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Abstract

Numerous international studies have reported the importance of the home numeracy environment in promoting early math skills in preschool children; however, there is a lack of research in the Cuban context. The present descriptive study investigated the relationship between counting skills of 100 4-year-old Cuban preschoolers and the influence of formal and informal activities used in the home numeracy environment in Cienfuegos, Cuba. Results indicated that 58% of children were able to identify between five and eight objects on a counting task. Binary logistic regression revealed that maternal education was the only factor that significantly predicted children’s counting abilities. In semi-structured interviews with mothers, it was found that most (68%) used three methods to promote counting skills, including television (informal method), assistance from older siblings, and workbooks (formal method). Multivariable logistic regression indicated that both television and workbooks predicted children’s counting skills. Among mothers who were unaware that their child could count (32%), television was identified as the primary source of how their child learned to count. The analysis of the home numeracy environment of the Cuban families studied revealed the frequent use of formal methods to promote cardinality principles in 4-year-olds. Mother’s education was also found to be a significant predictor of counting skills. The use of informal activities, such as television and mobile phones, was frequent. It is necessary to avoid passive educational methods and to increase the active involvement of adults to promote the development of counting skills.

Plain Language Summary

What is known: At 4 years old, it’s beneficial to encourage early mathematical development to support both present and future learning. During early childhood, emphasis can be placed on three key areas within early mathematics: numbers, relationships, and operations. Counting skills are essential precursors to later academic achievement. Children who grow up in high-quality home numeracy environments typically exhibit enhanced mathematical abilities and are more equipped for school. What this study adds: Cuba offers fertile ground for promoting early mathematics from the age of 4. A moderate percentage of Cuban preschoolers (58%) use the principle of cardinality with between 5 and 8 objects. Cuban mothers most frequently used informal activities (television and cell phone games) to stimulate their children at age 4. In addition, our analysis showed that fathers did not actively supervise educational methods, indicating a passive role in providing stimulation.

Keywords

home numeracy environment counting early mathematics numeracy

Introduction

The first 5 years of a child’s life are pivotal for early mathematical development. Physical, cognitive, and socio-emotional development are interconnected and mutually reinforce each other, much like a symphony orchestra, where development of skills in one domain guides and influences the skills in other domains (Bretherton et al., 2014; Nelson & McMaster, 2019). The harmonious development of early mathematical skills and knowledge in early childhood is essential for a smooth transition to primary school and lays the foundation for school success.

Meta-analyses summarizing three decades of research have concluded that cognitive precursors to mathematics are significant indicators of future academic performance, such as language, spatial, and counting skills (Z. Zhang & Peng, 2023; X. Zhang et al., 2020). Among the most relevant prospective-longitudinal studies, Duncan et al. (2007) examined data from six large international studies and found strong associations between math skills at school entry and subsequent performance in primary and secondary school, taking into account a series of control variables such as IQ, reading performance, attention control, and socio-emotional skills. Additionally, Douglas & Attewell (2017) suggest that mathematical knowledge is fundamental for accessing better-paid jobs in science, technology, engineering, and medicine. Therefore, investing in early math learning is crucial as an indicator of progress. Internationally, difficulty with mathematics reliably predicts school failure (X. Zhang et al., 2020). Therefore, school readiness in the first 5 years of life is fundamental for promoting early precursor math skills and avoiding school failure.

Counting Skills in Early Childhood

Strong theoretical consensus suggests that early math educational preparation comprises three domains (Burchinal et al., 2016; Case et al., 1996): (a) Number (number knowledge, counting skills, estimation of the number line), (b) Relation (seriation, comparison, and classification), and (c) Operation (addition and subtraction of small quantities). The number domain refers to the understanding and manipulation of numbers, including recognition and comprehension of numbers, the ability to count, understanding numerical sequences, understanding numerical magnitude (greater than, less than, equal to), and understanding numerical patterns. The operations domain focuses on developing skills for performing basic mathematical operations such as addition, subtraction, multiplication, and division. This involves understanding how to combine and separate groups of objects, understanding the relationships between operations, and solving simple mathematical problems. The relations domain refers to the understanding of spatial relationships and the comprehension of relationships between objects and quantities, including understanding concepts such as up/down, inside/outside, in front of/behind, as well as the ability to compare and order objects based on their size, shape, and other characteristics.

A comprehensive analysis of intervention studies over the past 25 years (Nelson & McMaster, 2019) indicates that counting skills play a crucial role in early childhood numeracy literacy. Counting skills are particularly important at this stage as they help children understand objects through cardinality, basic arithmetic (i.e., addition and subtraction of quantities), and set algebra (i.e., formation, identification, comparison, and decomposition of sets by size, shape, color, and quantity; Litkowski et al., 2020; Nogues & Dorneles, 2021; Wege et al., 2023). Nogues & Dorneles (2021) conducted a meta-analysis to identify factors influencing early math skills development. They reviewed 62 studies published between 2000 and 2020, in which 32 were longitudinal and 30 were concurrent. Results highlighted working memory, counting, number knowledge, comparison of quantities, and estimation of the number line as the most common precursors of arithmetic. Of these studies, 51 focused on children 4 to 7 years old, with 27 identifying counting skills as precursors. A meta-analysis on educational interventions in first grade revealed that activities involving comparison of magnitudes and numerical sequences had the most significant impact on arithmetic development (g = 0.61, 95% CI [0.43, 0.79]), followed by studies on addition and subtraction (g = 0.60; [0.41–0.78]; Charitaki et al., 2021). Additionally, a review of the 20 studies used in the meta-analysis found that counting skills were fundamental in guiding teaching strategies in most interventions, with educational methods such as explicit instruction, corrective feedback, the use of concrete manipulatives, and individualized teaching being employed (Daucourt et al., 2021). In summary, counting skills are essential precursors that, when combined with other skills, form the basis of mathematics in the early years of primary school. Therefore, fostering counting skills in the first 5 years of life, both in educational settings and at home, is crucial.

Home Numeracy Environment

The home literacy model proposed by Sénéchal and LeFevre (2002) emphasizes the importance of parental involvement in the development of preschool skills through both formal and informal activities. Formal activities include direct instruction by the caregiver, which may include music lessons, art, educational games, and reading aloud. On the other hand, informal activities include free play, family interactions, cooking together, and role playing. Within this theoretical framework, Skwarchuk et al. (2014) proposed the Home Numeracy Environment (HNE) model, defined as the formal and informal activities that parents engage in at home to promote their children’s mathematical skills. In this sense, formal activities are characterized by a didactic approach, where parents choose specific activities to teach their children mathematical skills such as mental addition, number recognition, counting small quantities, and identifying number symbols. Informal activities, on the other hand, allow children to acquire number skills incidentally (Skwarchuk et al., 2014). Examples include board games that incorporate mathematical content and playing cards. Although these informal activities provide opportunities to learn numeracy skills, they are not primarily designed to teach mathematics.

In the last five years, the study of formal and informal activities at home has been analyzed in several high-income countries to understand the relation between parental attitudes and children’s early mathematics development (Mutaf-Yildiz et al., 2020). Moreover, several studies have been published in the Latin American region (Cahoon et al., 2024; León et al., 2021; Leyva, 2019; Río et al., 2017; Susperreguy et al., 2020, 2021). In a systematic review, Mutaf-Yildiz et al. (2020) found that: (a) children whose parents use formal activities at home perform better in elementary school, regardless of their ethnicity, (b) parents of Chinese American and Taiwanese descent are more involved in formal activities than their European American counterparts, which is associated with more favorable math outcomes for their children, (c) there is a tendency to analyze more formal home activities than informal activities, which is a limitation for future studies, and (d) the home math environment is significantly related to children’s math achievement, over and above other differences such as individual characteristics, including intelligence, gender, age, and family socioeconomic status.

The findings presented by Mutaf-Yildiz et al. (2020) indicate similarities with studies conducted in Latin America (Cahoon et al., 2024; León et al., 2021; Leyva, 2019; Río et al., 2017; Susperreguy et al., 2020). In the Latin American context, studies have shown that the frequency of parent-reported numeracy activities is associated with children’s performance on numeracy tests, as observed in research from the United States and Europe (Mutaf-Yildiz et al., 2020). According to Mutaf-Yildiz et al. (2020), other meta-analyses (Charitaki et al., 2021; Daucourt et al., 2021), and longitudinal studies (Cabrera et al., 2020; Lehrl et al., 2020) have indicated that preschoolers who grow up in formal mathematics environments are better prepared for school, regardless of their ethnicity or income level (Tamis-LeMonda et al., 2019). However, some researchers (Dowker, 2021; Dunst et al., 2017; Elliott and Bachman, 2017) argue that the link between home learning and mathematical development is not always relevant.

Current Limitations of Studying the Home Numeracy Environment

The accumulation of research over the last decade has led to methodological recommendations to improve the analysis of the home numeracy environment. Dowker (2021) suggests the use of parental self-report and interviews to validate information provided, such that there may be discrepancies between home activities and children’s performance if parents do not accurately reflect the reality of their home environment. Niklas et al. (2021) suggest the importance of investigating the impact of digital media on HNE, given the increasing use of children’s screen time in the home environment, both for play and educational purposes. The term “screen time” refers to the amount of time a person spends in front of a screen, be it a television, computer, tablet, or mobile phone, that is, in front of digital media. This concept is particularly relevant in the context of digital device use and its impact on physical and mental health, child development, and social interactions (Stiglic & Viner, 2019). Similarly, Mutaf-Yıldız et al. (2020) emphasizes that studies should focus more on mothers, rather than considering both caregivers, and give greater relevance to formal versus informal activities. To help address the current limitations, Hornburg et al. (2021) proposed multidisciplinary guidelines for the study of HNE, as current evidence is not sufficient to implement a successful approach that engages all families, regardless of their background. The recommendations include organizing research into five areas: (a) operationalization and measurement of HNE, (b) child, family and community factors, (c) country and cultural factors, (d) numeracy and other mathematical domains, and (e) cognitive and affective characteristics of caregivers and children.

In recent years, a considerable amount of research has been conducted in response to the recommendations described (Dowker, 2021; Hornburg et al., 2021; Niklas et al., 2021) in high-income countries (Cosso et al., 2022, 2023; Davenport et al., 2023; Ehrman et al., 2023; Ellis et al., 2023; Hornburg et al., 2022; Mak et al., 2024; Ouyang & Chan, 2025; Wei et al., 2023). Several studies have also been published in Latin America (Cahoon et al., 2024; Leyva et al., 2022). However, in the case of Cuba, research on this topic has been scarce, with only three studies published (Cahoon et al., 2024; Campver et al., 2022; Rodríguez et al., 2022), highlighting the need to address this issue within the Cuban cultural context.

Counting Skills in Early Childhood and the Home Numeracy Environment in Cuba

Cuba is classified as a high-middle-income economy by the World Bank, but social and income inequality and premature mortality remain significant issues (Ross et al., 2022; World Bank, 2023). Preschool education readiness is a vital resource used by families, educators, and the government to promote children’s education and development while also addressing income disparities linked to various factors, such as global conflict, embargos, and an insufficient response of the country’s economic reforms in recent years (Alonso & Vidal, 2023; Weil-Barais, 2022).

Over the past two decades, early childhood education in Cuba has been systematic, orderly, and scientifically rigorous, reflecting the characteristics of the Cuban educational system (Batista et al., 2020). National data indicates that 85% of 4- to 5-year-old children can build sets based on shape, size, and color, while over 90% of 6-year-old children can identify 10 objects through counting (Morán & Leonard, 2021).

In Cuba, early childhood mathematics education follows the practices of Cruz & Cartaya (2016), which focuses on three theoretical aspects of early mathematics (i.e., number, relation, operation) for children aged 5 to 6 years. However, for children who are 4 years old, the priority is learning set algebra, which involves the study of sets and the operations that can be performed with them, such as their formation, identification, comparison, and decomposition based on their size, shape, color, and quantity (Cruz & Cartaya, 2016). In this context, the HNE can be crucial for developing counting skills and promoting set algebra in 4-year-old preschoolers, regardless of whether they attend educational institutions or not.

Research on HNE characteristics in Cuba has been limited. Two studies have shown that both formal and informal activities carried out by Cuban families support the development of non-symbolic mathematical skills in preschoolers, with factors such as parents’ experience and positive attitude toward mathematics playing a significant role (Campver et al., 2022; Rodríguez et al., 2022). Rodríguez et al. (2022) found that mapping tasks (i.e., identifying numbers, learning to count) were more frequent in Cuban households than operational tasks (i.e., manipulating digits or quantities, such as practicing mental math or comparing quantities). Regarding informal activities, parents more frequently engaged with their children in puzzles (96%), block games (76%), dominoes (71%), and cards (67%). However, only one study consisted of a sample of 4-year-olds (Rodríguez et al., 2022), while the other selected preschoolers between 5 and 6 years old.

In this context, research on 4-year-olds at the preschool stage is essential. First, there is little data on parental attitudes and early mathematical development at this stage. Secondly, at the age of 4, parents are not obliged to enroll their children regularly in an educational institution; instead, they can choose to stimulate learning at home or through the twice-weekly “Educa a Tu Hijo” (“Educate Your Child”) program run by the school closest to the family. Finally, the social changes that have taken place in Cuba in recent years, such as increased access to the Internet through mobile phones, high migration rates, and economic hardship, have changed family dynamics. The HNE could therefore be a valuable alternative for introducing early mathematics to 4-year-olds.

Current Study

Given the scarcity of research on the HNE in the Cuban cultural context, it is appropriate to examine the activities and methods, both formal and informal, that Cuban parents use at home to promote the counting skills as a driver of preschool children early mathematics. Furthermore, given that the cultural context is different from many countries in the region, it is essential to approach this topic from a developmental perspective. The objective of the current study is to examine the relationship between counting skills in 4-year-old Cuban preschoolers and the influence of formal and informal activities used in the HNE.

In Cuba, 5-year-olds receive systematic stimulation in the three theoretical domains of early mathematics, while at age 4 only set algebra (set operations such as union, difference, complement, intersection, Cartesian product) is emphasized (Cruz & Cartaya, 2016). In addition, 5-year-old preschoolers are required to attend an educational institution on a weekly basis, while 4-year-olds attend less regularly. This highlights the need to investigate the role of parents in the development of counting skills in the home of 4-year-old preschoolers. Counting is one of the first things that parents do when their children are young, so it is important to find out how many objects they can count and how much they can actually recognize, as parents can teach counting without checking whether the child recognizes the exact amount. In addition, it has been found that at the age of 4 it is common for children to make numerous errors when counting quantities, in particular they know how to count but cannot tell the exact number of objects they have counted in a set (Brooks et al., 2011; Fletcher & Pine, 2009; Shipley & Shepperson, 1990; Sophian & Kailihiwa, 1998; Wagner & Carey, 2003; Wege et al., 2023). In the sense, the current study was guided by the following four research questions:

Question 1: How many objects can 4-year-old Cuban preschoolers count following the principles of cardinality?

Question 2: What is the relationship between the counting skills of 4-year-old Cuban preschoolers and the home numeracy environment?

Question 3: What formal and informal methods do Cuban parents use to stimulate counting skills in the home numeracy environment?

Question 4: Which of the methods used in the home numeracy environment are the strongest predictors of counting skills in 4-year-old Cuban preschool children?

Methods

Participants

The current study included 100 preschoolers (48% boys), aged 4 years (between 49 and 58 months), mean age 53 ± 2.47 months, from three educational institutions in the city of Cienfuegos, Cuba. The centers were chosen because they were part of a larger project on neurodevelopment in early childhood. The study was approved by the scientific council. Informed consent was collected from the legal guardians of participating children. Data collection was conducted between 2018 and 2019.

The study population consisted of 360 children from five educational institutions in the Reparto “La Juanita,” in the city of Cienfuegos. In order to determine the sample size, we used the Decision Analyst STATS software (version 2.0), taking into account a maximum acceptable error percentage: 5%, an estimated percentage level of the sample: 10% or 90% and a confidence interval: 95%, obtaining a sample size of 100 children. A non-proportional or constant stratified random sample was used to select the sample, with strata defined on the basis of the 5 educational institutions and 20 children selected by simple random sampling in each educational institution. Additional criteria were implemented for the inclusion of participants in the study. It was decided that the children should be between 48 and 58 months of age and show typical development for their chronological age, as assessed by parents and educators.

Measures

Counting Skills

The subtest, Counting Quantities, (α = .76), of the Cuban Preschool Neurocognitive Battery (B-PREA-R; Ramírez et al., 2024) was used to measure children’s counting skills. The B-PREA-R is a quick and easy to apply test to assess neurocognitive development in preschoolers and informs a child’s readiness before starting basic schooling. The counting subtest is similar to the Utrecht Early Mathematics Assessment Test (Navarro et al., 2009) in that it assesses structural and resultant counting. The assessment requires children to count different quantities presented in an unordered array. The test consists of 10 items, and its complexity increases as the number of items to be counted increases, varying between 3 and 12 objects.

The task is presented in two parts: in the first part, there are several animals that children must count, and in the second part, objects related to the animals are shown, either in terms of actions they perform, such as eating or interacting. In the first part (counting), children must determine the exact number of animals in a picture (Figure 1). An evaluator asks the child, “How many pigs/cats are in the picture?” For example, in the first picture, the child must count three pigs. In the second part (counting + comparing), children have to identify the number of animals in the first picture and relate it to the number of other objects in a second picture below the first picture. The evaluator asks the child, “Where are the same number of pigs and plates?” For example, in the first picture, the child has to count three pigs and then look for the group with three plates in the second picture. This part of the task assesses principles of counting: (a) stable order of numbers, (b) one-to-one correspondence, (c) irrelevance of the order of objects counted, and (d) cardinality. The intention is that when children interact with the second part of the test, they will see a connection not only in terms of quantity, but also in terms of a narrative. The Counting Quantities subtest has been found to predict of arithmetic from first and second grade (Ramírez et al., 2022).

Figure 1.

Fragments of the Counting Quantities subtest (items 1 and 5).

The study evaluators were the children’s educators and were trained at the beginning of the school year through methodological workshops with two weekly sessions of 45 min each for 1 month. The counting task evaluations were generally carried out in the morning, using the standardized B-PREA-R protocol.

Home Numeracy Environment

Interviews were conducted with mothers about the activities or methods, both formal and informal, that they use at home to encourage counting. The interviews were conducted in the home and lasted between 15 and 25 min. The interviews were semi-structured, based on a questionnaire adapted from the Cuban Neurosciences Centre (CNC), as proposed by Rodríguez et al. (2022). The CNC questionnaire was translated into Spanish following the methodology described by Skwarchuk’s (2009). The interviews were conducted to identify relevant aspects related to early mathematics stimulation and to validate the information provided by parents about the numerical environment at home. Additional questions were included to the CNC questionnaire to understand the methods used to teach counting skills. Questions included: “Have you taught your child to count?,” “Where do you think your child learned to count quantities?,” “What method did you use to teach counting?,” and “What method do you think was the most effective in teaching counting?”

From the interviews, four aspects related to the development of counting skills at home were analyzed: (a) counting skills (0 = does not know how to count; 1 = knows how to count), (b) stimulation at home (0 = mother, father, siblings; 1 = television, cell phone, playing with table objects), (c) method used at home (0 = informal: watching TV programs related to numbers, playing with puzzles, watching educational programs, playing with blocks, dominoes, counting and number games in situations; 1 = formal: using structured methods such as counting objects under adult supervision, writing numbers, using fingers to count, learning about measurement, sorting geometric shapes or objects by size, and comparing groups of objects), and (d) importance of the method used (0 = less important, 1 = important, 2 = very important).

Socioeconomic Family Status

A socio-demographic data questionnaire was utilized to identify family’s socioeconomic status. The questionnaire was composed of four indicators: (a) number of children in the household (0 = one child, 1 = greater than or equal to two children), (b) salary of family members (sum of all salaries in the household), (c) number of family members (0 = three members, 1 = greater than or equal to four members), and (d) maternal education (0 = low, high school diploma, 1 = medium, high school, 2 = high, university). With the values of indicators 2 and 3, the socioeconomic status of the family was created: salary of family members/number of family members. The values obtained allowed classifying the family into low (<500 pesos), medium (500–1,000 pesos), and high (>1,000). Classifications of salaries were based on the category “average monthly salary in state entities by class of economic activity” in Cienfuegos (values taken from the Statistical Yearbook of Cienfuegos, 2018).

This procedure was used to determine the socioeconomic family status, because in Cuba the National Office of Statistics and Information (ONEI, acronyms in Spanish) does not provide percentiles to classify families according to their income (i.e., low, medium, high). However, every year the Office reports the average monthly salaries in each governmental entity by class of economic activity, by provinces and municipalities. Thus, with the information on the parents’ place of work, the average monthly salary reported by the ONEI, and using a formula that takes into account all the salaries of the family members divided by the total number of family members, it is possible to obtain a more precise measure of the socioeconomic status of families, similar to international standards.

Analytic Procedure

A preliminary analysis showed that the counting test data did not meet the assumptions of normality according to the Kolmogorov-Smirnov and Shapiro-Wilk tests, which indicated p-values <0.05. It was therefore decided to use non-parametric tests and to organize all the data into values of 0 and 1. This transformation was necessary in order to apply logistic regressions, which offer greater power to analyze the independent variables and their predictors (Sperandei, 2014). To convert the counting test results into these values, the Cuban B-PREA norms (Ramirez et al., 2024) were used, while for the interview data the values were considered on the basis of the presence or absence of data in the questions.

First, a Mann-Whitney test was conducted to compare the performance on the Counting Quantities subtest by children’s sex. Next, the information from the interviews with the mothers was analyzed. Two logistic regressions were conducted. The first to investigate the relationship between counting skills and the HNE (i.e., stimulation at home, method used at home, importance of the method used; n = 100 children), and the second to evaluate the impact of the methods used at home to promote counting skills in preschool children (n = 68 children). The latter focused on the mothers who mentioned educational methods to promote counting skills at home (68%), while the remaining 32% were evaluated by means of a decision tree technique, using the DMC method (Decision Making Criteria) in SPSS v.25. The latter analysis considered the possible informal methods that mothers used to justify their children’s counting skills, since they mentioned that they were not able to count quantities.

Results

Table 1 shows the descriptive data of the variables analyzed in the study. Most of the participants lived in urban areas (88 families, 88%), and 85% of the families had more than three members (85 families). Additionally, most of the mothers had a high school education (89 families, 89%) and were classified as upper-middle income (75 families, 75%). Seventy-five percent of the families earned between 500 and 1,000 pesos per month, while 25% had incomes below 500 pesos per month (see Table 1).

Table 1.

Descriptive Statistics of All Study Variables.

Variable and data source	M	SD	Frequency
N = 100
Child age (months)	53.6	2.47
			0	1
Sex (0 = male and 1 = female)			48	52
Population (0 = urban and 1 = rural)			88	12
Counting Skills. Counting (0 = 0–4 objects, 1 = ≥5 objects)			40	60
Counting Skills. Counting + Comparation (0 = 0–4 objects, 1 = ≥5 objects)			43	57
Socioeconomic family status (0 = low-level families, <500 pesos, 1 = medium-level families, e/ 500 and 1,000 pesos). There were no families with higher-level			25	75
Number of children in the household (0 = one child, 1 = greater than equal to two children)			82	18
Number of family members (0 = three members, 1 = greater than three members)			15	85
Maternal education (0 = medium, high school, 1 = high, university)			89	11
Interview
Counting skills (0 = can’t count, 1 = can count)			32	68
Method used (0 = informal, 1 = formal)			32	68
			0	1	2
Stimulation (0 = no stimulation, 1 = mother, father, sibling, 2 = television, cell phone, playing with tabletop object)			0	68	32
Importance of method used (0 = less important, 1 = important, 2 = very important)			0	55	45
N = 68			0	1	2
Mothers who reported that their children could count and who used the following methods (0 = television, 1 = sibling’s influence, 2 = workbook)			41	18	9
Importance of method used (0 = less important, 1 = important, 2 = very important)			0	1	2
Television			12	26	30
Brother’s influence			41	6	21
Workbook			30	17	21
N = 32			0	1	2
Mothers who reported that their children cannot count may have learned (32%; 0 = television, 1 = possibly on the television, 2 = did not know)			15	12	5

Note. M = mean; SD = standard deviation.

Counting Skills and Principles of Cardinality

Figure 2 shows that out of the 100 children tested on the first part of the Counting Quantities subtest, 10 could not count objects correctly, 6 could count up to three objects, 22 could identify four objects, 61 could count between five and seven objects, and only 1 child could count up to eight objects. In the second part of the subtest, 26 children were able to relate the number of objects in the first picture to the exact number of objects in the second picture, using four objects. Only 58 children were able to do this using between five and eight objects. Results of a U Mann-Whitney test indicated that there were no significant differences between males and females in solving the subtest in its two parts: first part (counting, U = 1,051.50; p = .163); second part (counting + comparison, U = 1,085.00; p = .242).

Figure 2.

Number of children who responded to the subtest in the first and second parts of the subtest.

Counting Skills and the Home Numeracy Environment (n = 100)

Multivariate logistic regression was used to test the significance of the predictor variables (i.e., counting skills, stimulation at home, methods used at home, importance of the method used, maternal education, family socioeconomic status, and number of children at home) on the dependent variable (counting skills). Two statistical models were used: (a) Model 1 included analysis between the dependent variable (first part of the subtest, counting quantities) and the predictor variables and (b) Model 2 included analysis between the dependent variable (first and second part of the subtest, counting + comparing quantities) and the predictor variables.

Results indicated that model 1 was not significant. However, model 2, which included both parts of the subtest (i.e., counting + comparing quantities) showed significant results (X² = 7.68, gl = 5, p = .01). Model 2 explained between 74%_{(Cox and Snell’s R²)} and 99%_{(Nagelkerke’s R²)} of the variance of counting skills. The overall correct prediction rate was 75%. The model was able to correctly predict 90% of the children who counted more than five objects and 64.2% of those who counted less than four objects or did not know how to count. Table 2 shows that maternal education was the only statistically significant predictor for both children who counted more than five objects (β = 1.33, p = .03) and those who counted up to four objects or could not count (β = 1.21, p = .03). In the group of children who counted between zero and four objects, the value of the odds ratio (OR = 0.26; 95% CI [0.08, 0.89]) was less than 1 (Table 3). In contrast, for children who counted more than five objects, the odds ratios (OR = 3.74; [1.11, 12.58]) were greater than 1.

Table 2.

Standardized Coefficients Reflecting the Relationship Between Home Numeracy Environment and Preschooler Counting Skills (n = 100).

Number of objectives identified		β	SE	Wald χ²	gl	p	OR	95% CI
0–4 objects	SFS	.27	0.502	.29	1	.585	1.316	0.491	3.525
	NCH	.05	0.492	.01	1	.918	1.052	0.401	2.762
	ME	1.21	0.617	4.57	1	.032	0.267	0.080	0.895
	CC	.25	0.565	.20	1	.649	1.293	0.427	3.917
	IM	−.36	0.538	.45	1	.499	0.695	0.242	1.996
≥5 objects	SFS	−.27	0.503	.29	1	.585	0.760	0.284	2.036
	NCH	−.05	0.492	.01	1	.918	0.951	0.362	2.496
	ME	1.33	0.601	4.07	1	.032	3.741	1.117	12.530
	CC	−.25	0.565	.20	1	.649	0.773	0.255	2.341
	IM	−.36	0.538	.45	1	.499	0.695	0.242	1.996

Note. β = standardized coefficient; SE = standard error; OR = odds ratio; CI = confidence interval; SFS = socioeconomic family status; NCH = number of children in the household. ME = maternal education; CC = child who can count; IM = importance of method used.

Table 3.

Standardized Coefficients Reflecting the Relationship Between Methods Used and Preschooler Counting Skills (n = 68).

Model/Steps	Predictors	β	SE	Wald χ²	gl	p	OR	95% CI
Step 1	Television***			11.50	2	.003
	Television*	3.88	1.14	11.42	1	.001	0.02	0.002	0.19
	Television**	2.21	1.04	4.49	1	.034	0.10	0.014	0.84
	Workbook			5.57	2	.062
	Workbook*	2.49	1.06	5.56	1	.018	0.08	0.010	0.65
	Workbook**	.74	0.86	.74	1	.389	0.47	0.087	2.59
	MEL	1.88	1.13	2.75	1	.097	0.15	0.016	1.40
	SFS	.73	0.85	.73	1	.390	2.08	0.389	11.21
	Cant.Children			1.61	2	.446
	Cant.Children1	2.32	1.84	1.58	1	.208	10.20	0.275	378.45
	Cant.Children(2)	2.45	2.02	1.47	1	.225	11.59	0.221	607.58
Step 2	Television			10.83	2	.004
	Television(1)	3.61	1.10	10.76	1	.001	0.02	0.003	0.23
	Television(2)	1.99	0.99	4.05	1	.044	0.13	0.020	0.94
	Workbook			5.72	2	.057
	Workbook*	2.44	1.02	5.68	1	.017	0.08	0.012	0.64
	Workbook**	.73	0.84	.74	1	.389	0.48	0.091	2.53
	MEL	1.72	1.11	2.39	1	.122	0.17	0.020	1.58
	SFS	.37	0.75	.24	1	.619	1.45	0.334	6.32
Step 3	Television***			10.79	2	.005
	Television*	3.61	1.10	10.74	1	.001	0.02	0.003	0.23
	Television**	1.95	0.98	3.92	1	.048	0.14	0.021	0.97
	Workbook			5.55	2	.062
	Workbook*	2.38	1.01	5.52	1	.019	0.09	0.013	0.67
	Workbook**	.71	0.84	.72	1	.396	0.48	0.093	2.56
	MEL	1.81	1.09	2.74	1	.098	0.16	0.019	1.39

Note. β = standardized coefficient; SE = standard error; OR = odds ratio; CI = confidence interval; SFS = socioeconomic family status; MEL = mother’s educational level.

Unimportant; **Important; *** Very Important.

Home Numeracy Environment, Counting Skills, and Formal and Informal Methods

Sixty-eight percent of mothers (n = 68) used some kind of method to teach their child how to count. Additionally, mothers rated how important the methods were (see Figure 3). The most commonly used method was television (i.e., an informal method; 41 out of 68 mothers). Mothers also mentioned two formal methods as important at home, which were the use of a workbook (9 out of 68 mothers) and the influence of siblings (18 out of 68 mothers).

Figure 3.

Type of method mothers used and level of importance.

Mothers who answered that they did not use any educational methods to stimulate counting (32 mothers, 32%) were asked additional questions about where they thought their child learned to count. Almost half of the mothers (15 out of 32 mothers) answered television (i.e., informal method) and 5 out of 32 mothers did not know where their child learned to count.

Methods Used and Importance of Mothers Who Reported Their Child Could Count (n = 68)

Logistic regression with maximum likelihood and backward steps was used to identify the most important (formal and informal) methods used in the home numeracy environment (i.e., mothers’ methods to stimulate counting skills at home: television, exercise books, and sibling influence) and their relationship with the dependent variable (counting skills, counting + comparing; see Table 3). In the analysis, the second part of the counting test (counting + comparing quantities) was used, as the first part did not show significant results.

After three backward steps, the best fitting model (step 3; X² = 20.59, df = 5, p = .001) explained between 26%_{(Cox and Snell’s R²)} and 35%_{(Nagelkerke’s R²)} of the variance of counting skills. The overall correct prediction was 75%. Television (β = 3.61, p = .001) and workbook methods (β = 2.38, p = .01) identified by mothers to stimulate counting skills were found to be statistically significant. The Odds Ratios (OR) values for television (OR = 0.02; 95% CI [0.003, 0.23]) and workbooks (OR = 0.09; [0.01, 0.67]) were below 1.

Methods Used of Mothers Who Reported Their Child Could Not Count

Figure 4 shows the results of the Classification and Regression Tree (CRT) technique for generating decision trees using automatic stepwise variable selection to identify mutually exhaustive and mutually exclusive subgroups within a population. In this analysis, classification models were developed without a validation method, based on one outcome variable (i.e., counting skills + compare) and eight predictors (i.e., television, possibly television, did not know, stimulation at home, number of children at home, number of family members, socioeconomic family status, maternal education). The model was able to correctly classify 92% of the children using five predictors (television, possibly television, number of family members, socioeconomic family status, maternal education).

Figure 4.

Decision trees relating home numeracy environment and counting skills in children who do not know how to count, as reported by their mothers (32% of the sample).

The highest probabilities of identifying 4-year-old preschoolers with high counting skills (counting + comparing; more than 5 objects) and whose mother reported no formal methods used are observed in two types of families: (a) those in where the child watches television without adult supervision (53.3%, node 2), there are more than five members in the household (100%, node 10), and the mother has a medium or high level of education (41.7%, node 5; 100%, node 6), and (b) families where the child does not spend much time in front of the TV (47.1%, node 1; 66.7%, node 4) and there are three members in the family (100%, node 7). On the other hand, the highest probabilities of 4-year-old preschoolers with low counting skills (counting + comparing; 0–4 objects) and whose mother does not indicate a formal method used occur in families where the child does not spend much time watching television (47.1%, node 1; 100%, node 3) and there are between three and four members in the household (100%, node 11; 50%, node 8).

Discussion

Results of this study suggest that Cuba represents fertile ground for promoting numeracy in children before formal school entry. More than half of the preschoolers were able to apply the principles of cardinality (57 children out of 100; counting + comparing quantities). However, the rest could not count or could not apply cardinality principles with more than four objects, which could be due to inadequate educational methods at home.

Children usually are able to count objects correctly using a number line sequence. However, at the conclusion, they did not know how many objects were in the set, an error typical in preschoolers (Wege et al., 2023). This significant error was confirmed by comparing the number of children who were able to count a quantity in the first part of the counting skills subtest and then was unable to identify the same quantity in the second part. That is, there were many children who counted X objects at first and then did not know how to identify that X amount thereafter (see Figure 2, where you can see that most children can count up to five objects well, but not all of them can identify this number or more in a set). This suggests that their knowledge of the counting sequence was present (employing three counting principles: stable order, one-to-one correspondence, order irrelevance), but that their one-to-one item to number correspondence was weak (cardinality principle).

Results are consistent with other studies of counting skills in preschool children (Brooks et al., 2011; Fletcher & Pine, 2009; Shipley & Shepperson, 1990; Sophian & Kailihiwa, 1998; Wagner & Carey, 2003; Wege et al., 2023). Evidence suggests that 3- to 6-year-olds can count whole objects when asked to count their parts, count each fragment of a broken object as if it were a whole object, and count all small actions in a sequence when asked to count their total number (Brooks et al., 2011; Shipley & Shepperson, 1990; Wagner & Carey, 2003). This skill development can be further promoted by pedagogical interaction with a motivated adult, underscoring the importance of the home numeracy environment as a conducive context for learning.

Our findings suggest that mothers have a limited understanding of how to support their children’s counting skills. We found that they often used informal methods (such as television, games and mobile phones) rather than more structured approaches such as workbook exercises. This finding is not consistent with the two studies conducted among Cuban preschoolers aged 5 to 6 years (Campver et al., 2022; Rodríguez et al., 2022). The discrepancy in our results could be due to the age of the children and the systematicity of the educational stimulation. Campver et al. (2022) and Rodríguez et al. (2022) found that Cuban families with preschoolers aged 5 to 6 years used, frequent formal methods of early mathematics stimulation, which we also observed, although with more informal methods. In addition, like Campver et al. (2022) and Rodríguez et al. (2022) we found that maternal education level was a key factor in promoting children’s mathematical skills in the home numeracy environment.

On the contrary, the difference in our results could be due to the age of the children of our sample, since in Cuba formal education starts at the age of 5 and early mathematics is promoted in the preschool class, which doesn’t occur at the age of 4. It is certainly crucial to include systematic early mathematics activities for 4-year-olds as this could improve their skills, especially in relation to the principles of cardinality when counting between five and eight objects.

Set algebra is an excellent way to promote early mathematics at this age and is taught daily in Cuba to children attending educational institutions from the age of 4. However, counting exact quantities is not currently included, as this requirement begins at the age of 5, according to the methodology of Cruz & Cartaya (2016). This should be reconsidered, as there are 4-year-olds who can meet these requirements in their development. In this sense, parents are fundamental, especially mothers to promote counting skills at home.

Indeed, logistic regression revealed that maternal education is a key factor in the development of counting skills in 4-year-old preschool children. This finding is supported by several studies from Latin America (León et al., 2021; Leyva, 2019; Río et al., 2017; Susperreguy et al., 2020, 2021) and from Cuba (Campver et al., 2022; Rodríguez et al., 2022). However, the analysis of maternal education in our study was interesting, as the majority of mothers had a medium level of education (high school).

This last argument may be relevant for the 68 mothers who reported using formal and informal methods to promote their children’s counting skills, as 32% of them were not aware of these skills. Surprisingly, half of these mothers (15 out of 32) did not know that their children could count up to five objects. This does not necessarily indicate a lack of interest, but rather a rather passive attitude toward their children’s mathematical education.

A recent cross-cultural study of Cuban and Mexican mothers confirms that some mothers are surprised that their children are able to solve some early mathematical problems without being taught (Cahoon et al., 2024). In both the cross-cultural study and the findings of the current study, mothers were found to use digital media as a method of education. Mobile phones, computers, and televisions are tools that children use to learn content because they are attractive to them (Stiglic & Viner, 2019). However, it is important to assess how many hours children spend interacting with different types of digital media and to consider the characteristics of the home environment.

In this context, a future study focusing on the use of digital media in Cuban homes for 4-year-olds is essential, as both our study and those of Cahoon et al. (2024), Campver et al. (2022), and Rodríguez et al. (2022) highlight the need for parental guidance. Digital media is not a problem if children can count and have other mathematical skills at this age; however, the lack of adult supervision during screen time, the number of hours spent in front of the screen, and the lack of learning content essential for their development could be detrimental to their future development (Clark et al., 2016; Stiglic & Viner, 2019).

Results of this study identify two possible needs of the Cuban family: (a) the family needs to be more active in the stimulation of early mathematics and (b) there should be promotion of the knowledge of educational methods to guide early mathematics at home. The mere presence of an adult is not enough in the education of the child, it is necessary to engage, avoiding passive methods such as the television and cell phone. Both needs could be goals to address in early childhood education in Cuba in the next 5 years that respond to the Sustainable Development Objectives 4.2.1 of UNESCO 2030 (UNICEF DATA, 2019).

In 2019, Cuba reported an adequate score in the Early Childhood Development Index 2030 compared to other Latin American countries (UNICEF DATA, 2019); however, the country aims to improve the quality of education by modifying indicators such as health, learning, and psychosocial well-being in early childhood. The results of this research can help inform organization of parent workshops. In particular, it is necessary to use exchange workshops between teachers to improve their preparation in terms of how to direct the stimulation of early mathematics and other contents of the early childhood educational process; as well as to develop monthly information campaigns for parents to facilitate educational methods at home that promote the development of early mathematics and other early learning skills.

This study has several limitations. First, the sample is small, with an imbalance between rural and urban families, 12 and 88, respectively. In relation to this limitation, future research should aim to expand the scope of the study in rural and urban areas of Cuba, as well as in the different educational modalities of the Cuban context. Another limitation is related to the use of nonparametric techniques, which tend to have lower power and can be less effective in identifying real differences or effects in the data. Therefore, in addition to increasing the sample size, it is suggested that parametric analyses be carried out in future studies to examine the relation between counting skills of preschooler children and HNE, as documented in the literature (Skwarchuk et al., 2014; Susperreguy et al., 2021).

In addition, the present study had several strengths. An important strength of this study is the use of parent interviews, which allowed us to identify the content used by mothers for stimulation and to analyze in depth some of the attitudes of mothers at home to direct early mathematics education. In addition, a test was used to assess the principles of cardinality in Cuban preschool children. Another strength of the study is that it adds to the evidence on different aspects of HNE in the Cuban context. In two other HNE studies in Cuba, Rodríguez et al. (2022) and Campver et al. (2022) found that in urban areas formal activities were more frequent in 5- and 6-year-old preschoolers. However, the current study in Cienfuegos shows that this trend is not observed at the age of 4, when informal activities predominate and mothers take a more passive approach to education. The studies in Havana found a gap in children between the ages of 5 and 6, while our study shows a gap in 4-year-old preschoolers. This suggests three lines of future research: (a) increasing the scientific evidence on the HNE variable in the Cuban context, (b) focusing on parents with medium or high levels of education to promote the active implementation of both formal and informal activities in children aged 4 to 6 years, and (c) conducting prospective studies to analyze the impact of HNE on the mathematical performance of children in the early grades of primary school.

In conclusion, educational methods used at home in Cuba to help foster children’s counting skills should include a responsible and systematic adult who can help direct a child’s learning to their maximum potential. Although Cuban parents view television and workbooks as typical educational preschool tools, parents need to be informed that these tools should represent the minimum of stimulation. The findings suggest that a population-based parent information campaign might help parents with concrete information about how to stimulate the foundations of cognitive preparedness prior to school entry as espoused in the extant literature (Burchinal et al., 2016; Case et al., 1996). Parents can be informed on how to highlight verbal and mathematical themes in daily life as they engage in preparation and administration of family meals, sorting laundry, and shopping for items. High income countries favor active parenting and childcare for stimulating cognitive development in childhood compared to passive modes of stimulation (Case et al., 1996). In low-income countries, it is necessary to reduce passive methods (i.e., use of television, cell phones, and computers) and promote daily activities to enhance the development of early mathematics.

Footnotes

Acknowledgements

We would like to acknowledge the important contribution of the project “Stimulation of early childhood neurodevelopment” developed and directed by the University of Cienfuegos, Cuba. We are grateful for the ISSBD 2 x 2 Grant for Early Career Scholars (International Society for the Study of Behavioral Development; ), which gave us the opportunity to interact with leading experts in the field of developmental science.

ORCID iDs

Yaser Ramírez-Benítez

Shawn L. Carlson

Natalia Józefacka

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Home Numeracy Environment and Counting Skills: A Descriptive Study in Cuban Preschoolers at Age 4 Years

Abstract

Plain Language Summary

Keywords

Introduction

Counting Skills in Early Childhood

Home Numeracy Environment

Current Limitations of Studying the Home Numeracy Environment

Counting Skills in Early Childhood and the Home Numeracy Environment in Cuba

Current Study

Methods

Participants

Measures

Counting Skills

Home Numeracy Environment

Socioeconomic Family Status

Analytic Procedure

Results

Counting Skills and Principles of Cardinality

Counting Skills and the Home Numeracy Environment (n = 100)

Home Numeracy Environment, Counting Skills, and Formal and Informal Methods

Methods Used and Importance of Mothers Who Reported Their Child Could Count (n = 68)

Methods Used of Mothers Who Reported Their Child Could Not Count

Discussion

Footnotes

Acknowledgements

ORCID iDs

Funding

Declaration of Conflicting Interests

Data Availability Statement

References