ABSTRACT
The ability to understand and compare non‐symbolic (e.g., dot arrays) and symbolic (e.g., Arabic numerals) magnitudes is a critical foundation for learning math. A meta‐analysis has revealed that symbolic magnitude processing is a stronger predictor of math performance than non‐symbolic, but the evidence base is restricted almost entirely to countries in the Minority World. It is unclear how the strength of the associations between symbolic and non‐symbolic magnitude processing and math performance varies across contexts. An examination of cross‐national similarities and differences in foundational numeracy skills is sorely needed. In the present study, we examine the predictive nature of symbolic and non‐symbolic magnitude processing in school‐aged children from Ghana (n = 350) and Côte d'Ivoire (CIV; n = 342), two West African countries in the Majority World. Contrary to prior studies from countries in the Minority World, we found that non‐symbolic magnitude processing was a significant and unique predictor of math performance in 5‐ to 13‐year‐olds from Ghana. The strong association remains significant when controlling for symbolic magnitude processing, literacy, executive functioning, and socioemotional skills. A second preregistered study with participants from Côte d'Ivoire revealed the same pattern of results. These associations diverged from those that have been found in the Minority World and underscore the importance of taking a global perspective for understanding the cognitive precursors for math development. The data also highlight the potential use of the Numeracy Screener to measure children's understanding of numerical magnitude in classrooms around the world.
Keywords: math achievement, numerical magnitude processing, sub‐Saharan Africa
Summary
Non‐symbolic magnitude processing is a strong correlate of math abilities in children from Ghana and Côte d'Ivoire.
The associations remain significant even when controlling for symbolic magnitude processing, literacy, executive functioning, and socioemotional skills.
Our results are inconsistent with those found in the Minority World, suggesting that there is contextual variation in the development of early precursors important for math development.
1. Introduction
School entry numeracy skills are strong predictors of future academic success (Duncan et al. 2007; Romano et al. 2010). Despite growing rates of children accessing school around the world (e.g., World Bank 2018), a large portion of children from the Majority World1 who attend school fail to learn functional numeracy skills in the first 3 years of primary school (Sandefur 2018). In sub‐Saharan Africa specifically, fewer than one in five children attend any formal preprimary education (McCoy et al. 2018) thus limiting children's exposure to formal learning environments before entering first grade. With global education goals shifting from access to school to access to high‐quality education (United Nations 2015), improving early numeracy skills is critical to ensure improved learning outcomes. A deeper understanding of which foundational numeracy skills support math learning across diverse contexts, including settings where children have limited access to early learning opportunities, is essential for developing equitable and contextually relevant educational interventions.
1.1. Associations Between Numerical Magnitude Processing and Math Performance
Learning abstract mathematical concepts, like mental arithmetic, stems from a basic understanding of numerical magnitude expressed using non‐symbolic (e.g., collection of items) or symbolic representational formats (e.g., “five” or “5”). Symbolic representations of magnitude are inventions that require direct instruction to learn; learning their meaning is a gradual and challenging process (e.g., Sarnecka and Lee 2009; Göbel et al. 2011). In contrast, the capacity to represent and mentally combine non‐symbolic magnitudes is present at birth and shared across a variety of animal species. For example, human infants, preschool children who have not received formal training, and monkeys can perform approximate calculations using non‐symbolic magnitudes (Barth et al. 2005; Brannon and Terrace 1998; Brannon 2002; Cantlon et al. 2016; de Hevia et al. 2020; Libertus and Brannon 2009; Mccrink et al. 2017; Pica et al. 2004; Rugani et al. 2013; Xu and Spelke 2000). Moreover, human adults from non‐industrialized societies who have limited symbolic numerical systems show similar patterns of behavioral performance when discriminating between non‐symbolic magnitudes relative to adults from industrialized societies (Piazza et al. 2013; Pica et al. 2004). The ability to process symbolic and non‐symbolic numerical magnitudes is often assessed using comparison tasks. In such tasks, participants are presented with either two arrays of dots (non‐symbolic comparison task) or two Arabic numerals (symbolic comparison task) and asked to select the numerically larger magnitude. Accuracy and reaction time data are used as indices of the underlying precision of non‐symbolic and symbolic magnitude representations.
Given the hierarchical nature of mathematics, a compelling theory is that non‐symbolic magnitudes serve as ontogenetic and phylogenetic precursors for acquiring symbolic math skills (Dehaene 1997; Piazza et al. 2010). According to this view, children learn the meaning of symbolic numbers by automatically mapping them onto pre‐existing representations of approximate non‐symbolic magnitudes. Support for this proposal comes from cross‐sectional and longitudinal studies showing that children and adults who are more accurate at discriminating between non‐symbolic magnitudes tend to score higher on standardized assessments of symbolic math ability (Chu et al. 2015; Feigenson et al. 2013; Halberda et al. 2008; Libertus et al. 2011). Although studies have failed to find a significant association between non‐symbolic magnitude processing and symbolic math performance (e.g., Holloway and Ansari 2009; Mundy and Gilmore 2009; Sasanguie et al. 2013). Two recent meta‐analyses have confirmed there is indeed a small but significant relation between non‐symbolic magnitude processing and symbolic math skills (Chen and Li 2014; Schneider et al. 2016). Some training studies have found that children who practice comparing or computing approximate magnitudes show significant gains in symbolic math skills (e.g., Hyde et al. 2014; Park et al. 2016), suggesting that non‐symbolic magnitude representations play a foundational and potentially causal role in acquiring symbolic math.
The extent to which non‐symbolic magnitudes play a role in developing formal math skills remains contentious in the field (see Leibovich and Ansari 2016; Szűcs and Myers 2017; Wilkey and Ansari 2019, for reviews). For example, researchers have argued that the observed association found between non‐symbolic magnitude processing and math achievement may instead reflect domain‐general cognitive processes, such as inhibitory control (Leibovich and Ansari 2016; Fuhs and McNeil 2013; Gilmore et al. 2013; but see also Starr et al. 2017) and/or visual perceptual processing of dot stimuli (Gevers et al. 2016; but also see DeWind et al. 2015). Thus, tasks assessing non‐symbolic magnitude skills may tap into several component skills, undermining the claim that they isolate core numerical skills and challenging the proposal that approximate magnitude processing plays a foundational role in symbolic math development. Further challenging this claim, several training studies have failed to find a causal link between approximate magnitude processes and symbolic math performance (e.g., Bugden et al. 2021; Ferres‐Forga and Halberda 2020; Kim et al. 2018; Szkudlarek et al. 2021), including a recent meta‐analysis (Qiu et al. 2021).
Alternately, studies that have examined the unique contributions of non‐symbolic magnitude processing and symbolic number knowledge to math development have found that, while non‐symbolic skills show a weak association with symbolic math, symbolic number knowledge is a stronger predictor, prompting researchers to argue for a greater emphasis on developing early symbolic number skills. For example, Nosworthy et al. (2013) found that the association between non‐symbolic magnitude processing, assessed using the Numeracy Screener (www.numeracyscreener.org)—paper and pencil non‐symbolic and symbolic comparison tasks—and arithmetic performance was no longer significant once they accounted for other variables, such as working memory, reading, and symbolic magnitude skills. Hawes and colleagues (2019) additionally found that symbolic comparison performance assessed using the Numeracy Screener (Nosworthy et al. 2013), in kindergarten predicted teacher‐assigned math grades in first grade. In contrast, non‐symbolic comparison performance was not a significant predictor of math grades (Hawes et al. 2019). These studies suggest that symbolic magnitude processing skills are a stronger predictor of math abilities (relative to non‐symbolic magnitude processing). This pattern of results has been corroborated in longitudinal studies showing that symbolic comparison performance at school entry is a stronger predictor of future math achievement (Xenidou‐Dervou et al. 2017) and future symbolic numerical skills (Lyons et al. 2018; Matejko and Ansari 2016) even when controlling for non‐symbolic magnitude processes. Compared to the research findings on non‐symbolic magnitude processing, there is stronger and more consistent evidence to support the proposition that symbolic magnitude skills play a more important role in developing math abilities. However, almost all of the studies exploring whether symbolic and non‐symbolic magnitude processes are foundational for developing formal math skills come from the Minority World. The associations between non‐symbolic and symbolic magnitude representations and symbolic math development across diverse countries and contexts (i.e., diverse learning environments and situational settings, including exposure to numbers in daily life) have been largely overlooked in the literature. It remains an open question to what extent the link between non‐symbolic magnitude representations and symbolic mathematics is universal across different cultures.
1.2. Symbolic and Non‐Symbolic Comparison Skills Across Cultures
Researchers have explored whether the unique associations between non‐symbolic and symbolic magnitude processing and arithmetic skills vary across different countries. Rodic et al. (2015) collected samples from China, the United Kingdom, Russia, and Kyrgyzstan. They found that symbolic comparison accounted for significant unique variance in arithmetic skills in all countries. Non‐symbolic comparison performance was not a unique correlate of arithmetic performance. Similarly, Tavakoli (2016) found that symbolic comparison performance measured using the Numeracy Screener in a large sample of second‐grade boys from Iran was a unique correlate of speeded and non‐speeded calculation skills when controlling for non‐symbolic comparison performance, working memory, processing speed, and long‐term memory. Consistent with the findings from Canadian samples using the Numeracy Screener (Hawes et al. 2019; Nosworthy et al. 2013), non‐symbolic comparison performance was not a significant correlate of arithmetic skills. These studies suggest that symbolic magnitude skills are an important foundation for acquiring symbolic arithmetic across different cultures.
1.3. Contextual Variation in Numerical and Math Development
Studies exploring the development of symbolic and non‐symbolic magnitude skills, as well as their associations with math achievement, are predominantly studied in the Minority World. Cross‐cultural research is therefore essential for testing whether the mechanisms underlying math development generalize beyond findings that stem from the Minority World (Henrich et al. 2010; Nielsen et al. 2017). There are several lines of evidence to suggest that sociocultural and educational contexts may influence numerical and mathematical development. One line of evidence comes from international comparisons that have consistently found that Asian students outperform students from Europe and the United States on general numerical and mathematical tests (e.g., Imbo and LeFevre 2009; Siegler and Mu 2008). Beyond cross‐cultural comparisons, the home math environment, which includes parents engaging in math‐specific activities and dialogue with their children, as well as their attitudes and beliefs about math, is associated with children's math achievement (e.g., Daucourt et al. 2021), suggesting that children's home experiences influence math development.
The transition to formal schooling also has a significant impact on the development of arithmetic and symbolic magnitude skills, independent of age‐related maturational changes (Vandecruys et al. 2025). While the ability to discriminate between non‐symbolic magnitudes has been considered universal across species and cultures (Dehaene 1997; Pica et al. 2004), Rodic et al. (2015) found that children from Russia and China outperformed children from the United Kingdom and Kyrgyzstan on the non‐symbolic comparison task. Similarly, Piazza et al. (2013) found that education level, more than age, predicted non‐symbolic comparison performance in an Indigenous group. Taken together, these findings provide support for the idea that culture and education shape both non‐symbolic and symbolic math development.
The broad aim of our study is to explore the associations between symbolic and non‐symbolic numerical magnitude processing and general math abilities in children from two Majority World countries in West Africa, where cultural and educational contexts differ from previously studied countries and where research is sorely lacking (Nielsen et al. 2017).
1.4. Education in Sub‐Saharan Africa
Compared to other Majority World regions, sub‐Saharan Africa has the largest proportion of children living in poverty and that are stunted, with some of the poorest learning outcomes globally (Angrist et al. 2021). Although global progress has been made to improve early childhood educational access, concerns about poor quality persist (Yoshikawa et al. 2018). Since 2000, the percentage of primary school children unenrolled in sub‐Saharan Africa has declined from 40% to 22% (UIS Data Center—UNESCO Institute for Statistics). Yet, many children and adolescents within the classroom are not achieving basic numeracy and literacy skills (Sandefur 2018). One way to improve learning outcomes is to supply teachers with feasible evidence‐informed screening tools for the classroom so they can monitor their students’ progress. Teachers who can identify gaps in their students’ learning can adapt their lesson plans and allocate already limited resources to the students who need them most (Linzarini et al. 2022). The first step to achieving this goal is to examine the underlying mechanisms that support math development across diverse sociocultural contexts.
1.5. The Ghanaian and Ivorian Contexts
We addressed this gap in the literature by conducting two studies exploring the foundational numeracy skills important for math learning in children from two Majority World countries: Ghana (Study 1) and Côte d'Ivoire (CIV; Study 2). While our study samples come from two neighboring countries in West Africa, Ghana and CIV provide an interesting point of comparison within the West African context. In 2004, the government in Ghana adopted the National Early Childhood Care and Development Policy, which highlighted access to quality early education as central to improving ECD and learning as well as to reducing inequalities in learning outcomes. In 2007, 2 years of preprimary education—called kindergarten 1 (KG1; the equivalent to pre‐K in the United States) and kindergarten 2 (KG2; the equivalent to kindergarten in the United States), respectively—were added to the universal basic education system that had previously begun in the first grade of primary school. Ghana has among the highest enrollment in preprimary school across the continent, with gross enrollment2 at 116% (World Bank 2020) and primary school gross enrollment rates at 98.2% (World Bank 2024). Despite high enrollment rates among school‐aged children in Ghana, learning outcomes remain slow. For instance, 70% of second‐grade students and 80% of fourth‐grade students are unable to read simple words or perform basic arithmetic problems (World Bank 2018). Our sample in Ghana is drawn from the Greater Accra region and is urban and peri‐urban and is the most densely populated and fastest‐growing region in the country. It holds significant diversity in terms of economic, linguistic, and ethnic groups (Ghana Statistical Service 2022).
On the other hand, CIV is a francophone lower‐middle‐income country with a similarly sized population of 31 million (World Bank 2024). CIV does not have a universal preprimary school system and has very low rates of preprimary school enrollment at 10.7% gross enrollment (World Bank 2022) but high rates of primary school gross enrollment at 93.3% (World Bank n.d.). Côte d'Ivoire ranks among the bottom 30 countries globally in learning outcomes (Angrist et al. 2021), with large inequalities between urban and rural regions (PASEC 2020). Our sample in Côte d'Ivoire is drawn from rural cocoa‐farming communities in the Aboisso and Bouaflé regions of Côte d'Ivoire. Thirty‐eight percent of children reported working in cocoa production to support their family's economic well‐being. Reports were higher among children living in rural areas (Lichand and Wolf 2025). Higher child employment is associated with higher school dropout rates and lower test scores (Lichand and Wolf 2025; Sadhu et al. 2020). Among primary schoolchildren in CIV, 19% of students in Aboisso met or exceeded the minimum proficiency level in reading, and 18% did so in math. In Bouaflé, only 9.4% achieved the minimum level in reading and 7% in numeracy. Together, these two samples from Ghana and CIV offer a valuable opportunity to examine the associations among non‐symbolic and symbolic magnitude processing skills and math readiness in children from two neighboring yet culturally distinct West African countries.
1.6. The Current Study
Study one was an exploratory investigation to examine whether individual differences in non‐symbolic and symbolic magnitude processing were associated with symbolic math performance in primary school children from Ghana. We administered the Numeracy Screener (www.numeracyscreener.org), which is an easy‐to‐use, free paper‐and‐pencil assessment tool designed to measure non‐symbolic and symbolic numerical magnitude knowledge across different educational contexts. In the symbolic condition, children compared pairs of Arabic numerals (e.g., “3 and 5”) and indicated which is larger, while in the non‐symbolic condition, they compared pairs of dot arrays. The Numeracy Screener has been shown to be a reliable and valid predictor of math achievement in Minority World contexts (Hawes et al. 2019; Nosworthy et al. 2013). Therefore, we examined whether performance on the Numeracy Screener was associated with performance on the Early Grade Math Assessment (EGMA; RTI International 2009a), a standardized tool developed to assess foundational math readiness skills in early primary school children, particularly in low‐ and middle‐income country contexts. Drawing on prior findings using the Numeracy Screener (e.g., Hawes et al. 2019; Nosworthy et al. 2013; Tavakoli 2016) and the strong emphasis placed on symbolic magnitude knowledge for developing math skills, our exploratory hypothesis is that symbolic comparison performance would explain unique variance in math readiness scores when controlling for non‐symbolic comparison performance. After completing Study 1, we conducted a second preregistered study in Côte d'Ivoire to examine whether the pattern we observed in Ghana could be replicated in a neighboring but different regional and educational context.
2. Study 1 in Ghana
2.1. Methods
2.1.1. Participants
Three hundred sixty‐nine children from Ghana participated in the study and were in either the first or second‐grade of primary school. Children were removed from the final data analyses if they obtained a score of 0 on either the symbolic or non‐symbolic conditions of the numeracy screener (n = 19). None of the children reached ceiling performance. The final sample included 350 children (male, n = 189; female, n = 159; unknown = 2). Accurate age data was difficult to obtain because families do not have birth certificates or track birthdays in the same way as is typical in Western contexts. Of the 350 children, we were able to collect age information using school records for 274 participants. Children were between 5 and 13 years of age (M age = 7.68 years, SD = 1.33). Children were sampled at the end of the school year and therefore had between 3 and 4 years of formal school.
2.1.2. Materials
2.1.2.1. Math Skills
Early numeracy and arithmetic skills were assessed using the EGMA (RTI International 2009a). The EGMA is an oral assessment of early numeracy and arithmetic operations. The Number Identification, Quantity Discrimination, Addition, Subtraction, Word Problems, and Missing Number subtests were administered (Cronbach's α = 0.87). Across all subtests, if children spent more than five seconds on one item, they were asked to move onto the next trial. Administration of a subtest ended when they made four successive errors. A score was calculated by computing a mean percent correct for each subtest. Participants’ math performance was calculated by computing a mean percent correct across all six math subtests.
Number Identification. The Number Identification subtest consists of 20 items that require children to identify increasingly larger single‐, double‐, and triple‐digit numerals. Children were presented a card with all the numerals on it and asked to point to each number and tell the experimenter what it is. Children were given one minute to complete as many items as they could.
Quantity Discrimination. Children were presented with pairs of either single‐, double‐, or triple‐digit numerals and asked to indicate which number was bigger. They were first given two practice trials with feedback, followed by 10 test trials. Five trials were shown on a stimulus card at a time. Children were given unlimited time to complete the test.
Addition and Subtraction. Children were shown a stimulus card 10 addition problems and asked to say the answer for each problem. If they did not know the answer, they were asked to skip it and move on to the next problem. When the first 10 problems were completed, they were given the next stimulus card with 10 more problems. The addition problems increased in difficulty, whereby the second half of the problems included double‐digit numerals. Children were given one minute to complete as many problems as they could. Participants were given paper, pencils, and counters if needed. The subtraction subtest was similar to the addition, but instead children completed subtraction problems.
Word Problems. Children were asked to solve verbally presented math story problems (e.g., There are 5 seats on the bus, and there are 2 children on each seat. How many children are on the bus altogether?). Children were given two practice trials with feedback, followed by six test problems. Children were given unlimited time to calculate the solution, as well as paper, pencil, and counters in case they were needed.
Missing Number. Children were presented with three numerals, with a space indicating a missing number in the sequence (e.g., 1, 2 __, 4 “Here are some numbers one, two and four”), and were asked what to identify the number that completes the missing part of the sequence (e.g., “What number goes here?”). Single, double, and triple‐digit numeral sequences were administered in increasingly more difficult order. A total of 10 test trials were administered. Five trials were presented on a stimulus card at one time. Children were given unlimited time to complete the test.
2.1.2.2. Literacy Skills
Literacy skills were measured across five domains of literacy, and preliteracy skills were measured primarily with the Early Grade Reading Assessment (EGRA; RTI International 2009b). Children completed an oral vocabulary task where they were presented with pictures of objects and asked to name them (8 items). To assess listening comprehension, the experimenter read a short story aloud and asked the participants three questions related to its content. Letter‐sound identification was assessed by asking children to produce the sounds of visually presented letters. Children also completed a nonword decoding task where they were presented with made‐up words in English and asked to read as many as they could. Across all subtests from the EGRA, with the exception of listening comprehension, children were given 60 seconds to answer as many items as they could correctly. A measure of phonological awareness from the International Development and Early Learning Assessment (IDELA; Pisani et al. 2018) was also included. In this task, children were presented with a target word and asked to select which of three options began with the same initial sound (e.g., moon starts with /m/; which one starts with /m/: pig, ball, or mouse?). The percent correct for each domain was computed, and the scores for each domain were averaged to create a total score (Cronbach's α = 0.76).
2.1.2.3. Executive Function
Working memory was assessed using the forward digit span. Children were asked to repeat sequences of numbers in the same order they were heard. The task increased in difficulty by adding one digit to each subsequent sequence (7 items). Cognitive flexibility was measured using an adapted version of the Dimensional Change Card Sort–Border version (Zelazo 2006; 12 items). Children sorted cards based on either shape or color. In the border version of the task, the sorting rule was by the presence or absence of a border around the card. Inhibitory control was assessed using an adapted version of the number Stroop task. In this task, children are shown a set of boxes with one to four repeating numbers (e.g., 1111, 44) and are asked to report how many numbers are in each box (see Obradović et al. 2019; 21 items). Finally, reaction time was assessed using the executive function Touch Bubbles ask, which was adapted to the Kenyan context (see Willoughby et al. 2019; 20 items) and piloted in Ghana. In this task, a series of blue bubbles was presented on a tablet, one at a time, and children were instructed to “pop” each bubble as fast as they could. The mean reaction time across all correctly answered items was used to index simple reaction time. To create an overall executive function score, the proportion correct for each domain was computed (Cronbach's α = 0.45 for the composite executive function score).
2.1.2.4. Socioemotional Skills
Socioemotional skills were measured using the IDELA subscale (Pisani et al. 2018) with 14 items grouped into five constructs: self‐awareness, emotion identification, perspective taking and empathy, friendship, and conflict and problem solving. For example, children were asked to identify something that makes them sad, what they do to feel better when they are feeling sad, and lastly, what makes them feel happy. They were also shown a picture of an upset girl and were told to imagine that the girl was his/her friend and to identify how the girl in the picture was feeling. They were next asked how they would help her feel better and whether there is anything else they would do for her. Participants could obtain a score up to three. In the sharing and conflict‐solving assessment, participants were told that they have one toy, but another child wanted to play with it, and they were asked what they would do. Participants received a score depending on whether they indicated that they would share (2), avoid conflicts (1), or provided an inappropriate response (0) Participants could obtain a maximum score of 6. Socioemotional skills are defined as the mean percent correct across subtests (Cronbach's α = 0.67).
2.1.2.5. Symbolic and Non‐Symbolic Numerical Magnitude Processing
Symbolic and non‐symbolic numerical magnitude processing were assessed using the Numeracy Screener. Children were presented with a booklet containing pairs of either single‐digit numerals (e.g., symbolic) or dot arrays (non‐symbolic) and asked to cross out the numerically larger quantity as quickly and accurately as possible. They were given one minute for each condition. The side of the larger magnitude was counterbalanced across trials. In the non‐symbolic condition, density and area were controlled across trials. To control for area and density, half of the trials were equated for total surface area, and the other half were equated for total perimeter. Many studies have found that dot discrimination is influenced by the visual‐spatial parameters of the stimuli. Therefore, to minimize reliance on such visual spatial cues, the sizes of the dots were heterogeneous within each array, and the order of perimeter‐matched and area‐matched trials was administered in a random set sequence. The order of stimuli varied slightly across conditions so that the order of presentation was not identical; however, they both began with easier pairs (small ratio; calculated small number: large number) and got increasingly more difficult by increasing the ratio between the pairs. Half the participants completed the symbolic condition first, followed by the non‐symbolic comparison, and vice versa. The Cronbach's for the non‐symbolic and symbolic conditions were α = 0.89 and α = 0.90, respectively. Test‐retest reliability has been previously reported in Hawes et al. (2019). The correlation for symbolic comparison (r = 0.72) and non‐symbolic comparison (r = 0.61) when tested on average 89.55 days apart (Hawes et al. 2019). Test‐retest reliabilities are similar to the SYMP test (Brankaer et al. 2017). Raw scores were the total number of correct trials completed within one minute for the symbolic and non‐symbolic conditions separately. We followed the procedure applied in Lyons et al. (2018) to compute an adjusted score in order to account for guessing in a timed assessment (Rowley and Traub 1977). The following formula was used to calculate the adjusted scores, where C is the total number of items correct, E is the total number of errors, and T is the total number of trials in the assessment Adj = C − E/(T − 1). Mean adjusted scores are reported in Figure 1.
FIGURE 1.
Mean symbolic and non‐symbolic comparison adjusted scores in the sample of children from (a) Ghana and (b) Côte d'Ivoire.
2.1.3. Procedures
Data come from an impact evaluation study of the Quality Preschool for Ghana project (Wolf et al. 2019a; Wolf et al. 2019b), which tested the impacts of a teacher in‐service training and parental‐awareness program in six districts in the Greater Accra Region of Ghana. In the summer of 2015, schools (n = 240) were randomly assigned to one of three treatment arms: (a) teacher training and coaching (82 schools), (b) teacher training and coaching plus parental awareness meetings (79 schools), and (c) a control group (79 schools). Impacts of the program have been presented in other papers (Wolf and Peele 2019; Wolf et al. 2019a; Wolf et al. 2019b). In this study, we use data from the third follow‐up collected in June 2018.
All schools in the six districts were identified using the Ghana Education Service Educational Management Information System (GES‐EMIS) database, which listed all registered schools in the country. Eligible schools had to be registered with the government and have at least one KG class. Schools were randomly sampled from the list, stratified by district and within districts by public and private schools. A school census was then conducted to confirm the presence of each school and to obtain information on each school's head teacher and proprietor. Because there were fewer than 120 public schools across the six districts (n = 108), every public school was sampled. Private schools (490 total) were sampled within districts in proportion to the total number of private schools in each district relative to the total for all districts (n = 132).
Children were then sampled within each school. Class rosters for all KG classrooms were collected, and an average of 15 children (eight from KG1 and seven from KG2) were randomly selected from each roster to participate in direct assessments. If a school had fewer than 15 kindergarten children enrolled across both classrooms, all children were selected. For schools with only one KG classroom, 15 children were randomly sampled from the classroom. At baseline, the total sample of children was 3,435 children, with an average of 14.3 children per school (range = 4–15). Children (49.5% female) were, on average, 5.2 years old at baseline (SD = 1.2; for KG1, M = 4.8, SD = 1.1; and for KG2, M = 5.7, SD = 1.2). These children were followed at each subsequent wave of data collection. At the 3‐year follow‐up (n = 2,421), children were on average 7.8 years old. In this study, a random sub‐sample of the 3‐year follow‐up was selected, stratified by treatment status, and administered the Numeracy Screener. Children who completed the Numeracy Screener did not significantly differ from the larger sample on measures of literacy, numeracy, socioemotional, and executive function skills (p values range: 0.17–0.71; BF10 ranges: 0.07–0.16; see Supplemental Analyses 1). All assessments were administered directly to children in their school. Data collectors were trained for 5 days and 2 additional days of field practice. They were from the local communities and spoke the local language. Assessments were translated and administered in their local language.
2.1.4. Analysis Plan
Frequentist statistics were carried out using R statistical software, and Bayesian statistics were carried out using JASP (V 0.18.3; JASP 2024). Across both studies, initial t‐tests and bivariate correlations were conducted to examine differences in performance between the symbolic and non‐symbolic conditions of the Numeracy Screener, as well as their associations with our measures of math, literacy, socioemotional, and executive function skills. Bayesian statistics are reported for bivariate correlations and t‐tests to evaluate the relative strength for or against the observed associations or differences (Lakens et al. 2020). Bayes factor (BF10) is a ratio of the likelihood of data fitting the alternative hypothesis relative to the null hypothesis (BF01 is the inverse and provides support for the null relative to the alternative hypothesis). We conducted a series of multiple regression analyses to test our main research question examining the unique associations between symbolic and non‐symbolic magnitude processing and math performance (model 1) while accounting for socioemotional (model 2), literacy (model 3), and executive function (model 4) skills. Gender was included as a covariate in all models. Next, we conducted multiple regression analyses to test the unique contributions of symbolic and non‐symbolic magnitude processing to performance on each of the individual subtests from the EGMA, controlling for socioemotional, literacy, and executive functioning skills. We preregistered and repeated the same analyses for Study 2 that was conducted in Côte d'Ivoire to examine the generalization of the results in Ghana.
2.2. Results
Descriptive statistics, Pearson correlations, and Bayes factors of the raw scores across all dependent measures administered in Ghana are reported in Table 1. In order to test whether there were performance differences between the symbolic and non‐symbolic comparison tasks from the Screener, we conducted paired samples t‐tests and found that children from Ghana were significantly more accurate in symbolic comparison (M = 23.43) relative to non‐symbolic comparison (M = 22.21), t(349) = 3.39, p = 0.0008, 95% CI [0.51, 1.91], d = 0.18, BF10 = 16.5 (see Figure 1a). The Bayes factor demonstrates that differences in accuracy between symbolic and non‐symbolic comparison tasks are 16.5 times more likely than finding no difference in accuracy.
TABLE 1.
Descriptive statistics, bivariate correlation matrix, and Bayes factors.
| Study 1 in Ghana | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mean | SD | Skew | Kurt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
| 1 | Numeracy screener | 45.67 | 17.37 | 0.05 | −0.26 | r | 0.93 ** | 0.93 ** | 0.46 ** | 0.39 ** | 0.26 ** | 0.30 ** | |
| 95% CI | 0.92, 0.95 | 0.92, 0.95 | 0.38, 0.54 | 0.30, 0.47 | 0.16, 0.36 | 0.20, 0.39 | |||||||
| BF10 | ∞ | ∞ | 1.09e17 | 1.13e11 | 1.26e4 | 7.78e5 | |||||||
| 2 | Symbolic | 23.43 | 9.23 | −0.15 | −0.46 | r | 0.74 ** | 0.33 ** | 0.28 ** | 0.20 ** | 0.20 ** | ||
| 95% CI | 0.67, 0.78 | 0.25, 0.43 | 0.18, 0.37 | 0.11, 0.31 | 0.11, 0.31 | ||||||||
| BF10 | 1.12e59 | 3.932e7 | 6.87e4 | 60.70 | 92.71 | ||||||||
| 3 | Non‐symbolic | 22.21 | 9.38 | 0.28 | 0.23 | r | 0.53 ** | 0.45 ** | 0.29 ** | 0.36 ** | |||
| 95% CI | 0.45, 0.60 | 0.36, 0.53 | 0.19, 0.38 | 0.26, 0.44 | |||||||||
| BF10 | 9.29e23 | 2.66e15 | 2.42e5 | 1.06e9 | |||||||||
| 4 | Math (EGMA) | 0.49 | 0.17 | −0.32 | −0.40 | r | 0.71 ** | 0.36 ** | 0.51 ** | ||||
| 95% CI | 0.65, 0.76 | 0.26, 0.45 | 0.43, 0.58 | ||||||||||
| BF10 | 2.47e51 | 1.23e9 | 2.6e21 | ||||||||||
| 5 | Literacy | 0.53 | 0.17 | −0.45 | −0.49 | r | 0.40 ** | 0.49 ** | |||||
| 95% CI | 0.31, 0.49 | 0.40, 0.56 | |||||||||||
| BF10 | 9.12e11 | 1.18e19 | |||||||||||
| 6 | Socioemotional | 0.66 | 0.14 | −0.64 | 0.36 | r | 0.31 ** | ||||||
| 95% CI | 0.21, 0.40 | ||||||||||||
| BF10 | 2.84e5 | ||||||||||||
| 7 | Executive function | 0.69 | 0.09 | −0.18 | 0.70 | ||||||||
Note: Literacy, socioemotional and executive function skills are mean percent correct. Significance levels are indicated as follows: p < 0.0023** Bonferroni corrected significance; p < 0.01*; p < 0.05†. BF10 represents the Bayes factor in support of the alternate hypothesis over the null. Interpretation of BF10 values is as follows: 0–3 indicates weak evidence for an association, 3–20 indicates positive support, 20 and 150 indicates strong support, and values greater than 150 indicate very strong evidence in favor of an association (Jeffreys 1961).
Abbreviations: CI = confidence interval, Kurt = kurtosis, M = mean, SD = standard deviation, Skew = skewness.
As seen in Table 1, we found significant positive associations between the adjusted scores of the Numeracy Screener and school readiness measures of math, socioemotional, literacy, and executive functioning skills. Bayesian correlation analyses resulted in Bayes factors that are greater than 150, which, according to Jeffreys (1981) criteria, provides strong evidence for the association between Numeracy Screener scores and our school readiness measures. In particular, we found that non‐symbolic comparison, r(348) = 0.53, and symbolic comparison, r(348) = 0.33, significantly correlated with the composite math score calculated from the EGMA (see Figure 2a,b). A Steiger's test revealed that the correlation between non‐symbolic number comparison and math composite scores was significantly stronger than the correlation between symbolic comparison and math composite scores, z = 6.2, p < 0.0001.
FIGURE 2.
Scatterplots of the relationship between non‐symbolic (a) and symbolic number comparison (b) adjusted scores and mean percent correct on the EGMA in the Ghana sample. Scatterplots showing the relationship between non‐symbolic (d) and symbolic number comparison (d) adjusted scores and mean percent correct on the EGMA in the Côte d'Ivoire sample. Note: In Ghana the mean percent correct was calculated across all subtests administered from the EGMA, including Missing Number, Number Identification, Addition, Subtraction, Word Problems, and Quantity Comparison. In Côte d'Ivoire the mean percent correct was calculated across a subset of the subtests from the EGMA: Missing Number, Number Identification, Addition, and Subtraction.
2.2.1. The Unique Associations Between Symbolic and Non‐Symbolic Comparison and Math Performance
We found that performance on both subtests of the Numeracy Screener significantly correlated with all of our measures of school readiness. To test the unique association between non‐symbolic numerical magnitude processing and math abilities, we ran a series of hierarchical regression analyses to control for symbolic numerical processing (step 1), socioemotional (step 2), literacy (step 3), and executive function skills (step 4) in children from Ghana. In the first model, we first tested whether symbolic and non‐symbolic comparison accounted for unique variance in math abilities (model 1). Contrary to our hypotheses, based on the results from Canada, we found that non‐symbolic number comparison was the only variable that accounted for significant unique variance in math performance (see Table 2). Symbolic and non‐symbolic comparison from the Numeracy Screener account for 28% of the variance in math composite scores. We next tested whether the association between non‐symbolic comparison performance and math ability remained significant when accounting for the variance associated with socioemotional skills (model 2), literacy skills (model 3), and executive function skills (model 4). Even when controlling for individual differences in socioemotional, literacy, and executive function skills, non‐symbolic comparison accounted for significant unique variance in math abilities (see Table 2). In other words, more proficient non‐symbolic magnitude skills were associated with higher math composite scores, even when controlling for symbolic number processing, socioemotional, literacy, and executive functioning skills. We also found that literacy and executive functioning were significant, positive, unique correlates of math performance. Notably, non‐symbolic, literacy and executive functioning skills remained significant correlates after controlling for age in the subset of children for whom age data were available (see Supplementary Analysis 2).
TABLE 2.
Multiple regression analyses predicting symbolic math abilities.
| Variable | Models predicting EGMA scores in Ghana | Models predicting EGMA scores in Côte d'Ivoire | ||||
|---|---|---|---|---|---|---|
| Model 1 | B | SEβ | β | B | SEβ | β |
| Intercept | 0.30 *** | 0.02 | 0.10 *** | 0.02 | ||
| Male | −0.01 | 0.02 | −0.04 | 0.03 | 0.02 | 0.08 |
| Non‐symbolic | 0.01 *** | 0.001 | 0.63 *** | 0.02 *** | 0.002 | 0.57 *** |
| Symbolic | −0.003 | 0.001 | −0.14 * | 0.000 | 0.002 | 0.02 |
| R 2 | 0.29 | 0.35 | ||||
| Adjusted R2 | 0.28 | 0.34 | ||||
| F(df) | 46.95 (3, 344) ** | 59.38 (3, 338) *** | ||||
| Model 2 | B | SEβ | β | B | SEβ | β |
|---|---|---|---|---|---|---|
| Intercept | 0.16 *** | 0.04 | 0.02 | 0.03 | ||
| Male | −0.01 | 0.02 | −0.02 | .03 * | 0.02 | 0.09 * |
| Non‐symbolic | 0.01 *** | 0.001 | 0.57 *** | 0.02 *** | 0.002 | 0.51 *** |
| Symbolic | −0.002 | 0.001 | −0.13 * | 0.000 | 0.002 | 0.02 |
| Socioemotional | 0.25 *** | 0.05 | 0.22 *** | 0.15 *** | 0.03 | 0.22 *** |
| R 2 | 0.33 | 0.39 | ||||
| Adjusted R2 | 0.33 | 0.38 | ||||
| F(df) | 43.04 (4, 343) *** | 53.86 (4, 337) *** | ||||
| Model 3 | B | SEβ | β | B | SEβ | β |
|---|---|---|---|---|---|---|
| Intercept | 0.06 | 0.03 | 0.06 * | 0.02 | ||
| Male | 0.003 | 0.01 | 0.008 | 0.03 * | 0.02 | 0.08 * |
| Non‐symbolic | 0.006 *** | 0.001 | 0.32 *** | 0.009 *** | 0.001 | 0.30 *** |
| Symbolic | −0.001 | 0.000 | −0.07 | 0.001 | 0.001 | 0.04 |
| Socioemotional | 0.06 | 0.05 | 0.05 | 0.03 | 0.03 | 0.04 |
| Literacy | 0.55 *** | 0.04 | 0.57 *** | 0.62 *** | 0.06 | 0.49 *** |
| R 2 | 0.57 | 0.54 | ||||
| Adjusted R2 | 0.56 | 0.53 | ||||
| F(df) | 88.77 (5, 342) *** | 79.05 (5, 336) *** | ||||
| Model 4 | B | SEβ | β | B | SEβ | β |
|---|---|---|---|---|---|---|
| Intercept | −11 * | 0.05 | −0.02 | 0.03 | ||
| Male | 0.006 | 0.01 | 0.02 | 0.03 * | 0.01 | 0.09 * |
| Non‐symbolic | 0.005 *** | 0.001 | 0.28 *** | 0.008 *** | 0.001 | 0.28 *** |
| Symbolic | −0.001 | 0.001 | −0.06 | 0.000 | 0.001 | 0.02 |
| Socioemotional | 0.04 | 0.04 | 0.04 | 0.01 | 0.03 | 0.02 |
| Literacy | 0.49 *** | 0.04 | 0.51 *** | 0.53 *** | 0.06 | 0.42 *** |
| Executive function | 0.32 *** | 0.08 | 0.16 *** | 0.24 *** | 0.07 | 0.17 *** |
| R 2 | 0.58 | 0.56 | ||||
| Adjusted R2 | 0.58 | 0.55 | ||||
| F(df) | 79.73 (6, 341) *** | 70.73 (6, 335) *** | ||||
Note: In Ghana the mean percent correct was calculated across all subtests administered from the EGMA, including Missing Number, Number Identification, Addition, Subtraction, Word Problems, and Quantity Comparison. In the Côte d'Ivoire the mean percent correct was calculated across the subtests administered from the EGMA, including Missing Number, Number Identification, Addition, and Subtraction.
* p < 0.05; ** p < 0.01; *** p < 0.001.
2.2.2. The Relationship Between Symbolic and Non‐Symbolic Comparison and Individual Subtests From the EGMA
To further probe the nature of the association between performance on the non‐symbolic comparison task and symbolic math abilities, we next tested whether individual differences in non‐symbolic and symbolic number comparison accounted for unique variance in predicting individual subtest scores from the EGMA. We were also interested in testing whether the symbolic number comparison task accounted for unique variance in particular subtests of the EGMA. We ran multiple regression analyses with each subtest as the dependent measure. We included literacy, socioemotional, and executive function skills as covariates in the models. Non‐symbolic comparison accounted for unique variance in Quantity Discrimination, Addition, and Subtraction performance. Symbolic comparison performance accounted for significant unique variance in word problem‐solving skills. Neither symbolic nor non‐symbolic comparison performance accounted for unique variance in performance on the Missing Number subtest (see Table 3). We also found that literacy skills significantly predicted performance on all math subtests in the EGMA, while executive functioning skills significantly account for unique variance in the Missing Number, Addition, Subtraction, and Word Problem Solving subtests from the EGMA. A closer examination of the standardized beta coefficients revealed that literacy, followed by non‐symbolic comparison skills, was the strongest predictor of most subtests, except for the Subtraction and Word Problems subtests. Non‐symbolic comparison performance was the strongest predictor of subtraction skills. Symbolic comparison performance was a significant correlate of word problem‐solving skills, while non‐symbolic comparison was not.
TABLE 3.
The unique associations between symbolic and non‐symbolic comparison and individual subtests from the Early Grade Math Assessment in Ghana.
| Variable | Numeral identification | Missing number | ||||
|---|---|---|---|---|---|---|
| B | SEβ | β | B | SEβ | β | |
| Intercept | 0.13 | 0.08 | −0.12 ** | 0.01 | ||
| Male | −0.008 | 0.02 | −0.02 | −0.000 | 0.02 | −0.000 |
| Non‐symbolic | 0.004 ** | 0.002 | 0.18 ** | 0.004 * | 0.001 | 0.13 * |
| Symbolic | −0.002 | 0.001 | −0.06 | −0.001 | 0.001 | −0.06 |
| Socioemotional | 0.01 | 0.07 | 0.01 | 0.000 | 0.06 | 0.000 |
| Literacy | 0.76 *** | 0.06 | 0.58 *** | 0.45 *** | 0.06 | 0.42 *** |
| Executive function | 0.18 | 0.12 | 0.07 | 0.24 * | 0.11 | 0.11 * |
| R 2 | 0.48 | 0.32 | ||||
| Adjusted R2 | 0.47 | 0.31 | ||||
| F(df) | 53.16 (6, 341) *** | 27.12 (6, 341) *** | ||||
| Variable | Addition | Subtraction | ||||
|---|---|---|---|---|---|---|
| B | SEβ | β | B | SEβ | β | |
| Intercept | −0.27 *** | 0.08 | −0.36 *** | 0.07 | ||
| Male | −0.01 | 0.02 | −0.01 | 0.01 | 0.02 | 0.02 |
| Non‐symbolic | 0.01 *** | 0.002 | 0.30 *** | 0.01 *** | 0.001 | 0.33 *** |
| Symbolic | −0.002 | 0.001 | −0.09 | −0.003 * | 0.001 | −0.15 * |
| Socioemotional | −0.01 | 0.07 | −0.01 | 0.07 | 0.06 | 0.06 |
| Literacy | 0.46 *** | 0.07 | 0.37 *** | 0.33 *** | 0.06 | 0.30 *** |
| Executive function | 0.50 *** | 0.12 | 0.20 *** | 0.49 *** | 0.11 | 0.22 *** |
| R 2 | 0.41 | 0.39 | ||||
| Adjusted R2 | 0.40 | 0.38 | ||||
| F(df) | 40.19 (6, 341) *** | 36.77 (6, 341) *** | ||||
| Variable | Quantity discrimination | Word problem solving | ||||
|---|---|---|---|---|---|---|
| B | SEβ | β | B | SEβ | β | |
| Intercept | 0.14 | 0.10 | −0.20 * | 0.08 | ||
| Male | 0.03 | 0.02 | 0.02 | 0.02 | 0.04 | |
| Non‐symbolic | 0.01 ** | 0.002 | 0.23 ** | 0.002 | 0.002 | 0.10 |
| Symbolic | −0.002 | 0.002 | −0.08 | 0.004 * | 0.001 | 0.17 * |
| Socioemotional | −0.02 | 0.08 | −0.01 | 0.19 ** | 0.07 | 0.14 ** |
| Literacy | 0.73 *** | 0.08 | 0.49 *** | 0.24 *** | 0.07 | 0.21 *** |
| Executive function | 0.21 | 0.15 | 0.07 | 0.27 * | 0.13 | 0.12 * |
| R 2 | 0.39 | 0.27 | ||||
| Adjusted R2 | 0.37 | 0.26 | ||||
| F(df) | 35.54 (6, 341) *** | 20.82 (6, 341) *** | ||||
* p < 0.05; ** p < 0.01, *** p < 0.001.
2.3. Discussion
In the present study, we examined the associations between symbolic and non‐symbolic magnitude processing and math skills in schoolchildren from Ghana. Based on prior findings from Canada and Iran (Hawes et al. 2019; Nosworthy et al. 2013; Tavakoli 2016), we hypothesized that symbolic comparison performance would be a stronger predictor of math performance relative to non‐symbolic comparison. Contrary to our expectations, we found that non‐symbolic comparison was a stronger predictor of math performance. To test the robustness of this finding and its generalization, we subsequently conducted a preregistered study in Côte d'Ivoire—Ghana's neighbor to the west (for the preregistration, see https://osf.io/y32d8/?view_only=1f0c09263e9c462b8a589876c2d6f8b7). Using essentially the same tasks and methods (subtle differences are discussed below in the methods), we test the hypothesis that non‐symbolic comparison is a stronger predictor of math performance in Côte d'Ivoire.
3. Study 2 in Côte d'Ivoire
3.1. Methods
3.1.1. Participants
Three hundred fifty‐four second‐grade children were tested in Côte d'Ivoire, West Africa. Children were excluded if they had a score of 0 on either the symbolic or non‐symbolic conditions of the screener (n = 12). A total of 342 children (female, n = 184; male, n = 158) were included in the final data analyses. Note that age data were not available; all children were enrolled in CP2, which is the equivalent of second grade, or primary 2). Children have received 1 year of formal schooling prior to data collection.
3.1.2. Materials
3.1.2.1. Math Skills
Children's math skills were assessed using eight tasks. Four tasks from the EGMA (RTI International 2009a), which included the Number Identification, Addition, Subtraction, and Missing Number subtests described above. Administration of the EGMA was the same across both the Ghana and CIV samples; however, there were some differences in the individual items in the subtests. In addition, four tasks from the IDELA (Pisani et al. 2018) were administered to assess number knowledge, one‐to‐one correspondence, shape identification, and sorting abilities based on color and shape. The percent correct for each domain was computed, and the score for each domain was averaged to create a total score (Cronbach's α = 0.86).3 The math readiness scores in the CIV sample were computed using the same subtests that were administered in Ghana. A mean percent correct score was computed across the Number Identification, Addition, and Missing Number subtests from the EGMA.
3.1.2.2. Literacy Skills
Literacy skills in French were assessed using eight tasks measuring preliteracy and literacy domains from two sources. Using the EGRA (RTI International 2009b), domains included letter‐sound identification, nonword decoding, and word reading. Four additional adapted subtasks from EGRA were used and included phonological awareness, phoneme segmentation, synonyms, and antonyms (Ball et al. 2022; Jasińska, Akpe, et al. 2022). Finally, one additional measure of phonological awareness from the IDELA (Pisani et al. 2018) was also included. The percent correct for each domain was computed, and the score for each domain was averaged to create a total score (Cronbach's α = 0.85).
3.1.2.3. Executive Function
Two executive functioning domains were assessed: cognitive flexibility was assessed using a tablet‐based Hearts and Flowers task (Diamond et al. 2007; α = 0.86). Short‐term memory was measured using a visual digit span, in which children were shown 13 series of numbers ranging from two to seven digits and asked to write down the numbers they saw in the same order after each series was presented (Finch et al. 2022; Cronbach's α = 0.79).
3.1.2.4. Socioemotional Skills
Socioemotional skills were measured using the IDELA subscale (Pisani et al. 2018). The same subtests that were administered in Ghana were also administered in Côte d'Ivoire (Cronbach's α = 0.62).
3.1.2.5. Symbolic and Non‐Symbolic Numerical Magnitude Processing
The instructions for the Numeracy Screener administered in the Côte d'Ivoire were translated and administered in French (Nosworthy et al. 2018).
3.1.3. Procedures
Data for this study come from the EduqPlus intervention study conducted in 100 schools in the Aboisso and Bouaflé regions of Côte d'Ivoire (Wolf and Lichand 2022). This school‐randomized control trial examined impacts of a text‐message‐based intervention to parents and teachers related to educational engagement and improvement. Fifty public schools within each region (N = 385 in Aboisso, 612 in Bouaflé) were selected by the district education office to participate in the study. Schools were then randomly assigned to (i) receive the Eduq+ intervention, administered to caregivers and teachers (n = 50), or (ii) a control group (n = 50).
In each school, the class rosters of CP2 (equivalent to primary 2) were obtained. Thirteen children were randomly chosen from the roster, and data were collected in the schools in the fall (November 2018; beginning) and spring (June 2019; end) of the school year. At follow‐up, data was collected on 2246 (89.84%) of those children. A random sub‐sample, stratified by treatment status, was selected and administered the Numeracy Screener at follow‐up. In contrast to our sample in Ghana, we found that relative to the larger sample, Ivorian children who completed the Numeracy Screener had significantly lower literacy, numeracy, socioemotional, and executive function skills (all p values < 0.001 and BF10 > 212.45; see Supplemental Analysis 1). All assessments were administered directly to children in their school. Data collectors were trained for 5 days and 2 additional days of field practice.
3.2. Results
Descriptive statistics, Pearson correlations, and Bayes factors of the raw scores across all dependent measures administered in Côte d'Ivoire (CIV) are reported in Table 4. We found significant positive associations between the adjusted scores of the Numeracy Screener and school readiness measures of math, socioemotional, literacy, and executive functioning skills (see Table 4). Bayesian correlation analyses resulted in Bayes factors that are greater than 150, providing very strong evidence for the association between Numeracy Screener scores and school readiness measures (Jeffreys 1981). One exception was that the association between symbolic comparison and socioemotional skills failed to reach significance once Bonferroni correction was applied (BF10 = 0.51). These results are consistent with those reported in Ghana, further showing that early numeracy skills are related to a broad range of school readiness measures in CIV. Paired samples t‐test and Bayesian analyses revealed strong evidence to support that children from CIV are more accurate on the symbolic comparison (M = 14.90) relative to the non‐symbolic comparison task (M = 12.53), t(341) = 7.14, p < 0.0001, d = 0.39, 95% CI [1.71, 3.02], BF10 = 1.03 × 109 (see Figure 1b). Adjusted non‐symbolic and symbolic comparison scores significantly correlated with math performance (non‐symbolic: r(340) = 0.58, p < 0.0001, and symbolic: r(340) = 0.35, p < 0.0001; see Figure 1c,d, respectively). We replicated the finding that the relationship between non‐symbolic comparison and math composite scores was significantly stronger than the correlation between symbolic comparison and math composite scores in the CIV sample, z = 5.75, p < 0.0001.
TABLE 4.
Descriptive statistics, bivariate correlation matrix, and Bayes factors.
| Study 2 in Côte d'Ivoire | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mean | SD | Skew | Kurt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
| 1 | Numeracy Screener | 27.45 | 11.97 | 0.96 | 1.26 | r | 0.89** | 0.89** | 0.53** | 0.44** | 0.20** | 0.40** | |
| 95% CI | 0.86, 0.91 | 0.87, 0.91 | 0.45, 0.60 | 0.35, 0.52 | 0.09, 0.30 | 0.30, 0.48 | |||||||
| BF10 | ∞ | ∞ | 4.50e22 | 5.30e14 | 59.46 | 2.32e11 | |||||||
| 2 | Symbolic | 14.90 | 6.60 | 1.02 | 1.23 | r | 0.59** | 0.35** | 0.27** | 0.11† | 0.30** | ||
| 95% CI | 0.51, 0.65 | 0.26, 0.44 | 0.17, 0.37 | 0.01, 0.22 | 0.20, 0.39 | ||||||||
| BF10 | 3.50e29 | 3.55e8 | 3.67e4 | .61 | 3.11e5 | ||||||||
| 3 | Non‐symbolic | 12.53 | 6.85 | 0.76 | 0.70 | r | 0.58** | 0.51** | 0.24** | 0.41** | |||
| 95% CI | 0.51, 0.65 | 0.42, 0.58 | 0.14, 0.34 | 0.32, 0.49 | |||||||||
| BF10 | 1.43e29 | 5.12e20 | 1229.53 | 1.92e12 | |||||||||
| 4 | Math (EGMA) | 0.33 | 0.20 | 0.26 | −0.50 | r | 0.68** | 0.34** | 0.53** | ||||
| 95% CI | 0.61, 0.73 | 0.24, 0.43 | 0.45, 0.60 | ||||||||||
| BF10 | 3.60e43 | 8.42e7 | 5.75e22 | ||||||||||
| 5 | Literacy | 0.19 | 0.16 | 1.20 | 1.29 | r | 0.46** | 0.56** | |||||
| 95% CI | 0.38, 0.54 | 0.48, 0.63 | |||||||||||
| BF10 | 4.54e16 | 2.82e26 | |||||||||||
| 6 | Socioemotional | 0.64 | 0.28 | −0.55 | −0.69 | r | 0.37** | ||||||
| 95% CI | 0.27, 0.45 | ||||||||||||
| BF10 | 2.02e9 | ||||||||||||
| 7 | Executive function | 0.49 | 0.14 | 0.35 | −0.28 | ||||||||
Note: Literacy, socioemotional and executive function skills are mean percent correct. Significance levels are indicated as follows: p < 0.0023**, Bonferroni corrected; p < 0.01*; p < 0.05†. BF10 represents the Bayes factor in support of the alternate hypothesis over the null. BF10 values between 0 and 3 indicate weak evidence in support for an association, 3–20 indicate positive support, 20–150 indicate strong support, and values greater than 150 indicate very strong evidence in favor of an association (Jeffreys 1961).
Abbreviations: Kurt = Kurtosis, M = Mean, SD = standard deviation, Skew = skewness.
3.2.1. The Unique Associations Between the Numeracy Screener and Math Abilities
We ran a series of hierarchical regression models using the EGMA composite score calculated from the subtests administered in CIV as the dependent measure. We replicated the same pattern of results in Ghana in CIV. Non‐symbolic number comparison accounted for significant unique variance in math performance even when controlling for symbolic number comparison, socioemotional, literacy, and executive function skills (see Table 2). In contrast to prior studies (e.g., Hawes et al. 2019; Nosworthy et al. 2013; Tavakoli 2016), we found that non‐symbolic comparison, but not symbolic comparison, accounted for significant unique variance in math abilities in Ghana and CIV.
Although children in Ghana and CIV showed higher performance on the symbolic comparison task relative to the non‐symbolic comparison task, they showed poor performance on the Numeracy Screener relative to first‐ and second‐grade children from Canada (Nosworthy et al. 2013) and second‐grade boys from Iran (Tavakoli 2016). One hypothesis for finding a stronger relationship between non‐symbolic comparison and math performance is that a large portion of children in Ghana and CIV do not recognize all numerals from 1to 9. However, when children who cannot recognize their numerals are removed from the analyses, the same pattern of results holds such that non‐symbolic comparison performance is a significant correlate of math scores when symbolic comparison, executive function, socioemotional, and literacy skills are accounted for in the regression model (see Supplementary Analysis 3; Figure S1 and Table S4).
We next tested the unique associations between symbolic and non‐symbolic comparison and individual subtests from the EGMA administered to children in CIV. We found that although non‐symbolic number comparison remained a consistent predictor of performance on the individual subtests from the EGMA, there were some differences in the pattern of results from what was found in the study conducted in Ghana. In contrast to the pattern of results found in Ghana, non‐symbolic comparison accounted for significant unique variance in the Missing Number subtest. We additionally found that both symbolic and non‐symbolic numerical abilities accounted for significant unique variance in subtraction performance (see Table 5). We preregistered exploratory secondary analyses that do not inform nor alter the interpretations of our main conclusions. We have included them in the Supporting Information for transparency and in case they are of use to other researchers.
TABLE 5.
The unique associations between symbolic and non‐symbolic comparison and individual subtests from the Early Grade Math Assessment in Côte d'Ivoire.
| Variable | Numeral identification | Missing number | ||||
|---|---|---|---|---|---|---|
| B | SEβ | β | B | SEβ | β | |
| Intercept | 0.17 * | 0.07 | −0.09 | 0.06 | ||
| Male | 0.07 * | 0.03 | 0.10 * | 0.02 | 0.03 | 0.03 |
| Non‐symbolic | 0.01 *** | 0.003 | 0.26 *** | 0.008 ** | 0.003 | 0.18 ** |
| Symbolic | −0.002 | 0.003 | −0.05 | −0.000 | 0.002 | −0.000 |
| Socioemotional | 0.005 | 0.06 | 0.004 | 0.04 | 0.05 | 0.04 |
| Literacy | 0.66 *** | 0.13 | 0.31 *** | 0.89 *** | 0.12 | 0.43 *** |
| Executive function | 0.35 * | 0.14 | 0.14 * | 0.39 ** | 0.12 | 0.16 ** |
| R 2 | 0.33 | 0.44 | ||||
| Adjusted R2 | 0.32 | 0.43 | ||||
| F(df) | 27.39 (6, 335) *** | 44.66 (6, 335) *** | ||||
| Variable | Addition | Subtraction | ||||
|---|---|---|---|---|---|---|
| B | SEβ | β | B | SEβ | β | |
| Intercept | −0.06 | 0.04 | −0.11 *** | 0.03 | ||
| Male | 0.03 | 0.02 | 0.08 | 0.03 | 0.01 | 0.10 |
| Non‐symbolic | 0.008 *** | 0.002 | 0.31 *** | 0.002 | 0.001 | 0.12 |
| Symbolic | 0.002 | 0.002 | 0.07 | 0.003 * | 0.001 | 0.14 * |
| Socioemotional | −0.02 | 0.03 | −0.02 | 0.01 | 0.02 | 0.02 |
| Literacy | 0.36 *** | 0.07 | 0.31 *** | 0.20 *** | 0.05 | 0.25 *** |
| Executive function | 0.08 | 0.07 | 0.06 | 0.15 ** | 0.06 | 0.16 ** |
| R 2 | 0.37 | 0.28 | ||||
| Adjusted R2 | 0.36 | 0.27 | ||||
| F(df) | 32.44 (6, 335) *** | 22.13 (6, 335) *** | ||||
* p < 0.05; ** p < 0.01; *** p < 0.001.
3.3. General Discussion
The majority of studies conducted in the Minority World have found that individual differences in symbolic magnitude processing are a stronger predictor of math achievement than non‐symbolic magnitude skills. (e.g., Nosworthy et al. 2013; Schneider et al. 2017). Given these findings, researchers have downplayed the role of non‐symbolic magnitudes for learning math and have suggested that symbolic magnitude knowledge is a critical foundation for successful math development (e.g., Merkley and Ansari 2016). However, there is a pressing need for researchers to adopt a global perspective to evaluate whether the foundations for learning math are universal. In the present studies, we examined whether the Numeracy Screener, a paper‐and‐pencil assessment of symbolic and non‐symbolic magnitude processing, was associated with general math skills in children from Ghana and Côte d'Ivoire (CIV). We specifically tested the hypothesis that symbolic magnitude processing is a stronger correlate of math abilities relative to non‐symbolic magnitude processing.
Contrary to our hypothesis, we found that non‐symbolic magnitude processing was a stronger correlate of general math abilities than symbolic magnitude processing. Across both West African countries, we found consistent evidence to support a moderate association between non‐symbolic magnitude processing and general math skills, even when controlling for symbolic magnitude knowledge, executive functioning, socioemotional skills, and literacy skills. Children from Ghana and CIV were more accurate on the symbolic comparison relative to the non‐symbolic comparison task, demonstrating that the association between non‐symbolic magnitude processing and math achievement was not driven by higher performance on the non‐symbolic comparison task.
Our results diverge from previous studies that have used the Numeracy Screener to assess symbolic and non‐symbolic magnitude processing. For example, Nosworthy et al. (2013) found that symbolic comparison performance was a unique correlate of math achievement in first through third grade Canadian children when accounting for non‐symbolic magnitude, literacy, and working memory skills. Similarly, Hawes et al. (2019) found that symbolic comparison performance in kindergarten children accounted for significant unique variance in arithmetic skills and teacher‐assigned math grades a year later. The symbolic comparison condition of the Numeracy Screener also showed greater sensitivity relative to the non‐symbolic comparison condition in distinguishing school‐aged children who demonstrated persistent low math difficulties from their typically performing peers (Bugden et al. 2021). The importance of symbolic magnitude knowledge in the development of arithmetic skills was further supported by a study conducted in Iran. Tavakoli (2016) found that performance on the symbolic comparison task accounted for significant unique variance in arithmetic scores in second‐grade boys. Across studies showing symbolic number comparison to be a stronger correlate of math performance, closer examination of the standardized beta coefficients for the non‐symbolic comparison task reveals small non‐significant contributions typically ranging from −0.095 to 0.128 (Hawes et al. 2019; Nosworthy et al. 2013; Tavakoli 2016). In contrast, non‐symbolic magnitude skills demonstrated moderate associations with symbolic math skills, with standardized beta coefficients ranging from 0.13–0.60 across models conducted in Ghana and Côte d'Ivoire. The pattern of results found in West Africa also conflicts with studies that have used computerized paradigms to assess symbolic and non‐symbolic magnitude processing. They also diverge from a meta‐analysis showing that the association between symbolic magnitude processing and math achievement is stronger than the relationship between non‐symbolic magnitude processing and math achievement (Schneider et al. 2016). Prior meta‐analyses examining the association between non‐symbolic comparison and math achievement have reported the following average effect sizes: 0.20, CI [0.14, 0.26] (Chen and Li 2014); 0.22, CI [0.20, 0.25] (Fazio et al. 2014); and 0.24, CI [0.20, 0.28] (Schneider et al. 2016). We found stronger correlations between non‐symbolic comparison and math performance in Ghana (r = 0.53, CI [0.45, 0.60]) and CIV (r = 0.58, CI [0.51, 0.65]). Taken together, our finding that non‐symbolic magnitude processing is a moderate predictor of math achievement is inconsistent with studies conducted in the Minority World showing that symbolic magnitude processing is a stronger correlate of math achievement.
It is unclear what is driving the conflicting pattern of results found across studies, and therefore, we offer several hypotheses that require further investigation to understand how context influences math development. It remains unresolved whether the approximate magnitude system is involved in learning symbolic representations of numbers (Sella et al. 2021; vanMarle et al. 2014), or whether it is tangentially related later in development once symbolic representations are learned (Carey and Barner 2019). One explanation for the diverging patterns of findings across studies is that the approximate magnitude system does play a foundational role for learning math, but that the timing and duration for which it does varies across contexts. For example, our data may suggest that non‐symbolic magnitude processing plays a critical role for learning symbolic math in first‐ and second‐grade children in West Africa. Studies conducted in the Minority World that have failed to find support for this hypothesis could be capturing a developmental window when non‐symbolic magnitudes are no longer involved. Evidence to support this idea comes from Fazio and colleagues, who found that the relationship between non‐symbolic magnitude processing and math performance is stronger in children younger than 6 years old. Moreover, studies have found that non‐symbolic magnitude skills support the acquisition of symbolic magnitude knowledge in preschool North American children (Chu et al. 2015; vanMarle et al. 2014). One possibility is that non‐symbolic magnitudes support symbolic math development earlier in development, but once children acquire symbolic representations of magnitude, through practice and experience, they begin to form stronger associations among symbols and no longer require accessing non‐symbolic magnitudes. Counter evidence to this proposal is that recent findings from the Minority World have found that symbolic magnitude processing at school entry is a stronger predictor of growth in non‐symbolic skills than the reverse, suggesting that acquiring symbolic magnitude skills directly influences non‐symbolic magnitude representations (while the converse is not true) (e.g., Kolkman et al. 2013; Lau et al. 2021; Lyons et al. 2018; Matejko and Ansari 2016). However, because children tested have acquired some symbolic number knowledge, a microgenetic approach starting prior to children learning the meaning of number symbols is needed to fully understand when and how non‐symbolic magnitudes support symbolic number acquisition. In other words, our data might support the hypothesis that non‐symbolic magnitude processing plays a small role early in development, and then as children acquire symbolic number and math knowledge in school, the non‐symbolic system plays a less critical role. If this were the case, then one might speculate that in countries where children have less experience using symbolic numbers, they rely on non‐symbolic magnitudes to carry out symbolic math across a wider developmental window. Follow‐up studies are necessary to test whether symbolic magnitude processing becomes a stronger predictor of math performance in older children from Ghana and CIV later in development.
A second interpretation, although not mutually exclusive from the first, is that there are environmental factors operating at both proximal and distal levels to the child that directly or indirectly influence how children think and learn about numbers (Whitehead et al. 2024). For example, proximal factors, such as socioeconomic status and parental education, are associated with math achievement (Lefevre et al. 2009). Specifically, research conducted in Minority World countries has shown that the home learning environment prior to starting formal school is associated with future math skills, suggesting that exposure to an enriched learning environment sets children up for success when they start school (Muñez et al. 2021). Cross‐cultural evidence also suggests that variability in the home learning environment extends past the Minority World. For example, Susperreguy et al. (2022) found differences in the types of activities that parents engaged in with their children between Chile, Mexico, and Canada. A recent study conducted in rural communities in Côte d'Ivoire found that the home environment predicted executive functions, which supports the development of numeracy and literacy skills (Jasińska, Zinszer, et al. 2022). These findings suggest that children's experiences with numbers outside of school shape how they learn about math in school. Ghanaian culture features a lot of non‐symbolic representations in terms of how food products are sold. In particular, Ghana is one of the countries in West Africa where selling by weight and using standard measures is uncommon. For example, tomatoes are grouped in varying quantities in bowls and baskets, leaving the buyer to estimate which grouping contains more tomatoes. This practice is very common and extends to children's daily lives, particularly those who support their family work. CIV is the largest producer of cocoa in the world. However, in cocoa‐producing communities, there are high levels of poverty, with many families surviving on $1–2 a day (Institut National de la Statistique de la Côte d'Ivoire 2015). Many children assist their family by working in cocoa production and therefore spend less time in the classroom (or drop out altogether). Numeracy exposure at home, school enrollment, and attendance rates all of which affect children's math learning trajectories.
There are also distal factors, such as school quality and curriculum, that can affect how and when symbolic and non‐symbolic numerical processing relate to overall math ability. We found that mean scores across both conditions of the Numeracy Screener were lower for children in CIV and Ghana relative to children from Canada and Iran. Although there have been several initiatives to improve early education in Ghana, it has been documented that children in both countries are not always attending school and therefore may receive less math instruction. Studies have also shown that children in Ghana begin learning about numbers when they start formal schooling, and reports have found that children spend an average of 3.9 hours of math instruction a week (USAID 2018). It is also the case that instructional practices are described as teacher‐centered and children are viewed as passive learners. Observational studies have shown that children are taught by rote learning, copying and imitation, as well as chorus responses, and therefore, focusing on rote rehearsal (Agbenyega 2018; Akyeampong 2017). For example, students in the classroom will often recite the count sequence and memorize visually presented numerals. The curriculum remains prescriptive and does not allow teachers to flexibly adapt the curriculum to meet individual students’ learning needs. Without opportunities to flexibly engage with symbolic number representations, children in Ghana and Côte d'Ivoire may develop a surface‐level understanding of symbolic numerals. For example, they know that 4 is larger than 2 and 5 is smaller than 9, knowledge that likely reflects rote learning and supports performance on symbolic comparison tasks. However, they may not be drawing on the semantic meaning of numbers to complete these tasks, nor have they had sufficient opportunities to use numbers flexibly in ways that would foster stronger and more precise representations.
In addition to non‐symbolic magnitude processing, we also found that literacy and executive function skills were significant correlates of math skills in children from Ghana and CIV. Our finding showing that non‐symbolic comparison remains a significant correlate of math performance when accounting for executive function skills, including inhibitory control, is consistent with previous research suggesting that non‐symbolic comparison tasks capture core quantitative skills (e.g., DeWind et al. 2015; Starr et al. 2017). Across almost all models, the standardized beta coefficients were larger for literacy skills relative to non‐symbolic comparison, suggesting that literacy skills are an important correlate of math development. Our findings in Ghana and CIV are also consistent with a previous study conducted in CIV (Whitehead et al. 2024), as well as with findings from Minority World contexts (Vanbinst et al. 2020) demonstrating that early precursors of reading are associated with math skills, suggesting that reading and math share overlapping cognitive processes (Hübner et al. 2022).
3.3.1. Limitations
It is important to consider several limitations when interpreting results from the present study. First, our assessment of non‐symbolic magnitude processing from the Numeracy Screener includes small quantities (e.g., 1–4) that are within the subitizing range, as well as large quantities (e.g., 5–9) that are thought to be processed using the approximate magnitude system (Feigenson et al. 2004). It is unclear which underlying cognitive mechanisms are driving our results, and future research should include assessments that separate both cognitive systems. Second, we were unable to collect accurate age data for all children in Ghana and Côte d'Ivoire, and therefore, we are unable to account for age in our regression models. Third, our subsample of Ivorian children who completed the Numeracy Screener significantly differed from the broader sample in their literacy, numeracy, socioemotional, and executive function skills, which limits the generalizability of the Côte d'Ivoire findings. Lastly, drawing conclusions based on cross‐cultural and cross‐study comparisons is challenging because different studies adopt different methodological approaches that may account for diverging results. A strength of our study is that we administered the same measures in both Ghana and Côte d'Ivoire, enabling us to make direct comparisons across two countries. Importantly, while the math assessments used in these studies are widely used in Majority World countries, they differ from those used in previous studies in the Minority World that also used the Numeracy Screener. We administered the EGMA, whereas Minority World studies have used measures such as the Math Fluency and Calculation Subtests from the Woodcock Johnson Tests of Achievement (Nosworthy et al. 2013); teacher‐assigned math grades (Hawes et al. 2019); and experimenter‐developed single‐digit (Hawes et al. 2019; Tavakoli 2016) and double‐digit addition and subtraction tasks (Tavakoli 2016). We note that all these studies, including our own, administered a single‐digit arithmetic measure. Although the assessments vary slightly, for example, in whether they were timed or untimed, the association between non‐symbolic magnitude processing and arithmetic knowledge remains stronger in Ghana and Côte d'Ivoire compared to studies from the Minority World.
3.3.2. Implications and Future Directions
Nonetheless, our findings have important implications for the debate surrounding the relationship between symbolic and non‐symbolic magnitude processing and general math competencies across development. Much of the debate has focused on whether non‐symbolic magnitude processing supports symbolic math development. Counter arguments have focused on alternate cognitive explanations, such that any relationship found between non‐symbolic magnitude processing and math can be explained by domain‐general cognitive processes (Gilmore et al. 2013; Leibovich et al. 2017; Leibovich and Ansari 2016). Our findings suggest that contextual variability is an important consideration for understanding the dynamic associations between symbolic and non‐symbolic magnitude processing and math development.
Our results may also have important educational implications. Obtaining quality education is key to breaking the cycle of poverty (UNESCO) and improving economic growth (World Bank 2001). Efforts to improve early education can protect against poor health outcomes, and lead to higher economic return (Heckman 2006). A global approach is necessary to understand how to best invest resources in early childhood programs to reduce the achievement gap between disadvantaged children and their more advantaged peers. The associations found between performance on the Numeracy Screener and math abilities suggest that this simple 2‐min paper‐and‐pencil assessment of numerical magnitude processing has the potential to be used to monitor students’ progress in countries in the Majority World. Early screening is essential to identify students who are struggling to grasp fundamental skills needed to excel in school. Adopting Westernized tools and approaches might not serve all children. Here, we demonstrate that performance on the Numeracy Screener strongly predicts math achievement. Trained research assistants collected the data reported in our study; future investigations are needed to evaluate whether teachers in the Majority World also report practical utility of the Numeracy Screener to assess numerical magnitude knowledge in the classroom.
4. Conclusions
The current study has revealed important insights not only for numerical cognition but also for the fields of cognitive science and education more broadly. We present novel results showing that non‐symbolic magnitude processing is a strong and unique correlate of math achievement in school children from Ghana and Côte d'Ivoire. These findings conflict with the majority of studies conducted in Minority World countries, highlighting the need for researchers to adopt a global approach to understanding human cognition and the role that context plays in learning. It is important for researchers to acknowledge that evidence stemming from the Minority World cannot easily be applied and implemented globally, but instead, researchers need to consider the contextual influences.
Ethics Statement
All procedures were approved by the Institutional Review Boards at the University of Zurich and the University of Pennsylvania.
Conflicts of Interest
The authors declare no conflicts of interest.
Supporting information
Supporting File 1: desc70129‐sup‐0001‐SupMat.docx
Acknowledgments
The research was supported by the Jacobs Foundation, which funded the original project from which the Côte d'Ivoire data is drawn, as well as the United Bank of Switzerland Optimus Foundation, the World Bank Strategic Impact Evaluation Fund and Early Learning Partnership, and the British Academy which funded the original project from which the Ghana data were collected through grants provided to Sharon Wolf. The Eunice Kennedy Shriver National Institute of Child Health and Human Development (5K99HD098329‐02) provided support for Stephanie Bugden's time and contributions to this project. We thank the committed staff at Innovations from Poverty Action Ghana and Côte d'Ivoire offices, who provided diligent management and execution of all aspects of data collection. We also thank Maite Deambrosi for research assistance, as well as field coordination by Nicolo Tomaselli, on the project in Côte d'Ivoire. Finally, a special thanks to the children and families for participating in our research, as well as the schools for coordinating and supporting the research process.
Endnotes
Terminology varies across international studies when referring to certain countries (e.g., non‐Western, educated, industrialized, rich, and democratic [non‐WEIRD] countries; low‐ and middle‐income countries [LMICs]; and the Global South). These terms can be problematic because they can perpetuate false hierarchies and dichotomies (Draper et al. 2023); however, they can serve a purpose to highlight inequalities and under‐representation in developmental psychology research. We chose to adopt terminology recommended by Draper and colleagues to use Majority and Minority World to collectively reflect groups of countries where the majority and minority of the world's population live (Alam 2008). The term “Majority World” was coined as an alternative to terms like “Third World,” aiming to reframe the perspective by emphasizing what these countries have rather than what they lack (Alam 2008). Majority World countries are primarily in Africa, parts of Asia, and Latin America. The Minority World countries represent a small fraction of the world's population and hold a disproportionate share of global wealth. They are typically located in North America, Western Europe, and Australia/New Zealand.
The gross enrollment rate (GER) is defined by the World Bank as the total number of students enrolled in the primary school regardless of age. Therefore, GER includes students who are younger or older than the official age range for primary school and can exceed 100%. Rates above 100% mean that total enrollment at the primary school exceeds the size of the official primary school‐age population, often due to grade repetition or late/early school entry.
We preregistered that math readiness scores for the CIV sample would be computed using the Numeral Identification, Addition, Subtraction, and Word Problem subtests. However, pilot testing in CIV revealed that the Word Problems subtest from the EGMA was too difficult for children, and therefore, it was not administered in our sample. The Missing Number subtest was administered instead and was included in the math composite score.
Data Availability Statement
The data that support the findings of this study are publicly available. For Cote d'Ivoire, the data can be downloaded at the following location: https://osf.io/hx8ve/. For Ghana, the data can be at the following location: https://microdata.worldbank.org/index.php/catalog/3439.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Supporting File 1: desc70129‐sup‐0001‐SupMat.docx
Data Availability Statement
The data that support the findings of this study are publicly available. For Cote d'Ivoire, the data can be downloaded at the following location: https://osf.io/hx8ve/. For Ghana, the data can be at the following location: https://microdata.worldbank.org/index.php/catalog/3439.