Digit comparison and order processing performance predict children's later arithmetic skills in the elementary years, presumably because they assess foundational symbolic number knowledge (i.e., cardinal and ordinal associations). However, the influence of earlier arithmetic on later magnitude and order processing has rarely been assessed. Numeracy skills were assessed in two longitudinal cohorts (50% girls) in 2021 and 2022; grades 2-3 (N = 9,552; Mage = 7.4) and grades 3-4 (N = 3,189; Mage = 8.4). A multi-group cross-lagged panel model showed that the longitudinal contributions from earlier arithmetic to later comparison and ordering were stronger (ß = .11-.34) than those in the reverse direction (ß = .03-.09), indicating early math development is both hierarchical and integrated.

Executive functions (EFs) are related to academic performance, but interventions designed to leverage EFs to improve academic outcomes have shown inconsistent results. Academic performance is also subject to layers of personal, social, task-relevant, and cultural contexts, all of which impact students’ EF engagement in any given task. The EF+Math Program explored the potential for EFs to positively impact math achievement by supporting inclusive research and development of EF learning approaches that are contextually embedded and attend to the needs of diverse students. Across a portfolio of projects, researchers, developers, and educators worked collaboratively to co-design and evaluate learning approaches for middle school mathematics classrooms. Here we share examples of our contextualized research, and our updated conceptualizations of EFs arising from shared insights across different contexts. We conclude with calls to action for continuing inclusive research and development to advance insights across, theory, assessment, and intervention in EF research.

Collaboration across researchers and educators is needed to ensure that educators have access to effective, practical early mathematics assessment and instructional tools and strategies. The Assessment and Instruction for Mathematics (AIM) Collective is a dynamic community of researchers and educators in Canada committed to sharing evidence-informed, teacher-approved math education tools and resources. Through our partnerships, researchers and educators have learned from each other and achieved shared research goals. The model developed by AIM is one way of building and sustaining the relationships needed to support this collaborative work. In this paper, we share what we have learned about the importance of working collaboratively to ensure uptake of early assessment and instruction practices based in research and feasible in classrooms. We highlight one example project done in partnership with a school board that demonstrates impact on student mathematics achievement from combining researchers' strengths at assessment and educators' expertise at developing instructional activities that are well suited to their classrooms.

Working memory (WM) and socioeconomic status (SES) associations with math achievement are well established, but little work has considered whether WM contributions are the same across SES strata. Here, we focus on the extent to which verbal WM predicts math differently for children in low vs. higher SES homes in the US to disentangle how these relations might play out across development in differently resourced contexts, as well as the magnitude of these relationships across SES. Using data from a nationally representative sample of 13,527 children, we estimated a parallel process model to analyze the relation among the starting points and growth of verbal WM and math skills through elementary school. A multi-group model was used to compare the relative strength of associations between verbal WM and growth in math skills between low-income and not-low-income students. Results indicated that students with higher initial verbal WM levels developed math skills faster than those with lower verbal WM levels, especially in low-income households where verbal WM's effect size was nearly double relative to estimates for children in higher-income homes. Findings highlight the importance of providing families with the necessary resources to help children thrive in adverse contexts.

In the spring of 2023, a working group was formed to create a framework for how to co-construct professional development (PD) in education. The working group consisted of 12 multidisciplinary professionals related to the field of education. Most teacher professional development is not as effective as it could be, so this co-constructing PD framework provides important guidance for planning and implementing successful PD. The working group developed the framework through a process of co-construction, based upon shared expertise and knowledge of relevant research. The co-construction of professional development framework comprises four essential components: (1) an intentional teacher-centred design and multidisciplinary approach, (2) professional growth over time and in community, (3) professional development grounded in experiential learning and professional practice, and (4) measurement and monitoring of professional growth to foster improvement and document successes. This paper discusses the components of the framework, supporting research, and how to put the framework into practice.

Children learn the first few number words one at a time, before learning the meaning of counting. Past research, however, has focused on monolingual children, with only a handful of studies on bi/multilingual children. The current study investigated whether knowledge of number words in one language predicted knowledge of those same number words in another language. We studied Mandarin-, Malay-, and Tamil-English bilingual children (N = 131, ages 2-5) growing up in Singapore, a multilingual and multicultural society, and found that their number knowledge was strongly correlated between languages. Contrary to previous studies in the U.S., we also found some evidence that meanings for small number words are transferred across languages. Our findings point to a possibility that early number words can be learned as translation equivalents (e.g., "one" in English is "yi" in Mandarin Chinese) in bilingual children and highlight the importance of taking an inclusive, global approach to studying numerical development that goes beyond studying White monolingual children.

Executive functions (EF) are crucial to regulating learning and are predictors of emerging mathematics. However, interventions that leverage EF to improve mathematics remain poorly understood. 193 four-year-olds (mean age = 3 years; 11 months pre-intervention; 111 female, 69% White) were assessed 5 months apart, with 103 children randomised to an integrated EF and mathematics intervention. Our pre-registered hypotheses proposed that the intervention would improve mathematics more than practice as usual. Multi-level modelling and network analyses were applied to the data. The intervention group improved more than the control group in overall numeracy, even when controlling for differences across settings in EF and mathematics-enhancing practices. EF and mathematics measures showed greater interconnectedness post-intervention. In addition, disadvantaged children in the intervention group made greater gains than in the control group. Our findings emphasise the need to consider EFs in their integration with co-developing functions, and in their educational and socio-economic context.

The Give-N (give-a-number) task has become a popular assessment of children’s number words and counting knowledge since Wynn’s (1990; 1992) seminal work over 30 years ago. Using the Give-N task, numerous studies have shown that children learn the first few number words slowly, before they understand how counting represents number. This learning trajectory and children's associated behaviors on the Give-N task are represented by “knower-levels” and form the basis for a large body of research assessing children’s number learning. Recent research has started to critically analyze the theoretical conceptualisation and reliability of knower-levels. We added to this work by conducting a systematic review of studies using the Give-N task. This review provides an overview of methodological practices and variations in the task’s administration and scoring of knower-levels which have theoretical and methodological implications. We argue that advancing methodology and theory for research in children’s number learning requires (1) consideration of Give-N task administration and scoring in study design and reporting and (2) reflection on the assumptions and limitations of classifying children’s performance on the Give-N task in the knower-level framework.

Giving practitioners a voice is essential in developing intervention programs that are adapted to educator and child needs. We aimed to do so by involving educators in the codesign of an intervention supporting early mathematical and executive development, to maximize feasibility and implementation quality. N = 100 educators, N = 24 Early Years Centers (EYCs), and N = 16 education science experts took part. Educators expressed a need for feasible professional development coupled with practical activity suggestions (Phase I). A scientist/educator expert panel developed the intervention (Phase II), further refined via educator input (Phase III) to overcome implementation barriers (e.g., diverse children's needs). In Phase IV, mixed methods revealed successful solutions (e.g., differentiation guidance) and additional barriers (e.g., diverse staff demands). We demonstrate the value of an iterative codesign process for complex educator-led interventions to produce programs addressing specific needs of educators and children whilst retaining key theoretical principles.

The cardinal meanings of the first few number words are often assessed with the Give-N Task, and children’s knowledge of number words can be represented by “knower-level”, with N-knower representing children who have acquired cardinal knowledge of number words up to N. In the current study, we sought converging evidence for knower-levels by examining the correspondence of knower-level classifications between the Give-N Task and the Point-to-X Task. In Study 1, we tested 69 preschool-aged children and found that children at the higher knower-levels often did not receive the same classification across tasks. Further, children who were classified as having acquired the cardinal principle on the Give-N Task were more likely than subset-knowers to count on the Point-to-X Task, but they did not count very frequently. In Study 2, we conducted secondary data analysis on an existing study that included a Point-to-X Task with different stimuli and more trial types. We again found that children’s knower-level assessed with Give-N was not always associated with above chance performance for that number on the Point-To-X Task. These data suggest that knower-levels may adequately capture cardinal number knowledge for very small numbers but not for higher numbers. We discuss the practical implications of these findings and highlight a need for future studies to adopt a multi-method approach to establish a robust pattern of children’s number word acquisition.

Executive function (EF) theory and research continues to under-represent the contexts in which the majority of the world’s children reside, despite their potential to support, refute, or refine our current understandings. The current study sought to contribute to our understanding of EF in low-income settings in South Africa by investigating longitudinal associations of context-specific risk and protective factors for EF development in three- to five-year-old children who had limited access to ECCE services before the age of five. Child-caregiver dyads (N = 171) participated in two rounds of data collection (approximately seven months apart) during which child EF was assessed using the Early Years Toolbox; context-specific risk and protective factors were assessed through a caregiver questionnaire. Hierarchical linear regressions revealed that after controlling for age, attending ECCE services at time 2 (β = 0.30, p < 0.001), and diversity of caregivers at time 1 (β = 0.14, p = 0.041) were the only factors positively associated with EF at time 2. Other factors commonly associated with EF such as caregiver education, and household income were not significant, while resources in the home were significantly associated with EF (β = –0.18, p = 0.007) but in the opposite direction to what was expected. These results add to accumulating evidence that predictors of EF established in Minority World contexts may not be consistent across contexts, emphasising the need to broaden the EF evidence base. For instance, future studies could incorporate qualitative and ethnographic methods to better capture the cultural and contextual nuances relating to EF, to better inform our statistical and theoretical models.

The majority of the world's children live in low- and middle-income countries, yet the majority of early childhood cognitive research is done with a small proportion of high-income countries. These findings cannot be assumed to apply across all contexts. It is therefore necessary to confront entrenched systems of power and privilege in early childhood cognitive development research as they relate to researchers and vulnerable communities. South Africa (SA) is a previously colonized, Majority World country with a history of white supremacy and racial segregation. Although early cognitive development is a growing field of research in SA, power and privilege in this field of research are yet to be properly considered. Within SA's unique context, we highlight the valuable role of partnerships in shifting power asymmetries; in our case, between early cognitive development researchers and a community-based organization with a 50-year history of working in vulnerable communities to promote young children's development. Our work together thus far has largely focused on executive function and numeracy skills (inspired by Minority World country research) in vulnerable SA children. We reflect on the authors' positionality, the intersectionality of privilege where relevant, and discuss three themes: the assessment of young children's development in vulnerable SA settings; formation of a more equitable partnership with individuals and communities whose voices are not often heard in this research; and translation and dissemination of research findings. We include recommendations for researchers to help with decolonizing early cognitive development research in order to add value to research from diverse settings.

Research Findings: School readiness is highly salient in South Africa (SA), a country with extreme and persistent inequities that undermine early childhood development. The aim of this short-term longitudinal study was to identify social ecological factors associated with school readiness in young children from low-income settings in Cape Town, SA. Participants were 152 3-5-year-old children (55% female, not attending early childhood care and education (ECCE) settings at recruitment) and their primary adult caregiver from low-income settings. Linear regressions found that, compared to home- and community-level factors, child-level factors were the strongest predictors of scores on the International Development and Early Learning Assessment (IDELA, total and subscale scores for literacy, numeracy, social emotional, and motor). At the child level, attending ECCE services was the strongest predictor, followed by early numeracy and age. Household socioeconomic status positively predicted social emotional scores; dysfunction in the parent-child relationship negatively predicted literacy and total school readiness scores. Practice or Policy: These findings contribute to a contextually relevant understanding of school readiness in low-income SA settings. Greater understanding can lead to more effective mitigation of risks and amplification of protective factors within policy and practice so that early childhood development can be optimized in these settings.

Numerous studies have shown that number word learning is a protracted process. One challenge facing children learning the meaning of number word such as “one”, “two”, or “three” is that number words refer to a property of a set and not to individual objects. In this study, we focused on a sample of children who have not learned the meaning of small number words such as “two” and “three” and tested whether children could learn number words from examples of sets that help them focus on set size. Specifically, the experimental training condition included examples that highlight a common relational structure between sets through varying object properties in the sets (e.g., three yellow stars and three red hearts are both “three”), whereas the control condition did not vary object properties(e.g., two sets of three yellow stars with different spatial arrangement). We trained two- and three-knowers (N = 65) on the next number (i.e., three or four) and assessed their learning with a Two-Alternative-Forced-Choice task and Give-a-Number task. Overall, we found weak effects of training. We discuss our findings in the broader literature on number word learning and explore the possibility of analogical reasoning as a mechanism of number word learning.

Early knowledge of numbers, relations, and operations are foundations for student success. Weak foundational number skills can lead to later difficulties, thus early identification and targeted interventions for students with weak number skills can help stop them from falling further behind. In the current study, we tested the effectiveness of MATmatics, a tier 2 intervention that targeted early numeracy skills for at-risk students in grades 2 and 3. Students (N = 45) were quasi-randomly assigned to either an intervention group, or a wait-listed control group. Using a series of 2 (group: intervention, control) x 2 (test timing: pre-intervention, post-intervention) mixed ANOVAS, we found that the math skills (measured with the Early Math Assessment@School numeracy screener) of students assigned to the intervention group improved at a faster rate than the math skills of their waitlisted control peers. The intervention was effective.

Executive functions (EF) are crucial to regulating learning and are predictors of emerging mathematics. However, interventions that integrate to improve mathematics remain poorly understood. 193 four-year-olds (mean age = 3 years:11 months pre-intervention; 111 female, 69% White) were assessed 5 months apart, with 103 children randomized to an integrated EF and mathematics intervention. We hypothesized that the intervention would improve mathematics scores more than practice-as-usual. Multi-level modelling and network analyses were applied to the data. The intervention group improved more than the control group in overall numeracy, even when we controlled for differences across settings in EF and mathematics enhancing practices. EF and mathematics measures showed greater interconnectedness between EF and mathematics post-intervention. In addition, disadvantaged children in the intervention group made greater gains than in the control group. Our findings emphasize the need to consider EFs in their integration with co-developing functions, and in their educational and socio-economic context.

The current study focused on the collaboration between cognitive scientists and educators to co-develop and progressively refine the Orchestrating Numeracy and The Executive (“The ONE”) Programme, an evidence-based integrated Executive Functions and Mathematics intervention composed of professional development and play-based activities. This iterative process resulted in high ratings of acceptability and feasibility, as well as acceptable adherence and fidelity across settings, combined with knowledge gains for early years practitioners and preliminary evidence of improved early numeracy, in particular for disadvantaged children. At the same time, the study highlighted general and specific barriers to intervention implementation in early years settings, and multiple possible steps for future refinement. Given the initial preliminary evidence, the intervention is being further evaluated in a larger scale trial funded by the Education Endowment Foundation and The Stronger Practice Hubs.

Background:Water and sanitation are vital to human health and well-being. While these factors have been studied in relation to health, very little has been done to consider such environmental risk factors with child development. Here, we investigated possible relations between household water access/storage and early childhood development in four low-income settlements in the City of Cape Town, Western Cape province of South Africa. Our objectives were 1) to determine water access/storage practices in dwellings of children; 2) to assess early childhood development; and 3) and to understand the relationship between water access/storage practices in relation to early childhood development. Methods:We used a questionnaire to assess household water risk factors and the International Development and Early Learning Assessment (IDELA) tool to assess child early learning / cognitive, socio-emotional and motor development. Results:Mean age of the children (N = 192) was 4 years and 55% were female. The mean IDELA score was 48% (range: 36-54%) where the higher the score, the better the child's development. Around 70% of households had a tap inside their dwelling and half said that they stored water with the largest percentage of storage containers (21%) being plastic/no lid. Child IDELA scores were lower for children living in households that did not have an indoor tap and for households who stored water. Conclusions:Given the risks associated with climate change and the already poor conditions many children face regarding water and sanitation, research is needed to further investigate these relations to provide evidence to support appropriate interventions and ensure healthy child development.

School readiness is highly salient in South Africa (SA), a country with extreme and persistent inequities that undermine early childhood development. The aim of this short-term longitudinal study was to identify social ecological factors influencing school readiness in young children from low-income settings in Cape Town, SA. Participants were 152 3-5-year-old children and their primary adult caregiver from low-income settings. Hierarchical linear regressions found that, compared to home- and community-level factors, child-level factors were the strongest predictors of scores on the International Development and Early Learning Assessment (IDELA, total and subscale scores for literacy, numeracy, social emotional and motor). At the child level, attending ECCE services was the strongest predictor, followed by early numeracy and age. Household socioeconomic status only predicted social emotional scores, and dysfunction in the parent-child relationship predicted literacy and total scores. These findings contribute to a contextually relevant understanding of school readiness in low-income SA settings.

A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond correlation to causality, failures of transfer from executive functions interventions are, we argue, highly problematic for both applied and theoretical reasons. We review the existing correlational and intervention literature at complementary neuroscientific, cognitive, developmental and educational levels. We appraise distinct theories of change underpinning the correlations between EF and early mathematics, as well as explicit or implicit theories of change for different types of EF interventions. We find that isolated EF interventions are less likely to transfer to improvements in mathematics than integrated interventions. Via this conceptual piece, we highlight that the field of EF development is in need of (1) a clearer framework for the mechanisms underpinning the relationships between early EF and other developing domains, such as mathematical cognition; (2) clearer putative theories of change for how interventions of different kinds operate in the context of EF and such domains; (3) and greater clarity on the developmental and educational contexts that influence these causal associations. Our synthesis of the evidence emphasises the need to consider the dynamic development of EFs with co-developing cognitive functions, such as early math skills, when designing education environments. [234 words].