive flexibility and attentional focus was associated with a more efficient functioning of the prefrontal cortex. Another theory about MW is that it occurs more in individuals with lower metacognitive capacity (Smallwood 2013, Drescher, Van Den Bussche, and Desender 2018), which would fit with the decrease of MW with age in our results. However, as most cognitive abilities increase with metacognition and thus with age (e.g. Perner and Lang 1999), our data cannot directly address this hypothesis.

## Mind wandering and individual traits

Mind wandering has been associated with several disorders, and in particular Attention Deficit/Hyperactivity Disorder (ADHD; Frick, Asherson, and Brocki 2020, Lanier, Noyes, and Biederman 2021, Seli et al. 2015), but also dysphoria (Smallwood et al. 2007), depression and anxiety (Figueiredo et al. 2020, Seli et al. 2019, Yip, Jodoin, and Handy 2023). We chose to use part of the WSR (Weiss 2010) and the ASEBA (Achenbach and Rescorla 2000) questionnaires, not as diagnostic tools but to evaluate individual traits that might be linked to MW. A link between MW and anxiety, sadness and sleep difficulties, evaluated by the teachers and parents, was present. The triad anxiety, depression, sleep has been frequently described, even in non-clinical populations of children and adolescents (Alfano et al. 2008). MW has already been associated with anxiety (independently of ADHD, Figueiredo et al. 2020), sleep (Spruyt et al. 2019), sadness (Smallwood et al. 2007), and low mood (Teague et al. 2025), and our results extend these findings in preschoolers.

Our MW measure in preschoolers thus seems to reflect several individual traits and may be predictive of attentional, executive, and more generally educational outcomes. It would be interesting to explore further the temperament of these children, as temperamental effortful control (or self-regulation, Rothbart, Sheese, and Posner 2007) has been associated with lower MW, more cognitive flexibility, and better educational outcomes (Pereira, Gurguryan, and Ristic 2020, Quiñones-Camacho et al. 2019). In addition, the relationship between MW and individual traits in preschoolers is unexpectedly similar to that observed in older children, adolescents and adults, suggesting that very early self-regulation deficits may impact cognition at all stages of life.

## Limitations of the study

A relevant concern is whether DDFS self-reports reflect a genuine introspective assessment, or whether they may be influenced by other sources of variability—such as developmental differences in how children use rating scales. Prior research has shown that younger children tend to favor extreme scale values, potentially due to a still-developing understanding of gradation (Bishop & Martin, 1984, Chambers & Johnston, 2002). Figure 2A shows that four- and five-year-olds more frequently used the higher end of the scale (e.g., 4 and 5), while six-year-olds tended to avoid both extremes. This may reflect increasing cognitive maturity and a more nuanced understanding of intermediate options in the older children. Consequently, age-related differences in DDFS scores may partly reflect developmental changes in scale use, rather than pure differences in mind wandering *per se*. However, given the strong correlation between the DDFS self-reports and the teachers' independent assessments of MW, as well as the careful efforts made to ensure children understood the scale, we argue that DDFS scores still meaningfully reflect true variation in mind wandering propensity. Nonetheless, further experimental validation would help disentangle scale use tendencies from underlying cognitive constructs.
On another note, we report correlations between 0.889 and 0.907 between the self-reported mind wandering in preschoolers and the evaluations by the teachers (MWQ and DDFS-t respectively). In a second group of participants, correlations with DDFS-t in the test and retest phases remained strong (r = 0.771 and 0.781), providing also evidence for temporal stability. Although studies in older children (e.g., Keulers & Jonkman, 2019) report strong associations between self-reported measures and behavioral mind-wandering measures, comparable child-teacher correlation coefficients as we reported (r = 0.77-0.91) have not previously been documented in preschool samples. Our observations thus represent a novel and unusually high degree of agreement between preschool self-reports and teacher evaluations, given the young age of the participants and the metacognitive demands of self-reporting internal states. These patterns were consistently observed across three different self-assessments, in two independent groups of children and with two different raters, providing preliminary evidence for the reliability of the measure. One factor that may have contributed to this consistency is the use of a simplified 5-point visual scale with concrete, age-appropriate illustrations, which likely enhanced comprehension and reduced cognitive load and response noise. This format allowed children to relate to the scenarios presented and may have encouraged more reflective and accurate responses. The surprisingly high correlations may also reflect the strong teacher-child relationships established over the 5-6 months observation period. Given the daily contact in a familiar setting, teachers likely had a robust sense of each child's mind wandering patterns, which may have contributed to the convergence in ratings. Whether such high correlations would generalize to older children is an open question. While older children typically have more developed metacognitive skills and could arguably provide more precise self-evaluations, the match with teacher ratings may not necessarily improve. Older children may engage in more covert or internally regulated mind wandering, which may be harder for teachers to observe. Therefore, while self-reports may become more accurate with age, teacher reports might not track them as closely, potentially leading to lower correlations. Further studies are needed to compare the alignment between self- and teacher-reports across developmental stages using consistent measurement tools.

Last, while the SEM showed excellent fit indices, we recognize that the modest sample size (N = 60) limits the generalizability of the findings. However, our model involved a limited number of latent variables with strong indicator loadings (all > 0.7) and minimal model complexity, conditions under which SEM can produce robust and interpretable results even in smaller samples (Boomsma, 1985). Monte Carlo simulation studies have demonstrated that, for models with well-defined factors and strong loadings, adequate parameter recovery and model fit indices can be achieved with samples as small as N = 50-100 (Marsh et al., 2004; Wolf et al., 2013). Still, we acknowledge that these results should be interpreted with caution and considered exploratory. Replication in larger and more diverse samples is essential to confirm the stability and generalizability of our findings.

## Conclusion

To conclude, we have shown that mind wandering can be self-assessed in preschoolers, even if we obtain a rather coarse score that might also reflect distractibility. This measure constitutes a factor independent from attention and executive processes, but very highly linked to the children's attentional abilities. This suggests that during childhood, while all attentional and executive functions mature and are correlated, attentional maturation may be at the core of the child's development, both in terms of cerebral functioning, behavioral repertoire and propensity to mind wandering.
## Ethical considerations

This study was performed in school settings, with the formal agreement of school directors. Informed consent was obtained from parents and children.

### KEY POINTS

* Mind wandering has been associated with attentional and executive function deficits in children above eight years old and adults as well as with negative educational outcomes

* Mind wandering and how it interacts with attention in preschoolers has scarcely been studied

* We develop and evaluate an auto-evaluation test of mind wandering in preschoolers and we show that mind wandering scores correlated with the children's sustained attention, processing speed and cognitive flexibility and inhibition

* We show that mind wandering can be modeled by a latent factor independent from attention, processing speed, flexibility and inhibition, but very highly linked to attention

* This underscores the clinical and educational importance of enhancing the attentional function in preschoolers

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# SUPPLEMENTARY INFORMATION

## Supplementary Information SI1

### Tests and questionnaires

#### Assessment of mind wandering

Mind wandering can be evaluated via questionnaires. However, the existing questionnaires were designed for children eight years old or older (Cognitive Experience Questionnaire from eight years old (Mrazek et al. 2013); Mind Wandering Questionnaire for Children for children aged nine and older, (Creswell, O'Connor, and Brewin 2006); Control of Attention and Wandering Questionnaire for Children starting from 10-12 years old, (Ye et al. 2014); Children's Wandering Mind Questionnaire for eight years old and older (Luo et al. 2016). To assess mind wandering in the current study, we developed a questionnaire adapted from the Daydream Frequency Scale (DDFS, Stawarczyk et al. 2012; see **Supplementary Information SI2**). It consisted in a self-assessment of mind wandering with a single straightforward question directly asked to the child: "Where do you see yourself in the classroom?" Two arrows presented the possible visual choices: one depicted a student in a classroom, attentive to the teacher's words, while the other showed the same student, still in the classroom, with multiple thoughts represented by various icons in a speech bubble: a cat, parents, home, candies, outdoor
games – unrelated to the subject being taught. The child had to choose one of five levels under each picture along a gradient of green, going from "Never" corresponding to the lightest green, to "Almost Never," "Sometimes," "Frequently," and "Always" for the darkest green. The questionnaire was presented orally by the experimenter who explained the quotation and read the words to the child. The experimenter made sure the child understood by following several steps. First, the experimenter initiated a familiarization phase using a scale made of filled circles. The child gradually discovered that these circles represented different levels of quantity/frequency, ranging from an empty circle (‘never’) to a fully filled circle (‘always’). The experimenter provided concrete examples, such as scenarios about their snack or a game during class, to illustrate each level of filling. The experimenter used sentences like: "Look at these circles. Some are empty, some are partially filled, and others are completely filled. They help us understand how often something happens to you." Then the experimenter tested the understanding of the child with the following instructions: "Show me the circle that means this never happens to you. And now, the one that means it happens to you all the time?". If the child had difficulties, the experimenter reformulated and provided simple situations to anchor their understanding of the scale. Once the child demonstrated an understanding of the circle concept and could associate a level of filling with their experience, the experimenter proceeded to the actual test administration phase. After description of the pictures, the experimenter used sentences like "When you are in the classroom and listening to your teacher, do you sometimes think about something else, like your next snack or a cartoon?" and checked again the understanding of the "never" to "always" scale (e.g. "If this happens sometimes, which circle would you choose?"). In case of difficulties, the experimenter again probed the child with examples ("Does it happen as often as eating lunch?", "Does it happen more often than watching a cartoon?", "If I tell you to imagine a pink elephant right now, do you manage to stay focused on the elephant or do you think about something else right away?"). The detailed scenario followed by the experimenter is presented in **Supplementary Information SI3**. To enhance identification to the scale pictures, we provided separate versions for boys and girls. The scale went from 1 to 5, where 1 corresponds to "Never" and 5 corresponds to "Always". The highest values thus correspond to the highest mind wandering behavior. To be more easily compared to other scores, the DDFS raw scores were transformed in %.

In order to evaluate the responses to our adapted DDFS, we asked the teachers to fill out both the classical DDFS (which is an auto-questionnaire in older participants) and the Mind Wandering Questionnaire (MWQ, Mrazek et al. 2013) for all children. The DDFS (noted DDFS-t in this paper for DDFS-teacher) consisted in 12 statements on daydreaming for which the teacher had to choose between five levels of frequency. The MWQ consisted in five statements for which the teacher had to choose between "Never," "Rarely," "Sometimes," "Regularly," "Frequently," or "Always." These statements addressed various aspects of the children's ability to maintain attention: their ability to stay focused on simple or repetitive tasks, to follow the storyline of a read story in class, to engage in activities with full attention, to listen without being distracted by other thoughts, and to reduce instances of mind wandering during class periods. To ensure at best that the teachers' evaluations were based on the same cues for all the teachers, and that they evaluated MW and not inattention in their pupils, a training session was organized with neuropsychologists several months before data collection. During this session, the experimenter and neuropsychologists explained the concepts of MW and inattention. They used concrete examples and real-life situations to demonstrate the difference between a pupil whose mind wanders, one who is distracted by external events, and one who maintains sustained attention. They illustrated these situations with videos. Then, they detailed the scoring levels used in the questionnaires, through practical cases and concrete examples, but without referring to the exact items of the questionnaires. Two observation sheets were submitted to the teachers to distinguish the observation cues they could associate with inattention and MW. For inattention, the following items were listed: The child 1) seems easily distracted by external stimuli
(noise, movement, objects); 2) quickly loses interest in the ongoing task and turns to another activity; 3) interrupts work to talk to peers; 4) does not pay attention to details or makes inattention errors in schoolwork; 5) has difficulty remaining seated or moves constantly in the chair; 6) often leaves work unfinished because he/she moves on to other things before completion; 7) frequently loses school materials (pencils, notebook, eraser); 8) has difficulty concentrating on a long task without constant supervision. For MW, the following items were listed: The child 1) stares into space without interacting with the task; 2) loses track of what they were doing and seems elsewhere; 3) reacts late to instructions or seems surprised when spoken to; 4) interrupts work to talk about an unrelated subject; 5) plays with hands, clothes or other objects in the middle of an activity; 6) frequently changes subject in conversations with others; 7) appears to dream or tell imaginary stories in class; 8) has difficulty explaining what they were doing. This training session with the teachers occurred at the beginning of the school year, after ethical agreement of the school and the teachers. The actual filling of the DDFS-t and MWQ questionnaires was done at the same time as the children's testing, i.e. around 5 to 6 months after, allowing for the teachers to become acquainted with the children and their behavior in the classroom. The DDFS-t and MWQ raw scores were transformed in %, the highest scores corresponding to children exhibiting the highest level of mind wandering.

## Assessment of attentional functions

We used the Picture Deletion Task for Preschoolers (PDTP; Corkum & al., 1995) to evaluate selective and sustained attention (SA) in our participants. This paper-and-pencil test consists of three A4-sized sheets to be completed as quickly as possible, presented in a specific order ranging from the least difficult to the most difficult. The first sheet presented a series of geometric shapes, and the child had to cross out only the triangles (SA triangle). The second sheet featured images of cats in different positions (SA cat). The child had to cross out only the cats identical to the target image. The third sheet displayed images of fish oriented in different ways, and the child had to cross out only the fish identical to the target image (SA fish). At each stage, we recorded the time taken to complete the sheet, the number of correctly identified targets, and the number of false alarms. To reduce the number of measures described in the article, we computed the mean performance for the three sheets, expressed in % and noted AS for attention score.

We also used Zazzo cancellation test (Zazzo 1964), evaluating selective and sustained attention. This paper-and-pencil test consists of two A4-sized sheets each displaying 25 lines and 40 columns of symbols (squares with a slash) for which participants had to cross out the maximum of target symbols in 10 minutes. In the first sheet, one symbol (square with 45° upperleft slash) had to be crossed out. In the second sheet, two symbols (square with 45° upperleft slash and square with 90° right slash) had to be crossed out. Several measures were computed, and in particular: the time to complete sheets 1 and 2 (T1, T2), and one measure of performance for both sheets (efficiency of correctly crossing targets minus errors per minute, E1, E2). These scores were used in the exploratory factorial analysis and in the structural equation modeling.

## Assessment of executive functions – processing speed and cognitive flexibility

Processing time, reflecting both perception of visual geometric shapes and motor skills, was first assessed with a fourth sheet included in the Picture Deletion Task for Preschoolers (PDTP; Corkum, Byrne, and Ellsworth 1995). This sheet contained only circles to be crossed out. We measured the time necessary to cross all the circles (completion time) in seconds, and named it processing time (PT).

Second, processing speed was also assessed using an adapted version of the Trail Making Test (TMT; Amieva et al. 2009). The TMT is a paper-and-pencil test used to evaluate cognitive flexibility, executive
functions, and cognitive processing speed. It consists of two distinct parts. In Part A, participants are required to connect numbers in ascending order by drawing a continuous line. This task assesses their attention, concentration, and processing speed abilities. In Part B, participants must alternate between numbers and letters following an ascending sequence (1-A-2-B-3-C, and so on). This section evaluates mental flexibility, the ability to quickly shift attention, and inhibit automatic responses. TMT is not suitable for children aged four to six years as it requires basic skills such as number and letter recognition and literacy, which are not fully developed at this age. For the current study, we thus adapted a version tailored to their age (Supplementary Information SI4 and SI5). In Part A, children were asked to connect nine frogs starting from the smallest one (indicated by an orange ellipse) and proceeding to the largest. The arrangement of the frogs closely followed the layout of the 25 numbers presented in the original TMTA, resulting in a similar path. For instance, transitioning from the seventh to the eighth frog required passing by the ninth – the largest one – without stopping, analogous to how an older participant would pass by the number 24 while moving from 22 to 23 in the classic TMT. In Part B, we instructed children to connect a frog to a water lily while respecting the ascending size criterion. They had to alternate between frogs and water lilies, as older participants had to alternate between letters and numbers in the classic TMTB, with a lower number of connections to draw (9 vs 23). The smallest frog, marking the starting point, was highlighted, and instructions were illustrated by a frog leaping onto a water lily of its same size. For each part, we recorded the completion time and the number of errors. To reduce the number of measures described in the article, we reported the completion times in seconds to index processing time (noted TMTA time and TMTB time), and the difference between these two times to assess cognitive flexibility (noted TMTB – TMTA). For the exploratory factorial analysis and the structural equation modelling, we also considered the error rates (noted TMTAE and TMTBE).

## Assessment of executive functions – inhibitory functions

The Stroop Test assesses participants' inhibition, cognitive control and attention skills (Stroop 1935; Troyer, Leach, and Strauss 2006). This assessment is based on the Stroop effect, which refers to the interference caused by irrelevant information during the execution of a cognitive task. The test consists of four stages, spread across four A4-sized sheets, with each stage lasting 45 seconds (Golden 1981). The classic Stroop Test uses names of colors and letters written in different colors. To design the Children's Stroop, we drew inspiration from the works of (Baron 2004, Monette and Bigras 2010, Okuzumi et al. 2015) (Supplementary Information SI6) in which the word and letter content was absent. The first subtest (Stroop I – Colors, noted ST1) presented a series of 20 colored squares in red or yellow, randomly arranged. Children were required to quickly name the colors of the squares. This stage evaluated the subject's color recognition. The second subtest (Stroop II - Colored Fruits, noted ST2) displayed a series of 20 fruits (lemons and tomatoes) in their original colors, also randomly arranged. Children had to name the fruits without being influenced by an unexpected color. The third subtest (Stroop III – Black and White Fruits, noted ST3) presented the same 20 fruits (lemons and tomatoes), but this time in black and white. Children were asked to provide the original color of each fruit (yellow or red), allowing the assessment of their prototypical knowledge of color-fruits associations. Finally, the fourth subtest (Stroop IV - Interference Fruits, noted ST4) featured 20 fruits with colors that did not match the expected ones (e.g., a red lemon or a yellow tomato). Participants had to name the actual color of each fruit in real life, measuring their inhibition capacity and resistance to interference effects. We recorded the number of correct elements identified by the participants within 45 seconds, as well as the number of instances when the child hesitated (such as starting one word but finishing with another word; "partial errors" deducting 0.5 point), along with the number of errors (incorrect pronunciation of a complete word; "total errors" deducting 1 point). To reduce the
number of measures described in the article, we will only report the % of errors made for each subtest (noted ST1E, ST2E, ST3E, and ST4E), and the classical SIE Stroop interference index for error rates between ST3 and ST4 for the multilinear regression analysis.

To further assess inhibitory functions we also designed a Go/NoGo task based on colors, inspired by the works of (Durston et al. 2002; Kawashima et al. 1996; Konishi et al. 1998). A total of 100 trials was presented on a computer screen: 70 Go trials in which two green triangles were presented side by side, and 30 NoGo trials in which a red triangle was presented with a green triangle (on the left or the right). In the Go trials, the participants had to press on the spacebar of the keyboard during the 2.5 s of the presentation. In the NoGo trials, the participants had to suppress any keypress and the next trial was presented after 2 s. We recorded the number of hits (correct keypress in a Go trial), correct rejections (no keypress in a NoGo trial), omissions (no keypress in a Go trial), false alarms (keypress in a NoGo trial; Go/NoGo_FA), total number of errors (Go/NoGo_TE), and total time of test completion; Go/NoGo_T. To reduce the number of measures described in the article, we will only use the total number of false alarms (Go/NoGo_FA) and the total number of errors (Go/NoGo_TE), and also the completion time (Go/NoGo_T) for the factorial analysis and the structural equation modelling.

## Assessment of developmental and emotional difficulties

In order to assess the possible presence of learning or emotional disorders in the children who participated in the present study, we used a portion of the Weiss Symptom Record (WSR, Weiss 2010) and of the Achenbach System of Empirically Based Assessment (ASEBA, Achenbach and Rescorla 2000) questionnaires. For the WSR, we selected seven specific sections: inattention, hyperactivity and impulsivity, learning disorders, motivation, anxiety, sadness, and sleep. The four first sections were evaluated by the teacher, the last three sections by the parents. Inattention, and hyperactivity and impulsivity, were assessed respectively with seven and eight statements, associated each with four possible responses: "No" (0 points), "Occasionally" (1), "Moderately" (2), "Frequently" (3). A total of 21 points (resp. 24) indicated the highest level of inattention (resp. hyperactivity). Learning disorders were evaluated with four items and four possible responses: "No" (0), "Mild" (1), "Moderate" (2), "Severe" (3), the highest score (12) reflecting high learning difficulties as compared to the overall typically developing population. Motivation was assessed through four statements, with three possible responses: "Very low" (1), "Moderate" (2), or "High" (3), the highest score (12) corresponding to the highest level of motivation. Parents assessed anxiety (nine statements), sadness (four statements), and sleep problems (six questions). For each item, response choices were: "No" (0 points), "Occasionally" (1), "Moderately" (2), "Frequently" (3), and the highest scores reflected a higher prevalence of these issues in the child. For the ASEBA, the teachers and parents were asked to evaluate several behaviors on a 5-level scale from "Never" (1 point) to "Always" (5). Only the responses pertaining to anxiety, sadness, and sleep problems are reported (the first two evaluated by the teacher for ASEBA and the parents for WSR, the last one only by the parents).
Supplementary Information SI2

Auto Mind Wandering Questionnaire for preschoolers aged 4 to 6 years old. (A) English version for boys. (B) English version for girls.

A

<figure><img src="image_9.png" /></figure>

B

<figure><img src="image_10.png" /></figure>

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# Supplementary Information SI3

## Scenario for Mind Wandering Evaluation in Preschoolers (translated from French)

General instructions for administrating the evaluation:

1. Strict adherence to the scenario: read each sentence/question word for word, without reformulation. In case of clear misunderstanding or if the child has his/her head in the clouds, a vague air, use the additional examples provided in the scenario.

2. Exclusive use of the visual circle scale, presented from left to right (empty / ¼ full / ½ full / ¾ full / full).

3. Appropriate physical positioning: sit at the child's level in a quiet environment, free from visual or auditory distractions.

4. Consistent tone of voice: warm, calm, never directive or didactic.

5. Neutrality in responses: never induce, suggest, or correct the child's answers. Use the written formulation, without leading.

6. Strict respect of the procedure: the steps of the protocol must be followed in the same order for all children, as well as the questions within each step. If you reach a STOP, then you stop the evaluation.

7. Controlled affective interaction: provide brief and consistent positive feedback without off-protocol chatter.

8. Management of difficulties: if the child struggles, interrupt the session. Never force participation.

## Steps of the scenario:

### 1. Confidence-building phase and familiarization with the circle scale

*Objective: Introduce the notion of frequency and ensure understanding of the measurement tool.*

Experimenter:

- "Hello! Today, we're going to play a little game where we talk about what's going on in your head when you're at school. Sometimes we listen well, and sometimes our head thinks about something else. Has this ever happened to you?"

*Wait for any coherent answer*

Presentation of the visual scale of circles (empty / ¼ full / ½ full / ¾ full / full):

*Put the paper scale on the table*

- "Look at these circles: this one is empty it means something that never happens to you; this one is a little full it means something that happens to you sometimes; this one is half full it means something average; this one is a lot full it means something that happens to you very often; this one is all full it means something that happens to you all the time."

- "Can you show me the circle that means 'it never happens to me'? "

*If response correct, go to next question. Otherwise re-present the scale and ask again the question. If still not correct, then STOP.*

- "And the one that means 'it happens to me all the time'?"

*If response correct, go to next question. Otherwise ask again the question. If still not correct, then STOP.*
Going to concrete examples:

- "If I tell you that you eat an icecream only once in a year, which circle would you choose"

If response correct (i.e. this rarely happens, second circle), go to next question. Otherwise use another question:

"Your birthday happens only one time in the year, which circle corresponds to your birthday?" or in the younger children to ensure understanding "When you have your own birthday cake, which circle would you choose?" If still not correct, then **STOP**.

- "And if you watch a cartoon everyday?"

If response correct (i.e. this always happens, fifth circle), go to next question. Otherwise use another question:

"Show me the circle that corresponds to when you brush your teeth everyday" or in the younger children "If I say to you, 'You eat a snack every day,' which circle shows that?" If still not correct, then **STOP**.

## 2. Introduction of mind wandering notion

Objective: Introduce the notion of thinking about something else

Experimenter:

- "When you eat your snack, do you often think about something else?" or for younger children "When you eat your snack, does your head think about anything else?"

Wait for any coherent answer

- "When you play your favorite game, do you often think about something else?" or for younger children "When you play with your toys, does your head think about anything else?"

Wait for any coherent answer

If the child is having trouble answering, suggest a pictorial situation:

- "Imagine you're thinking about a pink elephant! Does your mind (/head) stay on the elephant for a long time, or does it quickly think of something else?"

If the child still has difficulty (younger children), help with gestures or mime: "Look at me" You look at a fixed point and you say: "I look very much at the point, it's like when you listen carefully". Then you look everywhere around and you say: "And now it's like your head is thinking about something else". And then re-ask the question.

If not clear and engaged answer then **STOP**.

Check for internal coherence:

- "When you're drawing, do you often think about something else? (for younger children: /does your head think about anything else?)". Wait for any answer. Wait for 15-30 s without talking. "Do you stay focused when you're drawing? (for younger children: /does your head stay on your drawing when you're drawing?)". If answer does not correspond to the first answer, go again with the two questions but with "doing a puzzle" instead of drawing. If still not correct then **STOP**.
Correspondance between personal experience and the circle scale:

- "Tell me of something that you do very often?" *Wait for any answer.* "And show me the circle that corresponds?"

*If response correct, go to next question. Otherwise ask again the question. If still not correct, then STOP.*

**3. Analysis of trends and triggers**

*Objective: Identify the times when mind wandering is most common.*

Experimenter:

- "Let's talk about when you think about something else (*for younger children*: /when your head thinks about anything else). When does that happen to you more often?"

*Wait for any coherent answer*

- "Does it happen to you more often in the morning or afternoon?"

*Wait for any coherent answer*

*In case of clear misunderstanding or if the child has his/her head in the clouds or a vague air, associate with images of the morning (sun) and the afternoon (afternoon snack). "Show me the morning" Wait for correct pointing. "Show me the afternoon" Wait for correct pointing. If not correct **STOP**. If correct go back to the initial question with the help of the images.*

- "Does it happen to you more often after recess?"

*Wait for any coherent answer*

- "During which activity in class do you think about something else (*for younger children*: /does your head think about anything else) most?"

*Wait for any coherent answer. If no answer prompt with examples: "Story, drawing, exercise, song..."*

*Wait for any answer. If the child has his/her head in the clouds or a vague air, use an example: "When you're drawing, does your mind think about something else (*for younger children*: /does your head think about anything else) more often than when you're listening to a story?"*

*Wait for any coherent answer. If still vague/not engaged then **STOP**.*

**4. Question phase about time periods**

*Objective: Check whether mind wandering is stable or varies over time.*

Experimenter:

- "Now we're going to talk about several days. Do you remember what you did yesterday?"

*Wait for any coherent answer*

- "Do you remember what you did yesterday at school?"

*Wait for an answer compatible with activities at school. If not prompt "At school?". If answer not correct then **STOP**.*

- "Yesterday at school, did you happen to think about anything else (*for younger children*: /did your head think about anything else) during an activity?"

*Wait for any coherent answer*
- "And last week, when you were working in class, did you ever think about anything else (for younger children: /did your head think about anything else)?

*Wait for any coherent answer*

- "Since the start of the school year, how often have you had trouble concentrating?"

*This question is more abstract: if the child does not understand, suggest comparison* "Is it more often than you have your lunch everyday?". Or for younger children "Since school started, does your head often think about other things?" If the child does not understand, rephrase: "Since you came back to school after the vacations, has it happened to you a lot? A little? Never?"

*Wait for any coherent answer. If still vague, use examples to help him/her situate himself/herself in time:* "Do you remember when school started?" *Wait for any coherent answer.* "Since that day, do you often think about other things in class?" *Wait for any coherent answer.*

**5. Classroom situations**

*Objective: Identify specific classroom moments when mind wandering occurs*

Experimenter:

- "Now we're going to talk about what happens when you're in class with the teacher. When you're listening to a story the teacher is telling, do you ever think about anything else?" *or for younger children* "When the teacher tells a story, do you always listen, or does your head think about something else?"

*Wait for any coherent answer*

- "When you're doing an exercise with the teacher, do you ever think about something else, like your snack or a game?" *or for younger children* "When you're drawing a picture, does your head ever think about something else, like your snack or a game?"

*Wait for any coherent answer*

- "When the teacher is talking, do you ever think about playing outside?"

*Wait for an answer compatible with the two previous answers.* If not, then reengage: "Let's do a little test! Take a good look at me. Now think about your favorite snack. Are you still listening to me, or are you thinking about the snack?" *Observe reaction and if coherent then re-ask the three previous questions.* If still not coherent then **STOP**.

- "Can you show me on the circles how often it happens?"

*Check for consistent pointing on the circle scale.* If not correct then **STOP**. This is the last comprehension check before the actual evaluation on the MW scale.

**6. MW scale scoring**

*Put the color scale of the DDFS cartoon on the table above the circle scale and align the two scales so that the five levels match.*

Matching of the two scales:

- "You see this scale, this level corresponds to this circle, this one to this one..." *Show for the five levels/circles, from never to always.*

- "You see on this cartoon that the child is always concentrated on the activities and never thinks about anything else" *or for younger children:* "You see on this cartoon the child, his/her head is always listening to the teacher, is always doing his/her drawing, and his/her head never thinks about anything
else". Show the cartoon on the left. "And on this one he/she is always thinking about something else" or for younger children: "And on this one his/her head is always thinking about something else". Show the cartoon on the right.

- "Can you show me on the scale how often all this happens to you?"

Wait for a frank and direct pointing on the scale and note the score.

## 7. Acknowledgements

Experimenter:

- "Thank you so much for playing with me and answering my questions! You participated very well!"

- "Would you like a sticker or a little magic stamp on your hand?"
## Supplementary Information SI4

Adapted TMTA. Children were asked to connect nine frogs starting from the smallest one (indicated by a red contour) and proceeding to the largest.

### Adaptation du Trail Making Test pour les enfants de 3 à 6 ans
### Partie A

Code du sujet : __________

Ton objectif : relie les grenouilles de la plus petite à la plus grande.

<figure><img src="image_12.png" /></figure>
## Supplementary Information SI5

Adapted TMTB. Children were asked to connect alternatively frogs and water lilies with an ascending size criterion. They had to start from the smallest frog (indicated by a red contour), then the smallest water lily, then the second smallest frog, etc, until the largest water lily.

### Adaptation du Trail Making Test pour les enfants de 4 à 6 ans
### Partie B

Code du sujet : __________

**Ton objectif** : relie la grenouille au nénuphar en partant de la plus petite grenouille avec le plus petit nénuphar jusqu'à la plus grande grenouille avec le plus grand nénuphar.

<figure><img src="image_13.png" /></figure>
**Supplementary Information SI6**

Adapted Stroop test for inhibition in preschoolers aged 4 to 6 years old. (A) ST1. Instruction: from left to right, name as fast as possible the color of each square. (B) ST2. Instruction: from left to right, name as fast as possible the color of each fruit. (C) ST3. Instruction: from left to right, name as fast as possible the **real** color of each fruit. (D) ST4. Instruction: from left to right, name as fast as possible the **real** color of each fruit.

A

<figure><img src="image_14.png" /></figure>
B

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C

<figure><img src="image_35.png" /></figure>

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D

<figure><img src="image_55.png" /></figure>
Supplementary Information SI7

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- Dinno A (2024). `_dunn.test`: Dunn's Test of Multiple Comparisons Using Rank Sums_. R package version 1.3.6, <https://CRAN.R-project.org/package=dunn.test>.

- Elzhov TV, Mullen KM, Spiess A, Bolker B (2023). `_minpack.lm`: R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds_. R package version 1.2-4, <https://CRAN.R-project.org/package=minpack.lm>.

- Kassambara A (2023). `_rstatix`: Pipe-Friendly Framework for Basic Statistical Tests_. R package version 0.7.2, <https://CRAN.R-project.org/package=rstatix>.

- Kassambara A, Mundt F (2020). `_factoextra`: Extract and Visualize the Results of Multivariate Data Analyses_. R package version 1.0.7, <https://CRAN.R-project.org/package=factoextra>.

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- Pinheiro J, Bates D, R Core Team (2022). `_nlme`: Linear and Nonlinear Mixed Effects Models_. R package version 3.1-157, <https://CRAN.R-project.org/package=nlme>. Pinheiro JC, Bates DM (2000). `_Mixed-Effects Models in S and S-PLUS_`. Springer, New York. doi:10.1007/b98882 <https://doi.org/10.1007/b98882>.

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# Supplementary Results R1

## Adaptation of TMT evaluates different levels of cognitive flexibility in preschoolers

To assess our adapted TMT, we checked two aspects: first, we checked if part A of the adapted TMT reflected the processing speed ability, and second, we checked if part B of the adapted TMT was more difficult than part A, as it is supposed to require both mental flexibility and inhibition. The first aspect was assessed by correlating TMTA completion time with the processing time (PT) measured in the easy circles cancellation sheet of the PDTP. As illustrated in **Figure S1A**, we found a strong significant correlation between TMTA and PT (r=0.980, p<1e-41; linear regression: $r^2_{adj}=0.934$; polynomial regression: $r^2_{adj}=0.943$). For the second aspect, we directly compared the completion times of TMTA and TMTB. We found that a significantly higher time was necessary to complete the TMTB as compared to the TMTA (Wilcoxon test, p<1e-10), reflecting the higher difficulty of TMTB (**Figure S1B**).

## Adaptation of Stroop test evaluates increasing levels of inhibition in preschoolers

Several adaptations of the Stroop test with non-verbal material have been developed. In order to document that the adapted version we used respected the classical Stroop pattern, we directly compared the number of errors made in each of the four subtests designed to implement increasing levels of difficulty. We found a significant difference in the scores of the different Stroop subtests (Kruskal-Wallis, p<1e-10). Post-hoc Dunn pairwise comparisons revealed that significantly more errors were committed in subtest 4 (ST4) as compared to any of the other subtests (ST4 vs ST1: $p_{adj}<1e-9$; ST4 vs ST2: $p_{adj}<1e-7$; ST4 vs ST3: $p_{adj}<1e-5$; **Figure S1C**). The other subtests did not show any significant difference across pairs.
# Supplementary Results R2

## Mind wandering evaluated by the teachers decreases with age

The amount of mind wandering evaluated with the MWQ decreased with age (mean ± s.e.: four-year-olds: 73.71%±3.6, five-year-olds: 70.73%±3.8, six-year-olds: 49.67%±1.4; **Figure S3A**), with a significant effect of age groups (Kruskal-Wallis, p<1e-5), and the scores for the six-year-old group were significantly different from the other two groups (Dunn post-hoc: four- vs six-year-old: p$_{adj}$<1e-4; five-vs six-year-old: p$_{adj}$<1e-4; four- vs five-year-old: p$_{adj}$>0.05). Sex had no effect on the MWQ scores (two-way ANOVA, main effect of age: p<1e-5, no effect of sex nor interaction). A negative correlation between MWQ scores and age in months was observed (r=-0.583, p<1e-5; linear regression: r²$_{adj}$=0.328; polynomial regression: r²$_{adj}$=0.323; **Figure S3B**). Similarly, the amount of mind wandering evaluated with the DDFS-t significantly decreased with age (Kruskal-Wallis, p<1e-5; mean ± s.e.: four-year-old: 75.24%±3.6, five-year-old: 71.40%±3.8, six-year-old: 51.58%±1.5; **Figure S3C**) and the scores for the six-year-old group were significantly different from the other two groups (Dunn post-hoc: four-vs six-year-old: p$_{adj}$<1e-5; five-vs six-year-old: p$_{adj}$<1e-4; four-vs five-year-old: p$_{adj}$>0.05). Sex had no effect on the DDFS-t score (two-way ANOVA, main effect of age: p<1e-5, no effect of sex nor interaction). A negative correlation between DDFS-t scores and age in months was observed (r=-0.558, p<1e-5; linear regression: r²$_{adj}$=0.312; polynomial regression: r²$_{adj}$=0.308; **Figure S3D**).

## Sustained attention improves with age

We analyzed the performance on the PDTP in order to assess the evolution of sustained attention (SA) as a function of age. First, we considered the performance for the three age groups and observed a significant increase of performance with age (Kruskal-Wallis, p<1e-6; mean ± s.e.: four-year-olds: 57.24% ±3, five-year-olds: 59.92%±3, six-year-olds: 72.63%±1; **Figure S4A**). Post-hoc Dunn comparisons showed a significant difference between the six-year-old group and the two other groups (p$_{adj}$<=1e-5 for both comparisons; **Figure S4A**). As can be observed, the two younger groups showed a large variability in their performance while the six-year-old group was much more homogeneous (Levene test, p<0.0013). We performed a two-way ANOVA with age groups and sex as categorical factors: there was a significant effect of age groups (p<1e-5), but no effect of sex nor interaction. We then considered age as a continuous measure and performed a correlation between age and performance. We observed a significant correlation between performance and age (r=0.532, p<1e-5), performance increasing linearly with age (linear regression: r²$_{adj}$=0.271; polynomial regression: r²$_{adj}$=0.264; **Figure S4B**).

## Executive functions improve with age

### Processing time decreases with age

As expected, processing speed and manual dexterity increased with age in preschoolers. We measured processing time (PT) in the easy circles cancellation sheet of the PDTP and observed a decrease with age: four-year-olds completed the sheet in a mean time of 88.95 s (±9.47, mean ± s.e.), five-year-olds in 85.25 s (±9.53), and six-year-olds in 60.15 s (±3.51) (**Figure S4C**). A statistical analysis revealed a main effect of age groups (Kruskal-Wallis, p=0.010) with a significant difference between six-year-olds and the two other groups (Dunn post-hoc: p$_{adj}$=0.012 for both comparisons; **Figure S4C**). Sex had no effect on the PT (two-way ANOVA, main effect of age: p=0.033, no effect of sex nor interaction). The two younger groups showed a large variability in their processing time while the six-year-old group was much more homogeneous (Levene test, p<0.025). A correlation analysis between PT and age in months
showed a significant negative relationship between the two measures (r=-0.278, p=0.032; linear regression: $r^2_{adj}=0.061$; polynomial regression: $r^2_{adj}=0.057$; **Figure S4D**).

### Cognitive flexibility increases with age

We used the adapted TMT to test cognitive flexibility abilities in preschoolers. Difference in completion time for both parts (TMTB time – TMTA time) significantly decreased with age as can be observed in **Figure S4E**: four-year-olds completed TMTB in a mean supplementary time of 24.2 s (±2.3, mean ± s.e.) compared to TMTA, five-year-olds in 21.6 s (±2.5), and six-year-olds in 12.8 s (±1.7). We obtained a significant effect of age groups on TMTB-TMTA time (Kruskal-Wallis, p<0.001), post-hoc Dunn comparisons revealing a significant difference between six-year-old children and the two other groups ($p_{adj}<0.006$ for both comparisons; **Figure S4E**). Sex had no effect on the TMTB-TMTA time (two-way ANOVA, main effect of age: $p=0.005$, no effect of sex nor interaction). The two younger groups showed a large variability in their processing time while the six-year-old group was much more homogeneous (Levene test, $p<0.008$). A significant negative correlation was observed (r=-0.418, p<0.001; linear regression: $r^2_{adj}=0.120$; polynomial regression: $r^2_{adj}=0.154$; **Figure S4F**).

### Inhibition abilities increase with age

To assess inhibition abilities, we reported the percentage of errors for the Stroop subtest 4 (ST4E) and the number of false alarms (FA) and total errors (TE) for the Go/NoGo test. For ST4, we observed a decrease of the number of errors with age (mean ± s.e.; four-year-olds: 69.05% ±2.90; five-year-olds: 67.25% ±3.09; six-year-olds: 50.00% ±3.06; **Figure S4G**). The effect of age groups on the percentage of errors was significant (Kruskal-Wallis, $p=0.0005$), with significantly lower errors for six-year-olds than for the other two age groups (Dunn post-hoc, four- vs six-year-olds: $p_{adj}=0.0007$; five- vs six-year-olds: $p_{adj}=0.002$). Sex had no effect on the percentage of errors (two-way ANOVA, main effect of age $p<1e-4$, no effect of sex nor interaction). A significant negative correlation between the percentage of errors and age in months was also observed (r=-0.484, $p=10e-5$; linear regression: $r^2_{adj}=0.221$; polynomial regression: $r^2_{adj}=0.260$; **Figure S4H**).

For the Go/NoGo test, we observed a decrease in the number of errors with age, both for the number of FA and the TE (mean ± s.e.; four-year-olds: FA 5.05 ±0.33 TE 15.7 ±0.96; five-year-olds: FA 4.85 ±0.32 TE 15.05 ±0.80; six-year-olds: FA 3.45 ±0.33 TE 10.5 ±0.60; **Figure S4I** and **Figure S4K**). The effect of age groups on the percentage of errors was significant for both numbers of errors (Kruskal-Wallis, FA $p=0.0005$, TE $p<1e-4$), with significantly lower errors for six-year-olds than for the other two age groups (Dunn post-hoc, four- vs six-year-olds: FA $p_{adj}=0.0006$, TE $p_{adj}<1e-4$; five- vs six-year-olds: FA $p_{adj}=0.002$, TE $p_{adj}=0.0002$). Sex had no effect on the percentage of errors (two-way ANOVAs, main effect of age FA $p=0.0017$, TE $p<1e-4$, no effect of sex nor interaction). A significant negative correlation between the number of errors and age in months was also observed (FA: r=-0.433, $p<0.001$; linear regression: $r^2_{adj}=0.148$; polynomial regression: $r^2_{adj}=0.176$; **Figure S4J**; TE: r=-0.489, $p<1e-4$; linear regression: $r^2_{adj}=0.221$; polynomial regression: $r^2_{adj}=0.229$; **Figure S4L**).
# Supplementary Results R3

## Sustained attention correlates with mind wandering and executive functions

We performed multilinear regressions between the PDTP sustained attention score (SA) and other parameters (Figure S5). For mind wandering, we tested scores from the DDFS, the DDFS-t, and the MWQ. We observed a significant multilinear regression ($r^2_{adj}=0.897$, p<1e-15) between SA scores and mind wandering parameters, with a significant impact of DDFS-t (p<1e-8). For processing time, we tested processing time (PT) measured in PDTP and execution times of TMTA and TMTB. We observed a significant multilinear regression ($r^2_{adj}=0.716$, p<1e-14) between SA scores and processing time parameters, but no significant effect of individual scores. For flexibility, we tested several parameters extracted from the TMT test (TMTB-TMTA time, number of errors in TMTA and TMTB). We observed a significant multilinear regression ($r^2_{adj}=0.378$, p<1e-5) between SA scores and flexibility parameters, with a significant effect of TMTB-TMTA time only (p<0.0001). For inhibition, we tested several parameters extracted from the Stroop and Go/NoGo tests (Stroop: ST4E number of errors for ST4, SIE Stroop interference index for error rates between ST3 and ST4; Go/NoGo: number of FA false alarms and of TE total errors). We observed a significant multilinear regression ($r^2_{adj}=0.857$, p<1e-15) between SA scores and inhibition parameters, with a significant effect of both Go/NoGo parameters (FA: p<1e-9, TE: p<1e-15) and marginally significant effect of ST4E (p=0.066). The global multilinear regression analysis thus included the following parameters: DDFS-t, PT, TMTB-TMTA, ST4E, Go/NoGo_FA, and Go/NoGo_TE. This analysis was significant ($r^2_{adj}=0.949$, p<1e-15), revealing a significant effect of DDFS-t (p<1e-15), PT (p<0.02), Go/NoGo_C (p<0.05), Go/NoGo_TE (p=0.0005).

## Sustained attention correlates with developmental and emotional difficulties measures

Sustained attention performance was also correlated with developmental and emotional aspects evaluated by the partial WSR and ASEBA questionnaires. We focused on anxiety, sadness, and sleep problems, the first two being evaluated by the teacher, the last one by the parents. We observed a significant negative correlation between SA and anxiety (Figure S6D) measured by WSR (r=-0.917, p<1e-15; linear regression: $r^2_{adj}=0.834$; polynomial regression: $r^2_{adj}=0.880$) and ASEBA (r=-0.889, p<1e-15; linear regression: $r^2_{adj}=0.715$; polynomial regression: $r^2_{adj}=0.774$), sadness (Figure S6E) measured by WSR (r=-0.894, p<1e-15; linear regression: $r^2_{adj}=0.765$; polynomial regression: $r^2_{adj}=0.811$) and ASEBA (r=-0.548, p<1e-5; linear regression: $r^2_{adj}=0.285$; polynomial regression: $r^2_{adj}=0.281$), and sleep problems (Figure S6F) measured by WSR (r=-0.950, p<1e-15; linear regression: $r^2_{adj}=0.796$; polynomial regression: $r^2_{adj}=0.903$) and ASEBA (r=-0.771, p<1e-12; linear regression: $r^2_{adj}=0.579$; polynomial regression: $r^2_{adj}=0.599$). To summarize, children with better sustained attention abilities were the ones with the less sleep troubles and were the less anxious and less sad.
# Supplementary Results R4

## *MWQ scores correlate with attentional and executive functions*

For attention, we tested scores from the PDTP and Zazzo tests (SA: PDTP combined sustained attentional score, Zazzo\_E1 and \_E2: efficiency on sheets 1 and 2). We observed a significant multilinear regression (r²adj=0.914, p<1e-15) between MWQ scores and attentional parameters, with a significant impact of SA (p=0.0026) and of Zazzo\_E2 (p=0.048). For processing time, we tested processing time (PT) measured in PDTP and execution times of TMTA and TMTB. We observed a significant multilinear regression (r²adj=0.664, p<1e-12) between MWQ scores and processing time parameters, but no significant effect of individual scores. For flexibility, we tested several parameters extracted from the TMT test (TMTB-TMTA time, number of errors in TMTA and TMTB). We observed a significant multilinear regression (r²adj=0.474, p<1e-7) between MWQ scores and flexibility parameters, with a significant effect of TMTB-TMTA time only (p<0.0005). For inhibition, we tested several parameters extracted from the Stroop and Go/NoGo tests (Stroop: ST4E number of errors for ST4, SIE Stroop interference index for error rates between ST3 and ST4; Go/NoGo: number of FA false alarms and of TE total errors). We observed a significant multilinear regression (r²adj=0.765, p<1e-15) between MWQ scores and inhibition parameters, with a significant effect of both Go/NoGo parameters (FA: p<0.0005, TE: p<1e-15). As for the DDFS-t analysis, we included in the global multilinear regression analysis the following parameters: SA, Zazzo\_E2, PT, TMTB-TMTA, ST4E, Go/NoGo_FA, and Go/NoGo_TE. This analysis was significant (r²adj=0.893, p<1e-15), revealing a significant effect of SA (p<1e-13) and TMTB-TMTA time (p=0.029), but not inhibition parameters on MWQ scores.
# Supplementary Results R5

## DDFS-t scores correlate with developmental and emotional difficulties measures

Mind wandering was also correlated with developmental and emotional aspects evaluated by the partial WSR and ASEBA questionnaires. We focused on anxiety, sadness, and sleep problems, the first two being evaluated by the teacher, the last one by the parents. We observed a significant positive correlation between DDFS-t scores and anxiety (Figure S6A) measured by WSR (r=0.935, p<1e-15; linear regression: r²adj=0.909; polynomial regression: r²adj=0.909) and ASEBA (r=0.897, p<1e-15; linear regression: r²adj=0.771; polynomial regression: r²adj=0.777), sadness (Figure S6B) measured by WSR (r=0.912, p<1e-15; linear regression: r²adj=0.849; polynomial regression: r²adj=0.846) and ASEBA (r=0.563, p<1e-5; linear regression: r²adj=0.325; polynomial regression: r²adj=0.313), and sleep problems (Figure S5C) measured by WSR (r=0.967, p<1e-15; linear regression: r²adj=0.932; polynomial regression: r²adj=0.943) and ASEBA (r=0.792, p<1e-13; linear regression: r²adj=0.630; polynomial regression: r²adj=0.625). To summarize, children exhibiting the less mind wandering in the classroom were the ones with the less sleep troubles and were the less anxious and less sad.

Note that all these scores were also significantly correlated with age (WSR anxiety: r=-0.583, p<1e-5, linear regression: r²=0.351, polynomial regression: r²adj=0.331; ASEBA anxiety: r=-0.555, p<1e-5, linear regression: r²=0.322, polynomial regression: r²adj=0.299; WSR sadness: r=-0.557, p<1e-5, linear regression: r²=0.332, polynomial regression: r²adj=0.314; ASEBA sadness: r=-0.406, p=0.001, linear regression: r²=0.185, polynomial regression: r²adj=0.158; WSR sleep troubles: r=-0.513, p<1e-4, linear regression: r²=0.294, polynomial regression: r²adj=0.285; ASEBA sleep troubles: r=-0.389, p=0.002, linear regression: r²=0.169, polynomial regression: r²adj=0.163).
<figure><img src="image_56.png" /><figcaption>Supplementary Figure S1</figcaption></figure>

**Figure S1.** (A) TMTA time (in s) as a function of processing time PT (in s). Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I. (B) Distribution of TMTA and TMTB times (in s). Violin plots: density curves of data distribution; individual data points color-coded for age (darker points correspond to younger children); blue (red) point: mean (median). ***: p<0.001. (C) Distribution of ST1E, ST2E, ST3E and ST4E (in %). All else as in B. ***: p<0.001.
<figure><img src="image_57.png" /><figcaption>Supplementary Figure S2</figcaption></figure>

**Figure S2.** MWQ scores (in %) as a function of DDFS-t scores (in %). Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.
<figure><img src="image_58.png" /><figcaption>Supplementary Figure S3</figcaption></figure>

**Figure S3.** (A) MWQ (in %) as a function of age group. Violin plots: density curves of data distribution; individual data points; blue (red) point: mean (median). **\*\*\***: *p*<0.001. (B) MWQ (in %) as a function of age (in months). Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I. (C) DDFS-t (in %) as a function of age groups. All as in (A). (D) DDFS-t (in %) as a function of age (in months). All as in (B).
<figure><img src="image_59.png" /><figcaption>Supplementary Figure S4</figcaption></figure>

**Figure S4.** (A) SA (in %) as a function of age groups. Violin plots: density curves of data distribution; individual data points; blue (red) point: mean (median). (B) SA (in %) as a function of age (in months). Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I. (C) PT (in s) as a function of age groups. All as in (A). (D) PT (in s) as a function of age (in months). All as in (B). (E) TMTB time – TMTA time (in s) as a function of age groups. All as in (A). (F) TMTB time – TMTA time (in s) as a function of age (in months). All as in (B). (G) ST4E (in %) as a function of age groups. All as in (A). (H) ST4E (in %) as a function of age (in months). All as in (B). (I) Go/NoGo_FA number of False Alarms (in absolute number) as a function of age groups. All as in (A). (J) Go/NoGo_FA number of False Alarms (in absolute number) as a function of age (in months). All as in (B). (K) Go/NoGo_TE number of Total Errors (in absolute number) as a function of age groups. All as in (A). (L) Go/NoGo_TE number of Total Errors (in absolute number) as a function of age (in months). All as in (B). \*: p<0.05, \*: p<0.01, \*: p<0.001.
<figure><img src="image_60.png" /><figcaption>**Figure S5.** DDFS-t (in %) (A), PT (in s) (B), TMTB time – TMTA time (in s) (C), ST4E (in %) (D), Go/NoGo_FA number of False Alarms (in absolute number) (E), and Go/NoGo_TE number of Total Errors (in absolute number) (F) as a function of SA (in %). Color gradient of data points codes for age, darker points corresponding to younger children. Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>
<figure><img src="image_61.png" /><figcaption>**Figure S6.** Anxiety (A,D), sadness (B,E), and sleep problems (C,F), assessed by WSR (left axis, black points) or ASEBA (right axis, light gray points), as a function of DDFS-t (in %) or SA (in %). Dashed blue (red) line: linear (polynomial) fit. Shaded areas: 95% C.I.</figcaption></figure>
<figure><img src="image_62.png" /><figcaption>Supplementary Figure S7</figcaption></figure>

**Figure S7.** Structural equation model. Latent variables for attention (Att), processing speed (Spd), inhibition (Inh) and flexibility (Flx). Standardized regression weights and covariance estimates are presented on the corresponding links. Bold fonts and continuous arrows indicate significant links.
<table><caption>Supplementary Table S1</caption><thead><tr><th rowspan="2"></th><th rowspan="2">SA</th><th rowspan="2">Zazzo_E1</th><th rowspan="2">Zazzo_E2</th><th rowspan="2">DDFS</th><th rowspan="2">DDFS-t</th><th rowspan="2">MWQ</th><th rowspan="2">PT</th><th colspan="2">Correlations (N=60)</th><th rowspan="2">Go/NoGo_T</th><th rowspan="2">TMTAE</th><th rowspan="2">TMTBE</th><th rowspan="2">TMTB-TMTA</th><th rowspan="2">ST3E</th><th rowspan="2">ST4E</th><th rowspan="2">Go/NoGo_FA</th><th rowspan="2">Go/NoGo_TE</th></tr><tr><th>Zazzo_T1</th><th>Zazzo_T2</th></tr></thead><tbody><tr><td>SA</td><td>1.00</td><td>0.95</td><td>0.95</td><td>-0.87</td><td>-0.95</td><td>-0.93</td><td>-0.77</td><td>-0.75</td><td>-0.77</td><td>-0.79</td><td>-0.36</td><td>-0.40</td><td>-0.50</td><td>-0.43</td><td>-0.43</td><td>-0.62</td><td>-0.88</td></tr><tr><td>Zazzo_E1</td><td>0.95</td><td>1.00</td><td>0.98</td><td>-0.85</td><td>-0.95</td><td>-0.94</td><td>-0.65</td><td>-0.66</td><td>-0.69</td><td>-0.69</td><td>-0.35</td><td>-0.40</td><td>-0.48</td><td>-0.46</td><td>-0.43</td><td>-0.60</td><td>-0.85</td></tr><tr><td>Zazzo_E2</td><td>0.95</td><td>0.98</td><td>1.00</td><td>-0.86</td><td>-0.95</td><td>-0.95</td><td>-0.66</td><td>-0.68</td><td>-0.71</td><td>-0.71</td><td>-0.33</td><td>-0.38</td><td>-0.49</td><td>-0.41</td><td>-0.40</td><td>-0.58</td><td>-0.84</td></tr><tr><td>DDFS</td><td>-0.87</td><td>-0.85</td><td>-0.86</td><td>1.00</td><td>0.91</td><td>0.89</td><td>0.66</td><td>0.71</td><td>0.72</td><td>0.75</td><td>0.37</td><td>0.41</td><td>0.50</td><td>0.45</td><td>0.41</td><td>0.55</td><td>0.80</td></tr><tr><td>DDFS-t</td><td>-0.95</td><td>-0.95</td><td>-0.95</td><td>0.91</td><td>1.00</td><td>0.97</td><td>0.68</td><td>0.70</td><td>0.71</td><td>0.78</td><td>0.36</td><td>0.41</td><td>0.52</td><td>0.43</td><td>0.42</td><td>0.59</td><td>0.85</td></tr><tr><td>MWQ</td><td>-0.93</td><td>-0.94</td><td>-0.95</td><td>0.89</td><td>0.97</td><td>1.00</td><td>0.67</td><td>0.68</td><td>0.70</td><td>0.76</td><td>0.41</td><td>0.48</td><td>0.55</td><td>0.48</td><td>0.46</td><td>0.59</td><td>0.82</td></tr><tr><td>PT</td><td>-0.77</td><td>-0.65</td><td>-0.66</td><td>0.66</td><td>0.68</td><td>0.67</td><td>1.00</td><td>0.97</td><td>0.96</td><td>0.88</td><td>0.32</td><td>0.33</td><td>0.61</td><td>0.28</td><td>0.38</td><td>0.49</td><td>0.69</td></tr><tr><td>Zazzo_T1</td><td>-0.75</td><td>-0.66</td><td>-0.68</td><td>0.71</td><td>0.70</td><td>0.68</td><td>0.97</td><td>1.00</td><td>0.99</td><td>0.89</td><td>0.28</td><td>0.31</td><td>0.61</td><td>0.26</td><td>0.34</td><td>0.49</td><td>0.69</td></tr><tr><td>Zazzo_T2</td><td>-0.77</td><td>-0.69</td><td>-0.71</td><td>0.72</td><td>0.71</td><td>0.70</td><td>0.96</td><td>0.99</td><td>1.00</td><td>0.88</td><td>0.29</td><td>0.32</td><td>0.59</td><td>0.26</td><td>0.36</td><td>0.52</td><td>0.72</td></tr><tr><td>Go/NoGo_T</td><td>-0.79</td><td>-0.69</td><td>-0.71</td><td>0.75</td><td>0.78</td><td>0.76</td><td>0.88</td><td>0.89</td><td>0.88</td><td>1.00</td><td>0.29</td><td>0.35</td><td>0.66</td><td>0.26</td><td>0.36</td><td>0.52</td><td>0.72</td></tr><tr><td>TMTAE</td><td>-0.36</td><td>-0.35</td><td>-0.33</td><td>0.37</td><td>0.36</td><td>0.41</td><td>0.32</td><td>0.28</td><td>0.29</td><td>0.29</td><td>1.00</td><td>0.81</td><td>0.35</td><td>0.81</td><td>0.93</td><td>0.22</td><td>0.28</td></tr><tr><td>TMTBE</td><td>-0.40</td><td>-0.40</td><td>-0.38</td><td>0.41</td><td>0.41</td><td>0.48</td><td>0.33</td><td>0.31</td><td>0.32</td><td>0.35</td><td>0.81</td><td>1.00</td><td>0.41</td><td>0.67</td><td>0.81</td><td>0.26</td><td>0.33</td></tr><tr><td>TMTB-TMTA</td><td>-0.50</td><td>-0.48</td><td>-0.49</td><td>0.50</td><td>0.52</td><td>0.55</td><td>0.61</td><td>0.61</td><td>0.59</td><td>0.66</td><td>0.35</td><td>0.41</td><td>1.00</td><td>0.40</td><td>0.39</td><td>0.42</td><td>0.48</td></tr><tr><td>ST3E</td><td>-0.43</td><td>-0.46</td><td>-0.41</td><td>0.45</td><td>0.43</td><td>0.48</td><td>0.28</td><td>0.26</td><td>0.26</td><td>0.26</td><td>0.81</td><td>0.67</td><td>0.40</td><td>1.00</td><td>0.87</td><td>0.26</td><td>0.33</td></tr><tr><td>ST4E</td><td>-0.43</td><td>-0.43</td><td>-0.40</td><td>0.41</td><td>0.42</td><td>0.46</td><td>0.38</td><td>0.34</td><td>0.36</td><td>0.36</td><td>0.93</td><td>0.81</td><td>0.39</td><td>0.87</td><td>1.00</td><td>0.21</td><td>0.33</td></tr><tr><td>Go/NoGo_FA</td><td>-0.62</td><td>-0.60</td><td>-0.58</td><td>0.55</td><td>0.59</td><td>0.59</td><td>0.49</td><td>0.49</td><td>0.52</td><td>0.52</td><td>0.22</td><td>0.26</td><td>0.42</td><td>0.26</td><td>0.21</td><td>1.00</td><td>0.85</td></tr><tr><td>Go/NoGo_TE</td><td>-0.88</td><td>-0.85</td><td>-0.84</td><td>0.80</td><td>0.85</td><td>0.82</td><td>0.69</td><td>0.69</td><td>0.72</td><td>0.72</td><td>0.28</td><td>0.33</td><td>0.48</td><td>0.33</td><td>0.33</td><td>0.85</td><td>1.00</td></tr></tbody></table>

Table ST1. Intercorrelations among the variables of interest (n=60). Background color groups variables as a function of a priori associated evaluated cognitive function: from light gray to dark gray: attention, mind wandering, speed, flexibility and inhibition.
Supplementary Table S2

Factor Loadings; Oblimin rotation; Principal axis factoring

<table><thead><tr><th></th><th>Factor 1</th><th>Factor 2</th><th>Factor 3</th><th>Factor 4</th></tr></thead><tbody><tr><td>SA</td><td><strong>-0.8310</strong></td><td>-0.1486</td><td>-0.0077</td><td>-0.0473</td></tr><tr><td>Zazzo_E1</td><td><strong>-1.0000</strong></td><td>0.0635</td><td>-0.0115</td><td>-0.0289</td></tr><tr><td>Zazzo_E2</td><td><strong>-1.0000</strong></td><td>0.0168</td><td>0.0270</td><td>0.0159</td></tr><tr><td>DDFS</td><td><strong>0.7776</strong></td><td>0.1366</td><td>0.0465</td><td>0.0049</td></tr><tr><td>DDFS-t</td><td><strong>0.9706</strong></td><td>0.0278</td><td>0.0014</td><td>-0.0083</td></tr><tr><td>MWQ</td><td><strong>0.9271</strong></td><td>0.0158</td><td>0.0808</td><td>-0.0006</td></tr><tr><td>PT</td><td>-0.0436</td><td><strong>0.9891</strong></td><td>0.0381</td><td>0.0093</td></tr><tr><td>Zazzo_T1</td><td>-0.0089</td><td><strong>1.0000</strong></td><td>-0.0153</td><td>-0.0084</td></tr><tr><td>Zazzo_T2</td><td>0.0412</td><td><strong>0.9456</strong></td><td>-0.0151</td><td>0.0173</td></tr><tr><td>Go/NoGo_T</td><td>0.2029</td><td><strong>0.7675</strong></td><td>-0.0089</td><td>0.0124</td></tr><tr><td>TMTAE</td><td>-0.0847</td><td>0.0205</td><td><strong>0.9771</strong></td><td>0.0264</td></tr><tr><td>TMTBE</td><td>0.0365</td><td>0.0353</td><td><strong>0.7868</strong></td><td>0.0344</td></tr><tr><td>TMTB-TMTA</td><td>-0.0093</td><td>0.5106</td><td>0.2263</td><td>0.1006</td></tr><tr><td>ST3E</td><td>0.1884</td><td>-0.1387</td><td><strong>0.8229</strong></td><td>0.0165</td></tr><tr><td>ST4E</td><td>-0.0069</td><td>0.0641</td><td><strong>0.9760</strong></td><td>-0.0405</td></tr><tr><td>Go/NoGo_FA</td><td>-0.0233</td><td>0.0064</td><td>0.0176</td><td><strong>1.0000</strong></td></tr><tr><td>Go/NoGo_TE</td><td>0.4953</td><td>0.1105</td><td>-0.0362</td><td>0.5016</td></tr><tr><td>Expl Var</td><td>5.95</td><td>4.19</td><td>3.39</td><td>1.53</td></tr><tr><td>Prop Var</td><td>0.35</td><td>0.25</td><td>0.20</td><td>0.09</td></tr></tbody></table>

**Table ST2.** Factor loadings, explained variance and proportion of total variance obtained from the exploratory factor analysis. Loadings in bold are >0.7.
# Supplementary Discussion D1

## Evolution of performances with age

The estimation of the degree of MW is very variable across studies (e.g. Killingsworth and Gilbert 2010, Lindquist and McLean 2011, Keulers and Jonkman 2019, Cherry, McCormack, and Graham 2022), probably depending on the nature of the assessment (questionnaire or sampling) and the context (laboratory or classroom). The relationship between MW and age has not been systematically explored, and the few studies reporting on this topic present conflicting results (no age effect in adolescents and young adults: (Stawarczyk et al. 2014), no age effect in six- to 11-year-olds: Cheery & al. (Cherry, McCormack, and Graham 2022); decrease with age in young adults: Lindquist & McLean (Lindquist and McLean 2011), decrease with age in older adults: Krawietz & al. (Krawietz, Tamplin, and Radvansky 2012). We observed a significant decrease of MW with age in our population, significantly correlated to increased attentional and executive performances. Before discussing the functional relationship between MW and attention and executive functions, it is worth noting that increased executive performance in preschoolers and children in general has also been associated with growing metacognitive and theory of mind abilities (e.g. Carlson and Moses 2001, Lockl and Schneider 2007, Perner and Lang 1999, Veenman, Van Hout-Wolters, and Afflerbach 2006). The older the children, the better they are at evaluating their own mental processes and their mental content. We could thus have expected less variability in the estimated MW in older preschoolers. This was however not the case, probably because of some individual differences having more weight than metacognition maturation (see the correlations with the partial WSR and ASEBA questionnaires Figure S6). We suspect that the high proportion of MW in very young children may reflect the immaturity of attentional and executive functions (Garon, Bryson, and Smith 2008).

Performances for attentional and executive tasks increased with age in our population, in a linear fashion (the linear fit was always better than a second order polynomial fit). Our findings replicated previous studies on attention (e.g. Breckenridge, Braddick, and Atkinson 2013, Corkum, Byrne, and Ellsworth 1995), processing speed (e.g. Kail and Ferrer 2007, Miller and Vernon 1997), cognitive flexibility (e.g. Deák and Wiseheart 2015), and inhibition (e.g. Diamond 2002, Espy et al. 1999). All these functions mature well beyond six years old, some reaching a plateau around 10-12 years old like attention (Klenberg, Korkman, and Lahti-Nuuttila 2001, Manly et al. 2001) and other not before adulthood (depending on the difficulty on the task; Klenberg, Korkman, and Lahti-Nuuttila 2001; processing speed: Kail 2007; flexibility and inhibition: Huizinga, Dolan, and Van der Molen 2006). It is worth noting that these cognitive functions did not evolve in a similar way from four to six years old. Indeed, for sustained attention and processing speed, six-year-olds exhibited a reduced variability compared to the two other age groups, while this was not the case for MW, cognitive flexibility and inhibition functions (Figures 3 and S4). Our latent function modeling (Figures 5 and S7) suggested that attention hugely influences processing speed (Unsworth, Robison, and Miller 2021), in line with the proposal that attention is at the core of the development of all executive functions (Friedman et al. 2007, Garon, Bryson, and Smith 2008, Reck and Hund 2011, Rothbart, Sheese, and Posner 2007, Swingler, Perry, and Calkins 2015). The reduced variability could thus arise from earlier attentional maturation, between five and six years old, as compared to MW, flexibility and inhibition. Our latent function modeling further suggests that the maturation of attention in preschoolers is tightly linked to the maturation of MW. However, while attention has been proposed to support the development of all executive functions, our modeling suggests that, in preschoolers, the maturation of MW might support attention maturation. This directional link will have to be confirmed by more targeted investigations.
# Supplementary Discussion D2

## Several attentional and executive latent factors are present in preschoolers

Many studies have tried to model latent functions to describe executive or attentional functions, and their development. Our study focused on MW and did not aim at confirming or disclaiming previous models. In the field of executive functions (EF), an overall pattern seems to emerge (see Introduction in Lee, Bull, and Ho 2013) with mainly one latent factor in preschoolers (Wiebe, Espy, and Charak 2008, Wiebe et al. 2011, Hughes et al. 2009, Willoughby et al. 2010, Willoughby et al. 2012, Fuhs and Day 2011), only a few studies showing a 2-factors model before 6 years old (working memory or updating, and inhibition: Miller et al. 2012, Lee et al. 2012). All these studies included working memory tasks, that we did not use, and tested a priori models with Confirmatory Factor Analysis (CFA) only. Studies focusing on attention in preschoolers, contrary to the current study, included several attentional tasks and described a 2-factors model (executive attention, sustained/selective attention, Steele et al. 2012) or a 2-factors evolving in a 3-factors model (3-4.5 years old: sustained attention, selection/response, 4.5-6 years old: sustained attention, selective attention, attentional control, Breckenridge et al. 2012) using Exploratory Factor Analysis (EFA). Relative organization of attentional and executive components in preschoolers falls a little bit in a grey zone for two reasons. First, most tasks usually involve several attentional and cognitive functions, and have been attributed to attention or EF depending on the goal of the study (e.g. Wiebe, Espy, and Charak 2008 used the Child Continuous Performance Test, that could be classified as a sustained attention task, and the NEPSY visual attention subtest, that could be classified both as an attention task and an executive inhibitory task). Second, attentional models describe an executive attention factor (e.g. Steele et al. 2012 and Breckenridge, Braddick, and Atkinson 2013), this executive attention (or attentional control) being a part of EF that could also be labelled cognitive control, set shifting or flexibility depending on the context. Our modeling results, before considering MW, showed that a 4-factors model best fitted our data, with an attention factor that could reflect sustained attention, a processing speed factor, a flexibility factor, and an inhibition factor. Our results could suggest that processing speed would be closer from selective attention than sustained attention (even if we observe a strong correlation between our attention and speed factors), in line with a previous study showing that, when considering processing speed as a possible independent factor, this factor was grouped with visual selective attention (Robertson et al. 1997). This factor is also similar to the selection/response factor described by Breckenridge & al. (2013) in 3-4.5 years old children. Our results are also in line with the model proposed by Manly et al. (2001) from 6 to 16 years old, that showed a 3-factors solution comprising selective attention, sustained attention and executive control (that includes inhibition). However, our model does not fit with the studies suggesting only one executive factor in preschoolers: for example Willoughby et al. (2010) and Fuhs et al. (2011) did not find that separating inhibition from shifting improved over a 1-factor model. Note that studies using CFA in preschoolers seem to be more prone to describe 1-factor solutions compared to studies using EFA and SEM (see Tables in the Introduction of Lee, Bull, and Ho 2013 and Supplementary material of Wiebe, Espy, and Charak 2008). In our data set, inhibition was separated from attention (confirming results from Reck and Hund 2011; and Steele et al. 2012) and speed, while attention (more than age) greatly correlated with the speed performance.
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