Supporting Young Children’s Development of Executive Function Through Early Mathematics

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Early math and executive function (EF) skills—which control thinking and behavior—link to later academic success. National and local policies should support early childhood educators, promoting both through quality early math, as EF benefits math and math benefits EF.

Key Points

Introduction

Early childhood teachers face competing instructional priorities to support the development of children’s early subject-matter content knowledge and more general learning abilities. As research shows interconnections between attaining subject matter and the cognitive skills that support learning, educators may teach both sets of skills simultaneously (Clements et al., 2016). This article synthesizes key findings from the research on executive function (EF)—skills that support the ability to control one’s thinking and behavior—focusing on (a) the importance of EF skills for young children’s learning and school readiness and (b) the relations between EF and academics, especially mathematics. After briefly reviewing interventions targeted to improve EF, the article investigates whether high-quality mathematics instruction may offer dual benefit by supporting an important content area and developing EF. Finally, implications for educational policy follow from this synthesis.

The Importance of EF Skills to Young Children

To learn, investigate, and solve problems, children need cognitive resources, including domain-general cognitive skills, such as EF, and subject-matter proficiencies, such as literacy and mathematics. EF skills support higher-order cognition necessary for planning, problem-solving, and other goal-directed behavior (e.g., Zelazo, 2015). These skills undergo rapid development during early childhood (e.g., Buttelmann & Karbach, 2017; Clark et al., 2014; Fuhs & Day, 2011), and due to their strong association with academic achievement and broader life outcomes (Moffitt et al., 2011), these skills are of increasing interest to early childhood practitioners, researchers, and policy makers. Researchers generally agree EF has three distinct but interrelated components: inhibitory control (resisting automatic responses), cognitive flexibility (shifting between thoughts or tasks), and working memory (mentally manipulating and updating thoughts; Miyake & Friedman, 2012). Despite debate about differentiating these components in young children (e.g., Fuhs & Day, 2011; Lee et al., 2013; Wiebe et al., 2008), this set of skills provides a useful framework for considering the role of EF in the classroom and for considering targets for instruction and intervention. This article addresses how EF and academic domain-specific cognitive resources together contribute to young children’s learning and development, focused specifically on early mathematics.

Cognitive processes related to EF link to students’ academic achievement (Litkowski et al., 2020): As children learn, focus attention, and consider new ways of thinking amid their past experiences and knowledge, they evaluate new information while attending to it. EF skills support learning across all subjects and may be particularly important to both learning and doing mathematics (Nguyen & Duncan, 2019). As one example, consider the following problem: A child with four red and five blue counting bears is asked, “How many red bears are there? How many bears are blue?” First, the child must focus attention on the task: count only one color at a time, inhibiting the first impulse to (incorrectly) count all the bears at the same time. Second, the child shifts attention and engages cognitive flexibility (switching focus from one aspect or view of a problem to another) when switching from first counting just the red bears to then counting just the blue bears. Working memory supports this attention shifting and involves mentally holding onto information while processing and adding to it. The child must think of and use strategies to help remember which bears they already counted and which they did not. Extensive correlational research associates EF with concurrent and future academic achievement and growth trajectories (e.g., Allan et al., 2014; Becker et al., 2014), especially mathematics (Nguyen & Duncan, 2019; also see Clements et al., 2016, for a review). Moreover, correlations between EF and mathematics are evident beginning in early childhood (e.g., Allan et al., 2014; Becker et al., 2014). Longitudinal studies of children from preschool into kindergarten show that EF and mathematics achievement scores predict each other over time (e.g., Schmitt et al., 2017); this is not so with literacy (e.g., Fuhs et al., 2014; Weiland et al., 2014). For some children, strong EF skills in first grade are associated with their persistently high levels of mathematics achievement throughout elementary school (Mazzocco & Kover, 2007). Although some studies of EF and mathematics in early childhood rely on composite measures that tap several components of EF simultaneously, other researchers find that inhibition and/or aspects of working memory seem particularly related to mathematics performance (Mononen & Niemivirta, 2021; Nguyen & Duncan, 2019).

The associations between EF and mathematics also vary across mathematics topics, with certain topics relying more heavily on EF than others. These associations vary throughout childhood and may even vary depending on children’s initial EF or mathematics achievement. For example, among school-aged children (5–17 years old), solving word problems and learning new procedures and strategies are associated with EF, more so than doing rote calculations (Clements et al., 2016; Mononen & Niemivirta, 2021). However, the specific EF skills underlying a new procedure or strategy will vary as children progress through school and learn more mathematics. For example, adults rely less on working memory to solve arithmetic problems because these processes are more automatic compared with children (Rivera et al., 2005). Furthermore, the association between EF and mathematics is stronger for preschoolers with lower mathematics competencies (Dong et al., 2020), perhaps because young children with the lowest mathematics competencies are learning almost all new mathematics material while more advanced preschoolers have some existing skills and strategies. Children with varying EF skills may benefit from different instructional approaches to mathematics (Veraksa et al., 2020), and children with varying levels of mathematics achievement may benefit differently from instructions that increase EF processing demands. For instance, children with low mathematics achievement may be more susceptible to the challenges imposed by working memory demands of some mathematics problems, compared to children with higher mathematics achievement (e.g., Herold et al., 2020).

Although ample evidence supports associations between EF and mathematics, the mechanisms remain unclear. One theoretical explanation posits that EF processes are prerequisites for academic learning and that EF skills may determine how much the child is able to learn (Bull et al., 2011). In addition, children’s EF skills, which allow them to control and reflect on their cognitive processes and thus their behavior, may allow children to pay attention to and subsequently benefit from classroom interactions and instruction (Clements et al., 2016; McClelland et al., 2006). Upcoming sections highlight key findings from interventions designed to develop EF skills, including studies that test whether EF skills are a prerequisite for academic learning. A later section considers an alternative explanation that posits a bidirectional relation between EF and mathematics.

Interventions That Enhance EF Skills

The rapid development of EF skills in preschool and their association with academic achievement have led to a proliferation of interventions designed to enhance EF. A large body of evidence indicates EF skills can benefit from various interventions, including direct training, curricula, mindfulness, and physical activity (Diamond & Lee, 2011). Here, the focus is on direct training of EF skills, the importance of reflection, and the contribution of curricula; a brief summary illustrates some of the promising findings from these approaches (for review, see Diamond & Lee, 2011).

Direct training interventions typically engage children in a (computerized or noncomputerized) game-like activity that enables explicitly practicing EF skills. Many training studies target a particular EF skill and often yield positive benefits for the targeted skill—at least immediately after training. For instance, working memory trainings often yield improvement in working memory skills—that is, evidence of “near transfer.” However, these training benefits typically do not extend to nontrained skills (even other EF skills)—suggesting limited evidence for “far transfer” (e.g., Kassai et al., 2019). In the learning sciences, far transfer is more likely to occur if children have opportunities to practice the new skills in a variety of contexts (Smith, 1982). Direct training often does not include a variety of contexts and typically involves practicing EF skills through repeated exposure to one EF task, likely with less potential for far transfer.

Reflection skills may enhance EF trainings and promote transfer (e.g., Espinet et al., 2013). Reflection is a neurocognitive skill that can improve with practice. Reflection occurs when one pauses an ongoing stream of thought to consider the problem at hand and take a “step back” from the immediate situation, such as when deliberating, thinking of another perspective, or engaging in pretend play (Zelazo, 2015). Reflection can help children understand why a skill is important and when to apply a skill—even in novel situations. The Iterative Reprocessing model of EF development postulates that the reprocessing involved in reflection provides a foundation for selectively and flexibly controlling attention during problem-solving (Zelazo, 2015). As noted, most EF training studies isolate the training to one context and omit reflection, which may partially account for the lack of far transfer in the meta-analytic findings of direct EF trainings (Kassai et al., 2019).

EF interventions that include a reflection component demonstrate promise for both EF growth and transferability. For example, one training directed 2- to 4-year-olds to pause and reflect before responding during a card-sorting task (Dimensional Change Card Sort; DCCS) that required sorting on different dimensions (e.g., color or shape). In that study (Espinet et al., 2013), children in the reflection training group improved on a nontrained version of the DCCS (i.e., showed near transfer) and also showed some far transfer on nonsorting tasks, compared with children who did not receive reflection training. Additional studies also show that embedding reflection into trainings may promote near and far transfer to other EF skills (e.g., Pozuelos et al., 2019).

A different intervention approach uses particular curricula or activities/trainings, added to existing curricula, to infuse opportunities to practice EF skills into games or classroom activities (e.g., Bierman et al., 2008; Diamond & Lee, 2011; Weiland et al., 2013). One popular preschool and kindergarten curriculum designed to support EF, Tools of the Mind (Bodrova & Leong, 2007), focuses on pretend play as key to developing EF. However, findings from evaluations of Tools are mixed. Some randomized control trials indicated the preschool version of the program promotes EF and demonstrates some transfer to academic skills (Barnett et al., 2008; Blair & Raver, 2014; Diamond et al., 2007), whereas other evaluations showed no effects on EF despite good implementation fidelity (Clements et al., 2020; Farran et al., 2011; Lonigan & Phillips, 2012).

EF training may benefit children differentially. In multiple studies, the EF benefits extend to the intervention group overall, whereas in other studies, the intervention effects are limited to children with the lowest EF skills. For instance, one 8-week self-regulation intervention comprised a series of music and movement circle-time games (Tominey & McClelland, 2011). EF benefits from intervention resulted only for children with low EF at pretest assessment. However, the same self-regulation intervention implemented in Head Start classrooms found greater gains in EF and academic achievement over the preschool year in the intervention group overall compared with controls (Schmitt et al., 2015). Similarly, Head Start Research-Based, Developmentally Informed (REDI), a preschool intervention targeting social-emotional learning, found overall EF benefits compared with controls; the long-term EF benefits were, however, sustained only for children with the lowest EF skills (Bierman et al., 2008; Sasser et al., 2017). Although curricula-based EF interventions may have different effects based on initial EF skill level, embedding EF strategies into daily activities remains worthwhile.

Another potential influence on the outcome of EF training studies is teacher support. The Chicago School Readiness Project (CSRP), which emphasizes behavior-management training and provides stress reduction workshops to teachers, is a curriculum add-on that yields positive EF benefits: 3- to 4-year-old children exposed to CSRP showed significantly increased EF skills at the end of the school year compared with controls (Raver et al., 2011). Long-term follow-ups revealed EF benefits for the CSRP group lasted 10 to 11 years postprogram (Watts et al., 2018).

Overall, successful strategies for developing EF in young children are challenged by lack of transferability, but including reflection components and embedding EF practice across multiple contexts are promising strategies to enhance EF intervention efficacy. A caveat is that many existing EF interventions do not evaluate long-term gains in EF skills nor subject-matter proficiencies, and both are necessary to support optimal learning and problem-solving across life. Therefore, the next logical question is whether EF and mathematics may be mutually supportive such that both can benefit from high-quality mathematics instruction.

Teaching EF Within Math Activities—Math Can Enhance EF

Despite robust associations between EF and academic outcomes, and despite some success from EF training (just summarized), causal links between EF and achievement are unclear. The evidence that EF training leads to improvement has limited evidence of transfer to other EF skills or academic skills. Some consider the converse: that EF skills develop in the context of subject-matter instruction, which in turn supports learning the subject matter (Iseman & Naglieri, 2011). This section briefly reviews the theoretical and empirical argument for bidirectional links between EF and mathematics.

Teaching Math to Develop Math and EF

The notion of a bidirectional association between EF and mathematics is partially based in studies of learning and doing mathematics, and these studies demonstrate that mathematics may be an especially important context for younger children’s development of EF skills. In the first functional neuroimaging study focused on developmental changes in arithmetic cognitive processing, 8- to 19-year-olds determined whether arithmetic equations appearing on a screen were correct or incorrect. Although accuracy was equally high for all participants, brain activation patterns during the task differed by age group. Younger children showed more activation of prefrontal brain regions associated with effortful strategies (e.g., attentional and working memory processes that compose EF skills), whereas adolescents showed more activation of left parietal regions associated with mental arithmetic, symbol recognition, and retrieval skills (Rivera et al., 2005). However, these findings are limited to simple arithmetic, which is automatized for most adolescents. Hence, children may be recruiting their EF skills when engaging in mathematics, particularly novel, effortful mathematics.

Developmental differences in arithmetic processing are not bound by age, as numerous studies reveal; effortful and immature calculation strategies persist for middle-school children with mathematics learning difficulties (Mazzocco & Kover, 2007). So, children with learning difficulties may especially benefit from verbalizing and reflecting on the strategies they engage to complete paper-and-pencil computations (Naglieri & Johnson, 2000), and from instruction on how to engage EF strategies to read mathematics word problems meaningfully (Capraro et al., 2011; more studies are reviewed in Clements et al., 2016). These benefits of embedding EF strategies into mathematics instruction likely extend to all children learning and practicing novel mathematics topics, such as when children regularly encounter new math topics throughout their school years beginning with early mathematics. Thus, until math skills are automatized, children benefit from, and practice, EF skills while engaging in mathematics—potentially building competence in both domains simultaneously.

If bidirectional associations exist between EF skills and academic competencies, then high-quality mathematics instruction may be especially effective for developing EF skills. Researchers have tested this notion with intervention studies. In one such study, 77 inattentive first-graders completed a computerized training in either attention or academic skills (in math and literacy), and both interventions positively affected their attention skills. Even still, more children receiving the academic training showed reduced inattention, compared with those trained on attention, and only the academic training group showed improved academic functioning (Rabiner et al., 2010). In another study with pre-K children, the combination of the Building Blocks (BB) preschool mathematics curriculum (Clements & Sarama, 2013) and the Opening the World of Learning (OWL) literacy curriculum resulted in unplanned, positive, albeit small but statistically significant increases in all EF skills (Weiland & Yoshikawa, 2013). This “spill-over” phenomenon supports the hypothesis that cognitively demanding curricula improve other cognitive developmental domains such as EF, even without targeting them specifically.

Finally, two large-scale evaluations of the Tools of the Mind program (summarized earlier as not consistently leading to EF gains) also examined the role of mathematics curricula. In one evaluation (Farran et al., 2011), although Tools did not result in EF gains, a focus on mathematics in the classroom was associated with children’s gains in both EF and math. The other evaluation (Clements et al., 2020) compared two interventions with a business-as-usual control. One intervention included only the BB mathematics curriculum; the other intervention combined BB mathematics with the scaffolded play from Tools. Despite only weak immediate pre-K results, delayed effects at the end of kindergarten showed the BB group significantly outperformed the business-as-usual (control) group on both math and EF and outperformed even the Tools + BB group on at least one EF measure. Follow-up analyses (Dong et al., 2020) revealed that EF was most highly associated with math learning for children who started pre-K with low math competence. Furthermore, the math BB-only intervention had a larger long-range benefit for children. Considered together, the “spill-over” phenomena from these intervention studies support the hypothesis that cognitively-demanding mathematics curricula improves EF skills.

Hypothesized Mechanisms by Which Math Supports EF

Several potential mechanisms may explain why mathematics supports the development of EF skills and mathematical proficiencies (Clements et al., 2016). First, mathematical thinking and learning provide opportunities for children to practice EF skills. According to the theory of hierarchic interactionalism (Sarama & Clements, 2009), this interaction between math engagement and cognitive growth begins in infancy, when important premathematical and general cognitive abilities (including those related to EF skills) emerge and support later development throughout early childhood and beyond. Mathematical activities may guide children’s thinking by providing logical structures and opportunities for deep engagement. That is, “logical-mathematical thinking” (Piaget, 1977/2001) is a core component of cognition and may evoke, enable, and exercise EF processes in young children.

Second, mathematical activities provide unique and practical affordances or scaffolds for strengthening EF processes, scaffolds not realized by other academic domains. For example, arithmetical problem-solving may engage working memory and foster flexibly shifting among (or attempting) possible problem-solving approaches. Reliance on working memory and flexible thinking requires inhibitory control, and these strategies are useful any time children face new math topics throughout the school years.

Third, high-quality mathematical tasks, activities, and conversations may be natural, playful, and motivating to children and thus this element of joy—shown to be important for EF and learning (e.g., Diamond, 2012)—can be inherently present in early math activities designed to be playful. Future research needs to specify the role each of these factors plays in the dual benefits of high-quality early mathematics for math and EF skills.

Policy Implications

As foundational cognitive resources, EF skills support lifelong learning and human interaction (e.g., Blair, 2002; Heckman, 2006), so high-quality preschool programs have increasingly focused on intentionally promoting the development of these skills in young children. This priority puts EF skills on teachers’ radars at a time when preschoolers’ EF skills develop most rapidly (e.g., Buttelmann & Karbach, 2017). The challenge for practitioners is to learn effective ways to build EF skills in children. The interconnected challenge for policy makers is to support teachers’ ability to do so, based on relevant research. These priorities may be especially crucial for children whose EF skills are relatively low when they enter school, and who may be attending underresourced schools. More research and development needs to evaluate the integration of EF and early math, an approach that stands out as promising for promoting EF.

Intentionality in Teaching, Policy, and Research Priorities

The intentional development of mathematics curricula is essential to simultaneously prioritize good math instruction and EF skills, which speaks to the importance of teaching practices, the role of policy in those practices, and research priorities. If teachers are to intentionally support the development of both academic and general cognitive resources necessary for children’s long-term academic success, they must have the resources to do so. Yet, preschool teachers rarely have paid instructional planning time or high-quality professional development (PD)—especially on early math or EF—so they devote personal time to planning (Grisham-Brown & Pretti-Frontczak, 2003; Whitebook & Ryan, 2011) and informal PD that may not be evidence-based. These pressures on early childhood teachers have resulted in stress, low job satisfaction, burnout, and high teacher turnover (e.g., Gooze, 2014; Greenberg et al., 2016; Sparks, 2017). Reducing demands on teachers’ time in the classroom and supporting time for planning and PD are necessary for both child and teacher success. Reaching these goals requires that administrators and policy makers deliberately support teachers’ ability to provide high-quality math instruction for young children. Given the precious few hours children have in early childhood settings, the limited time teachers have to implement instruction, and early educators’ relative discomfort teaching mathematics (Sarama & DiBiase, 2004), a single strategy to develop multiple critical competencies would be efficient for practice, and a research priority. As suggested by this review, a mathematics curriculum that focuses on rigorous mathematics while intentionally supporting EF seems to be the best curricular approach.

In addition to creating instructional activities that support the simultaneous development of math and EF, providing teachers with high-quality and accessible evidence-based PD is essential. PD is potentially impactful in two key ways. First, teachers need support to effectively implement curricula and benefit if the support includes high-quality PD. Therefore, any curricular approaches designed to support both math and EF must be paired with PD for teachers. Second, when teachers recognize and adjust the working memory demands of classroom activities, children improve academic outcomes (Elliott et al., 2010). This suggests that PD targeted at improving teachers’ ability to both (a) recognize the role EF plays in the classroom and (b) adjust instruction to meet children’s EF needs may improve children’s outcomes. Considering these two approaches together, pairing PD with a curriculum that translates those practices to the classroom may result in larger positive effects on children (Markussen-Brown et al., 2017) and may even reduce teachers’ discomfort with early math.

For these potentially efficacious approaches to make a difference, they must be more widely adopted, and this, too, requires two significant modes of support from policy makers. First is the need for resources to support the research and development of these approaches. To our knowledge, there are no widely available curriculum-plus-PD programs using the proposed approach of focusing on math while purposefully supporting EF, but rigorously testing these approaches is crucial. Second, interconnections between math and EF can be incorporated into early learning standards to help practitioners think about EF in the classroom context, rather than viewing EF as a separate, disconnected skill. In addition, this approach may encourage adoption of more efficacious approaches to support academics and EF simultaneously. Early childhood education would thus benefit from the addition of research funding and structural support for changing the standards of practitioners’ thinking about EF.

Teachers’ traditional sole focus on academic material is not sufficient to support children’s highest potential for growth and achievement. Consider the research presented here on the bidirectional impact of EF and math on one another: For many, this may require a shift—a shift in thinking, teaching, support, and funding. For our children, this shift can set the stage for an upward trajectory for their entire academic career and beyond.