Executive Functions: Going Places at Pace

ABSTRACT Research on children’s executive functions (EF) has continued apace for a long time. The papers in this special issue offer the reader a welcome opportunity to pause and reflect on whether existing conceptualizations of EF require a paradigm shift. This debate is informed by thoughtful discussion of the difficulties in assessing EF in different societal contexts, by innovative approaches to enriching the assessment of EF, and novel accounts of what underpins developmental change in EF, as well as how EF relates to other aspects of children’s cognitive development. My commentary is organized by the dimensions of place and time and concludes with insights gleaned from the special issue regarding ways of supporting children’s growing EF.

Developmental research on executive functions (EF) has flourished over the past few decades, catalyzed by evidence of associations between early EF and a host of important long-term outcomes (e.g., Moffitt et al., 2011), by studies that support the centrality of EF as a construct for understanding atypical development (e.g., Zelazo, 2020) and by growing interest in cultural contrasts in children's cognitive development (e.g., Schirmbeck, Rao, & Maehler, 2020). Understanding how EF develops and how early EF skills can be improved are thus key goals within psychological science. However, study findings have often proved puzzling, provoking fundamental questions about how to measure EF and how to assess changes in EF. For example, researchers typically report weak associations between scores on individual EF tasks, raising questions about whether EF should be viewed as a unitary construct or as an umbrella term with distinct components (Karr et al., 2018). In addition, differences in the number and type of tasks used to assess EF in different age groups make it hard to investigate potential age-related changes in the structure of EF. Furthermore, EF interventions often yield disappointingly narrow and limited benefits, raising questions about the extent to which EF skills are domain general or context specific. Together, these findings have led theorists to reexamine how EF should be conceptualized. Collectively, the articles in this special issue make a significant contribution to this re-visiting of theoretical issues. Several authors offer thoughtful discussions of the difficulties associated with comparing child EF performance across contexts and cultures. Others offer innovative ideas for new approaches to EF assessment, or insightful analysis of the tension between standardization and sensitivity to context. In addition, this special issue includes novel conceptualizations of developmental changes in EF, as well as fresh ideas regarding how EF might underpin children's broader cognitive development, including milestones in language and in mathematics.
For coherence, and in response to a recent philosophical work on the challenges of studying cultural variation in cognition (Packer & Cole, 2022;Bryan, Tipton, & Yeager, 2021), much of this commentary is organized along the two broad dimensions of place and time. Effects of cultural and community characteristics will be considered within the dimension of "place," while temporal effects -from intra-individual variation in reaction times, to effects of practice and intervention, to age-related developmental changes -will be considered within the dimension of "time." To ensure that research in this field has positive impact beyond academia, my commentary will conclude with insights gleaned from this special issue regarding how adults can support improvements in early EF skills.

Measuring EF in different places and contexts
As described by Packer and Cole (2022), alongside complex ethical issues, cross-cultural comparisons face three sets of challenges: (a) defining culture and finding representative samples, (b) defining cognition and identifying appropriate tasks; and (c) establishing ecological validity and interpreting the results. They argue that these challenges can be overcome by viewing culture as the medium of human action and cognition as situated in time and place. These proposals challenge the focus on endogenous neural mechanisms within developmental cognitive neuroscientific studies of EF development (for reviews, see Fiske & Holmboe, 2019;Li et al., 2022;Moriguchi & Hiraki, 2013) but align with other recent perspectives that put contextual factors center stage. In one such model (Doebel, 2020), age-related improvements on EF tasks reflect developmental changes in children's preferences, knowledge, and beliefs (e.g., regarding the benefits of controlling one's thoughts or actions). From this viewpoint, components of EF (e.g., inhibitory control, working memory) are not isolable from specific task goals and contexts.
This alternative perspective offers a fresh view of why children's EF performance may vary across the globe (and in any given country, across different communities). For example, many researchers, including my own research team, have shown that, compared with their Western counterparts, children from Confucian societies typically show superior performance on tests of EF (e.g., Xu, Ellefson, Ng, Wang, & Hughes, 2020) but do less well on tests of theory of mind (ToM) (e.g., Fujita, Devine, & Hughes, 2022;Hughes, Devine, & Wang, 2017). As there are robust associations between individual differences in children's performance on tests of EF and ToM (for a meta-analytic review, see Devine & Hughes, 2014), this pattern of contrasting profiles for site differences in EF and ToM is unexpected. A context-rich view of children's performance on cognitive tests may, however, help explain this apparent paradox. For example, studies of parent-child conversations indicate that exposure to mental state talk is related to false belief understanding; although much of the evidence comes from children in Anglo-Saxon cultures (e.g., de Rosnay & Hughes, 2006;Ensor, Devine, Marks, & Hughes, 2013), similar findings have been reported both for children in Islamic societies, such as Iran (Taumoepeau, Sadeghi, & Nobilo, 2019) and in Confucian societies, such as Hong Kong (e.g., Chan, Wang, Devine, & Hughes, 2020). At the same time, there is evidence that, compared with their Western counterparts, Chinese children hear fewer conversations about mental states (e.g., Doan & Wang, 2010), and so may lack the knowledge base needed to engage fully in the vignettes used to test ToM. By contrast, Chinese children understand from a very early age that their parents expect them to excel on academic tasks (Ng & Wei, 2020), and so are likely to show a predisposition to follow task instructions carefully, a crucial aspect of many EF tasks. Thus, the contrasting differences between "East-West" in EF and ToM may, at least in part, reflect differences in the extent to which the tasks used to assess these two constructs are culturally meaningful for young children. In other words, differences in knowledge and values may lead to contrasts in children's levels of engagement in EF and ToM tasks.
Consistent with this proposed role of contextual familiarity in EF performance, two papers in this special issue (Gaskins & Alcalá, 2023;Niebaum & Munakata) cite recent findings of content-specific cross-cultural contrasts in young children's delay of gratification performance. Specifically, compared with their American counterparts, Japanese children appear more willing to wait for a snack, but less willing to wait for a gift (Yanaoka et al., 2022). This effect of contrasting cultural values appears to persist into adulthood (Hedden, Ketay, Aron, Markus, & Gabrieli, 2008).
Adopting the culturally infused stance proposed by Doebel (2020) and others (e.g., Miller-cotto, Smith, Wang, & Ribner, 2022; Munakata & Michaelson, 2021;Perone, Simmering, & Buss, 2021), Gaskins and Alcalá distinguish between the general definition of EF as self-regulation (a culturally universal goal) and the operational measurement of EF through specific tests of inhibitory control, working memory and cognitive flexibility. Drawing on this distinction, Gaskins calls for researchers to study EF in culturally meaningful ways. For example, tasks that require children to ignore information may be especially unfamiliar and unengaging for children from cultures that value "open attention" (Gaskins & Paradise, 2010). Supporting this view, Gaskins and Alcalá note that Yucatec Mayan children show impressive levels of real-life organizational skills, but their responses to tasks presented by researchers often indicate a flat refusal to accept the underlying premises. Similar conclusions emerge from a study of American children in which differences in children's propensity to wait in the classic Marshmallow task (Kidd, Palmeri, & Aslin, 2013) reflected reasoned beliefs about whether waiting would ultimately pay off. That is, children whose prior encounters with the adult running the experiment led them to hold low expectations regarding the rewards of waiting were much less likely to delay gratification in the Marshmallow task.
The point made by Gaskins and & Alcalá echoes a viewpoint expressed almost twenty years ago by Salthouse, Atkinson, and Berish (2003) who, in a study of cognitive decline in older adults, noted that laboratory-based EF tasks are inherently limited in their ability to capture EF, as the experimenter plays a key role in organizing participant responses. Building on this view, Toplak, West, and Stanovich (2012) conducted a practitioner review of 20 developmental studies and concluded that EF tasks are weakly associated with adult ratings of child EF because these two types of assessment measure different constructs. That is, performance-based measures of child EF are valuable indicators of processing efficiency, but adult ratings of EF tell us more about children's success in rational goal pursuit. There is an obvious analogy with the literature on intelligence; a construct that is defined broadly but measured narrowly, highlighting what Stanovich (2009) has described as the contrast between the reflective and the algorithmic mind. These conceptual points highlight the danger of assuming that contrasts between children from different cultures in EF task scores indicate meaningful differences in EF competencies. As a first step, it is important to test for measurement invariance, to evaluate the conceptual equivalence of EF tasks for different cultural groups (e.g., Xu, Ellefson, Ng, Wang, & Hughes, 2020). The same point also applies to within-culture heterogeneity: reflecting contrasting exposure to stigma and racism, minoritized children may not respond to EF tasks in the same way as their peers (Miller-cotto, Smith, Wang, & Ribner, 2022).
Equally, however, global trends may result in certain methodologies having universal potential. For example, the growing ubiquity of screen-based devices underpins the likely universal appeal of tablet-based tasks. Supporting this view, Gaskins and Alcalá noted that Yucatec Mayan children performed equally well on manual and tablet-based versions of the Tower of Hanoi task. From a methodological perspective, this observation is encouraging, in that it supports the possibility of achieving a balance between ensuring tasks are culturally tailored and achieving standardized delivery.
In their contribution to this special issue, Zelazo and Carlson (2023) propose that developmental systems theory offers a means of resolving the tension between contextdependent and domain general models of EF. That is, conscious control emerges from multiple, simultaneous, and interacting causal influences, operating at many levels of analysis (cultural, social, cognitive, neural, and molecular). While recognizing the need to avoid reductionism, Zelazo and Carlson (2023) highlight the danger of a pendulum swing back to early models of EF that were beset by the philosophical problem of the homunculus. Instead, the "third way" proposed by Zelazo and Carlson (2023) hinges on adopting a broader view of the factors that underpin performance on "hot" and "cool" EF tasks, to encompass not only core cognitive processes (e.g., inhibitory control, working memory and attentional flexibility) but also meta-cognitive capacities for reflection -which are directly informed by children's knowledge, beliefs, and values. Gaining an understanding of the interplay between these two pillars of EF is likely to depend upon refining our approaches to measurement, to incorporate information about both accuracy and trial reaction times, as well as variability and patterning in these reaction times -a topic to which I will return in the next section of this commentary.
I share Zelazo and Carlson's (2023) view that this balancing act between competing models of EF is worth the effort, as it allows us to embrace new perspectives that offer a more positive portrayal of minoritized children than previous "deficit" based accounts, whilst also retaining advances that have been made in developmental science -for example, in understanding the neural basis of children's cognitive development.
Frick and Chevalier (2023) also adopt an integrative "third way" perspective, arguing against the need to distinguish between self-directed versus externally driven forms of control, which they view as two ends of a continuum, rather than as discrete constructs. This point echoes the growing use of the term "co-regulation" to highlight the socially embedded and dynamic nature of children's acquisition of early self-control (e.g., Gillespie, 2015;Gulsrud, Jahromi, & Kasari, 2010). Strengthening the notion of co-regulation, Holochwost et al. (2023) note that positive child-researcher rapport improves children's performance on measures of EF (Gidron, Sabag, Yarmolovsky, & Geva, 2020). Holochwost et al., (2023) focus on state rather than traits influences on EF performance and highlight the value of examining intra-individual variability in response times. By connecting perspectives of place and time, this focus on state influences on EF brings us neatly to the next section of this commentary, which considers temporal themes within contemporary EF research.

Insights from temporal perspectives on EF
As noted earlier, the weak association between scores on EF tasks and EF questionnaires indicates that they assess different constructs: EF tasks indicate the efficiency of cognitive processing, while rating scales index the success of goal-directed activities (Toplak, West, & Stanovich, 2012). This contrast suggests another distinction; namely that each type of measure relates to a different temporal scale: EF tasks capture moment-by-moment contrasts, whereas adult ratings of child EF reflect contrasts that emerge over much longer periods of time. Likewise, within this special issue, several papers highlight the value of analytical approaches that include a temporal perspective.
For EF tasks that include multiple trials (e.g., versions of the Stroop task), one might expect children's errors to creep up in later trials, as their ability to sustain attentional focus wanes. Interestingly, researchers have only recently begun to investigate how children monitor their performance on EF tasks. In a review aimed at highlighting the overlap and interplay between EF and metacognition, Roebers (2017) called for researchers to examine trial-by-trial variation in children's response times on EF tasks -for example, to assess children's propensity to slow down after a mistake.
Addressing this topic of intra-individual variability in response times in this special issue, Holochwost et al., (2023) outline the multiplicity of contributing factors. These include state-based influences on task persistence such as fatigue, stress, glucose sufficiency or diurnal variation in the activity of the hypothalamic-pituitary-adrenal (HPA) axis (c.f., Obradović, 2016). From a methodological perspective, the impact of state rather than trait factors highlights the potential advantages of giving the same task for children to complete several times (e.g., at different times of day, or in different situational contexts). When combined with information about both child factors (e.g., fatigue, stress) and situational factors (e.g., noise levels, time of day, novelty of testing context) repeated assessment would allow researchers to achieve more accurate estimates of intervention effects -and may help explain why interventions to boost EF often yield quite restricted benefits. Holochwost et al. (2023) outlines plans to apply this multi-assessment approach to investigate the correlates of intra-individual variation in EF task performance. A focus on variability in performance (alongside mean accuracy and reaction time) offers a valuable means of deepening our understanding of the multiple determinants of children's responses. With this aim in mind, several researchers have turned to recurrence quantification analysis (RQA), a means of capturing dynamic systems that are too complex for standard time series analysis. For example, in a study in which university students completed a random number generation task, Oomens, Maes, Hasselman, and Egger (2015) showed that RQA yielded more parsimonious and more interpretable data than traditional accuracy and reaction time measures (see also Oomens, Maes, Hasselman, & Egger, 2021). RQA has already proved fruitful in studies of reading fluency (e.g., Wijnants, Hasselman, Cox, Bosman, & Van Orden, 2012) and early developmental changes in eye-movement (e.g., Tomalski, López Pérez, Radkowska, & Malinowska-Korczak, 2021), and has recently been shown to distinguish between visual search response patterns of autistic children and children with ADHD (e.g., Seernani et al., 2020). In short, RQA appears to be a very promising tool for capturing the dynamics of both individual differences and developmental changes in cognition -an exciting prospect for future research, not least because it can be applied to existing datasets. Holochwost et al. (2023) posit that intra-individual variation in performance will be positively associated with ratings of home chaos/sleep disturbance and negatively associated with task persistence. Consistent with this view, Halliday et al. (2021) have reported that, beyond accuracy scores, intra-individual variation in response times on simple EF tasks (e.g., Go-No go test, interference tests) predicts ratings of ADHD symptoms even when accuracy scores are considered. Interestingly, however, recent findings using RQA suggest a more complex picture. Specifically, RQA of data from young children's EF task performance supports the idea of a Goldilocks-style "sweet spot" between high and low variability -i.e., between poor systematicity and rigid/inflexible responding, with children in this optimal range showing greater EF gains than their peers over a 12-month interval (Berry, November 2022, pers comm). Further work is needed to establish whether the role of intra-individual variability in response times as a predictor of later child outcomes varies with the difficulty of EF tasks.
Adopting this broader timescale of developmental change, two papers in the Special Issue (Ibbotson, 2023;Frick and Chevalier, 2023) offer new accounts of what underpins agerelated improvements in children's EF performance. Akin to Zelazo and Carlson's (2023) proposed integration of domain general and context specific views of EF, Ibbotson (2023) argues that improvements in children's cognitive flexibility can be understood as reflecting both an expanding repertoire of control strategies and more effective coordination of this repertoire (see also Chevalier, 2015). Neatly dovetailing the two dimensions of place and time, Ibbotson's (2023) account highlights a process of functional analogy that has roots in children's learning across multiple contexts: learning through play, trial-and-error learning, observational learning, explore-then exploit learning (Gopnik, 2020) and embodied interactions within a social context (Müller & Kerns, 2015).
Like other models of EF (e.g., O'Brien, Mitchell, Duncan, & Holmes, 2022), Ibbotson's (2023) model highlights an overlap with the concept of fluid intelligence. However, his model differs from other accounts in two respects. First, the domain-general process of functional analogy is viewed as contributing to (rather than resulting from) EF development. Second, drawing other areas of neuropsychology -notably, language acquisition -Ibbotson (2023) characterizes this process of functional analogy as being low-level in nature. For example, English-speaking children learn that the past tense for many verbs can be constructed by adding "ed" to the present tense (e.g., "look" changes to "looked" and "touch" changes to "touched"), and so begin to over-regularize, as evidenced by neologisms (e.g., "runned" instead of "ran"). This highlights children's propensity to apply learning across multiple contexts; with some transfers being more easily achieved than others. Likewise, with regards to EF, Ibbotson (2023) argues that resisting a tempting snack has more in common with controlling the impulse to respond aggressively to provocation than it does with updating information to follow a conversation.
Frick and Chevalier (2023) also present a new theoretical model of the development of self-directed cognitive control, which they portray as reflecting a shift from externally directed to self-directed control. They argue that this shift is underpinned by language acquisition, which enables children to use private speech to monitor and regulate their activities. Frick and Chevalier's (2023) model has two key components, context tracking and goal selection, with the first of these being especially relevant for developmental change as self-directed situations place particularly high demands on context-tracking.
Medrano and Prather's (2023) paper offers reflections on research findings related to the role of inhibitory control in mathematical cognition. While noting that contextual factors (e.g., support for numerical thinking within the home environment, social transmission of math anxiety) are likely to moderate the role of EF in numerical skills, this paper sets out to outline the different ways in which individuals apply inhibitory control in situations governed by mathematical concepts. Specifically, Medrano and Prather (2023) argue that good performance on mathematical operations hinges on the suppression of both irrelevant information and inefficient/misleading strategies. Although this point is not made explicitly, it follows that factors that may constrain the process of sifting out relevant information (e.g., difficulties in phonological processing or in reading comprehension) are likely to adversely affect mathematical performance -and indeed, problems with mathematics are often noted among individuals with dyslexia (e.g., Kay & Yeo, 2012). It is also worth noting that inhibitory control is only part of a picture, as findings from Emslander and Scherer's (2022) recent meta-analytic review indicate that, in the preschool years at least, individual differences in math intelligence show similar sized associations with the three core components of EF (inhibition, set shifting, updating). The role of inhibitory control in mathematical cognition therefore needs to be considered alongside the roles of other EF components -updating and set shifting.

Emerging insights on how to support EF development
Both theoretical models regarding the processes implicated in EF development discussed in this commentary have pedagogical implications. For example, Ibbotson's (2023) model of functional analogies highlights the clustering of skillsets that may help explain why training often leads to benefits that do not generalize to wider contexts (i.e., intervention effects often show near but not far transfer). In turn, this suggests that initiatives to boost children's EF should include strategies to support the process of functional analogies; for example, cueing children to similarities between the demands of a new task and those of previous successfully completed tasks. In other contexts (e.g., dialogical book sharing), the value of making connections between new material and children's own experiences is wellrecognized. Thus, in devising strategies to support the process of functional analogies, practitioners may be able to draw on existing work. For example, tips such as "count to 5" apply to all situations in which children may need to resist an impulsive response, and tips such as "say it aloud" or "write it down" apply to all situations in which children need to hold information in mind. Highlighting the universality of such strategies may help make them more accessible to children as they face novel situations.
Similar insights come from Frick and Chevalier's (2023) model, which highlights the importance of identifying contextual cues -an obvious focus for parental/teacher support. For example, in a situation that involves multiple elements of two distinct types (e.g., a math worksheet that includes adding and taking away sums), suggesting tips for reducing the additional load on cognitive flexibility (e.g., first grouping the sums by type) may help children avoid silly mistakes -whilst also encouraging them to reflect on the functional analogies/differences between different elements within this task (e.g., the order in which numbers are presented matters for subtraction but does not matter for addition).
Likewise, perspectives that highlight the importance of children's knowledge and beliefs also offer new insights for strategies to foster EF development. For example, rephrasing instructions to increase the familiarity or vividness of language is likely to help make instructions more memorable. To end this commentary on an informal note, an anecdotal illustration may be helpful. Last year, my research team organized a family-friendly event that included a workshop with novel wooden construction materials (Kapla). A key concept for building with Kapla is to alternate the orientation of blocks to create a regular structure. Rather than asking 4-year-old workshop participants to place blocks at right angles to each other, or to place blocks horizontally and then vertically, the instructor engaged them in a fun warm-up activity in which they either put blocks upright on their heads to make "rabbit ears" or flat along their upper lips to make a "moustache." The children then went on to build fabulous towers, alternating between rabbit ears and moustache with confidence. Having gained familiarity with the basics of Kapla building, planning ambitious constructions was, quite literally, child's play. Recognizing the importance of adopting playful context (c.f., Chu & Schulz, 2020;Doebel & Lillard, 2023) may help the design of EF interventions to achieve more widespread benefits -a wonderful challenge for future research!

Disclosure statement
The author reports no conflict of interest.