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Responsive Early Childhood Parenting, Preschool Enrollment, and Eventual Student Learning Outcomes: A Cross-Country Analysis Using Hierarchical Linear Modeling with TIMSS 2019 Data

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Title: Responsive Early Childhood Parenting, Preschool Enrollment, and Eventual Student Learning Outcomes: A Cross-Country Analysis Using Hierarchical Linear Modeling with TIMSS 2019 Data
Language: English
Authors: Aditi Bhutoria, Nayyaf Aljabri, Saheli Bose
Source: International Journal of Child Care and Education Policy. 2025 19.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 22
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Early Childhood Education
Descriptors: Early Childhood Education, Parenting Skills, Child Rearing, Preschool Children, Enrollment, Outcomes of Education, Comparative Education, Foreign Countries, Hierarchical Linear Modeling, Achievement Tests, International Assessment, Mathematics Tests, Mathematics Achievement, Science Achievement, Science Tests
Assessment and Survey Identifiers: Trends in International Mathematics and Science Study
DOI: 10.1186/s40723-025-00141-6
ISSN: 1976-5681
2288-6729
Abstract: This paper examines whether parental engagement in early childhood and preschooling act as substitutes, or whether their joint effect enhances students' learning outcomes. We utilize the TIMSS 2019 dataset and employ a hierarchical linear modeling (HLM) approach to analyze data from 52 countries, ensuring a robust examination of cross-national variations. Although extant literature proposes that parental engagement and preschooling are likely to function as substitutes, our analysis reveals that they can also serve as complements. For instance, a one-unit increase in the TIMSS ECEC parental engagement index is associated with an estimated increase of 0.58 and 0.85 units in math test scores for students with up to one and two years of preschooling, respectively. In the case of science, for students with three or more years of preschooling, our findings suggest a substitutive relationship between parental engagement and preschool participation. In addition, we find that home literacy and numeracy activities undertaken by parents influence both math and science scores, albeit differently. Furthermore, we observe that a higher degree of parental engagement, combined with preschooling, yields the largest test score gains in countries with a greater proportion of children already enrolled in preschool, thereby making a case for expanding preschool access.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1470797
Database: ERIC
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  Value: <anid>AN0185069215;[ds0u]10may.25;2025May13.02:17;v2.2.500</anid> <title id="AN0185069215-1">Responsive early childhood parenting, preschool enrollment, and eventual student learning outcomes: a cross-country analysis using hierarchical linear modeling with TIMSS 2019 data </title> <p>This paper examines whether parental engagement in early childhood and preschooling act as substitutes, or whether their joint effect enhances students' learning outcomes. We utilize the TIMSS 2019 dataset and employ a hierarchical linear modeling (HLM) approach to analyze data from 52 countries, ensuring a robust examination of cross-national variations. Although extant literature proposes that parental engagement and preschooling are likely to function as substitutes, our analysis reveals that they can also serve as complements. For instance, a one-unit increase in the TIMSS ECEC parental engagement index is associated with an estimated increase of 0.58 and 0.85 units in math test scores for students with up to one and two years of preschooling, respectively. In the case of science, for students with three or more years of preschooling, our findings suggest a substitutive relationship between parental engagement and preschool participation. In addition, we find that home literacy and numeracy activities undertaken by parents influence both math and science scores, albeit differently. Furthermore, we observe that a higher degree of parental engagement, combined with preschooling, yields the largest test score gains in countries with a greater proportion of children already enrolled in preschool, thereby making a case for expanding preschool access.</p> <p>Keywords: Early childhood education and care (ECEC); Trends in International Mathematics and Science Study (TIMSS); Hierarchical Linear Model (HLM); I21; A20; A21; C39; Education Specialist Studies In Education</p> <p>Supplementary Information The online version contains supplementary material available at https://doi.org/10.1186/s40723-025-00141-6.</p> <hd id="AN0185069215-2">Background</hd> <p>The design and development of Early Childhood Education and Care (ECEC) programs to optimize their benefits have garnered greater traction and policy focus in the recent years. Early childhood, typically defined as the period from birth to eight years, constitutes a crucial developmental phase characterized by rapid cognitive and noncognitive growth. Monetary investment in education during early childhood yields the highest returns on human capital formation, fostering long-term benefits, such as enhanced learning efficiency in later educational stages and higher lifetime earnings (Heckman, [<reflink idref="bib30" id="ref1">30</reflink>]). Studies across the United States show that early childhood investment is more effective in narrowing the learning gap between disadvantaged and advantaged children when compared with interventions implemented at later stages of education (Cunha et al., [<reflink idref="bib15" id="ref2">15</reflink>]; Cunha & Heckman., [<reflink idref="bib14" id="ref3">14</reflink>]). Additional benefits of early investment include favorable effects on social behaviors, reduction in childhood depression, enhancement of executive functioning skills, and reduction of crime rates, among others (Barnett & Nores, [<reflink idref="bib4" id="ref4">4</reflink>]; Yoshikawa & Kabay, [<reflink idref="bib63" id="ref5">63</reflink>]). Notably, the sustainable development goal (SDG) 4 recognizes the importance of quality education at early stages. It highlights the need for universal access to "quality early childhood development, care, and pre-primary education."</p> <p>Although numerous studies have reported a positive impact of ECEC on child development (Barnett, [<reflink idref="bib5" id="ref6">5</reflink>]; Barnett & Masse, [<reflink idref="bib6" id="ref7">6</reflink>]; Carneiro & Ginja, [<reflink idref="bib12" id="ref8">12</reflink>]; Heckman et al., [<reflink idref="bib31" id="ref9">31</reflink>]), others have found no significant effects of ECEC, specifically on certain populations (Blanden et al., [<reflink idref="bib7" id="ref10">7</reflink>]; Fitzpatrick, [<reflink idref="bib20" id="ref11">20</reflink>]). Alongside evidence of long-term positive effects of preschool learning on child development—particularly for children from low-income backgrounds—these benefits are often contingent upon the type of the preschool program, highlighting the sensitivity of preschool effectiveness to variations in program quality (Barnett, [<reflink idref="bib3" id="ref12">3</reflink>]; Sylva et al., [<reflink idref="bib54" id="ref13">54</reflink>], Melhuish et al., [<reflink idref="bib43" id="ref14">43</reflink>]). Literature also suggests that attending kindergarten might not always imply school readiness (Haeck et al., [<reflink idref="bib27" id="ref15">27</reflink>]). In fact, a few studies have highlighted the negative effects of preschool enrollment as well, albeit under particular contextual conditions (Baker et al., [<reflink idref="bib2" id="ref16">2</reflink>]). For instance, Yoshikawa et al., ([<reflink idref="bib64" id="ref17">64</reflink>]) observed that enrollment in preschools was found to be negatively associated with Grade 3 academic performance. Moreover, some studies have identified a link between daycare reform policies and worsening health problems in children (van den Berg & Siflinger, [<reflink idref="bib59" id="ref18">59</reflink>]).</p> <p>Furthermore, the heterogeneity in cultural or policy paradigms across countries may also influence the efficacy of ECEC programs. For instance, in Sweden and Finland, the Ministry of Education administers ECEC programs through an integrated cohesive school system for children under 6 years of age. Contrarily, Belgium, France, and Italy follow a split schooling model of childcare for children up to 3 years, and preschool enrollment thereafter. In Austria, Canada, Denmark, and Germany, ECEC for pre-primary children is regulated by multiple agencies. Moreover, there could be school-level differences that influence the ECEC program quality. Although more prevalent, public schools are often more likely to face challenges such as inadequate classroom equipment and greater heterogeneity in teacher qualifications, potentially affecting the quality of ECEC programs. (Yizengaw & Tessega, [<reflink idref="bib62" id="ref19">62</reflink>]). In this regard, Singh and Mukherjee ([<reflink idref="bib52" id="ref20">52</reflink>]) highlighted a higher cognitive performance of private preschool attendees when compared with those who attended public schools. On the other hand, Ghosh ([<reflink idref="bib24" id="ref21">24</reflink>]) found no significant difference between the type of preschool attended and the children's social and cognitive development. Concerning the returns from private schooling, it may be noted that the choice of public versus private schools depends on the socio-economic status, with the affluent and aspirational ones favoring upscale preschools (Ghosh & Dey, [<reflink idref="bib25" id="ref22">25</reflink>]). Overall, since children spend a lot of time at home, a nurturing home environment, involving parental engagement is important, as it serves as a socializing factor, owing to which, it may be proposed that the impacts of preschool on student development are effectively moderated by the home environment and parental engagement (Mayer et al., [<reflink idref="bib41" id="ref23">41</reflink>]).</p> <p>Parental engagement can be defined as the engagement of parents in their children's lives to influence their overall actions, where a parent may refer to any adult caregiver (biological or adoptive) through time spent on various intellectually stimulating activities, such as reading aloud (Kim, [<reflink idref="bib37" id="ref24">37</reflink>]). The home environment affects a child physically, intellectually, and emotionally, and thereby may impact the child's learning outcomes (Manolitsis et al., [<reflink idref="bib40" id="ref25">40</reflink>]; Rose et al., [<reflink idref="bib48" id="ref26">48</reflink>]). Therefore, spending time with children is expected to have a direct causal effect on their cognitive outcomes (Villena-Rodan & Rios-Aguilar, [<reflink idref="bib60" id="ref27">60</reflink>]), with the largest gains observed during the early years of a child's development (Desforges & Abouchaar, [<reflink idref="bib18" id="ref28">18</reflink>]). Examining the impact of familial involvement on children's test scores has indicated that types of parental involvement (behavioral, personal, and intellectual) and building institutional capacity explained a large proportion of cognitive advancement in children (Ma et al., [<reflink idref="bib38" id="ref29">38</reflink>]). A meta-analysis of 98 studies illustrates that parental participation in school governance, discussion of school-related matters, and parental academic expectation were all positively associated with student achievement; with the effects being more robust for well-educated parents (Tan et al., [<reflink idref="bib55" id="ref30">55</reflink>]). Among these factors, academic socialization – the nurturing of aspirations, discussions about learning strategies and study planning were found to be quite pertinent (Hill & Tyson, [<reflink idref="bib32" id="ref31">32</reflink>]). Likewise, a review of research also emphasizes that despite accounting for the child's intellectual ability, parental engagement in education was still robustly linked with children's academic performance and their perception of their cognitive competence (Topor et al., [<reflink idref="bib57" id="ref32">57</reflink>]).</p> <p>The 'Ecological Systems Theory' elucidates that a child's development is directly impacted by their immediate environment, which comprises of parents at home with whom most of their interactions take place (Bronfenbrenner, [<reflink idref="bib10" id="ref33">10</reflink>]). Parental engagement encompasses both involvement in a child's education and broader participation in their overall development (Grolnick & Slowiaczek, [<reflink idref="bib26" id="ref34">26</reflink>]). Moreover, certain parental engagement activities exert a stronger influence on children's academic achievement as compared to other forms of involvement (Singh et al., [<reflink idref="bib53" id="ref35">53</reflink>]). The intensity of such engagements varies across socio-economic status (SES). Kalil and Ryan ([<reflink idref="bib34" id="ref36">34</reflink>]) found that parents with higher SES are conspicuously more likely to cultivate their children's skills through reading, or taking them to museums vis-à-vis their counterparts (i.e., lower SES parents). Notably, parents from lower SES backgrounds often face time constraints and financial limitations, which may lead them to prioritize immediate gains over long-term investments in child development. Consequently, this tendency results in systematically lower educational investments and delays in developmental outcomes. Here, parental involvement can offset adverse effects of social class, family size, and parental education (Flouri & Buchanan, [<reflink idref="bib21" id="ref37">21</reflink>]). In fact, school curricula in some countries recommend integrating parental involvement in the early years. For instance, ECEC policy in many countries today emphasizes feedback between teachers and parents (Janssen & Vandenbroeck, [<reflink idref="bib33" id="ref38">33</reflink>]).</p> <p>Schools are clustered within country contexts. Within countries institutions and policies may create different incentives for parents to enroll their children into preschools. The varying degrees of public responsibility across countries could be a reason for cross-country differences in the parental choices as well as preschool enrollment. Kamerman ([<reflink idref="bib35" id="ref39">35</reflink>]) documents several dimensions based on which ECEC policy varies across select OECD countries. These dimensions include whether ECEC policies are implemented by national or sub-national governments, the targeted age group, nature of funding-private or public, among others. Further, Ünver, Bircan & Nicaise ([<reflink idref="bib58" id="ref40">58</reflink>]) find that the presence of private and unsubsidized provision for 3–6-year-olds adversely affects ECEC accessibility, although a harmonized and unitary ECEC system leads to higher accessibility across countries. Wotipka et al. ([<reflink idref="bib61" id="ref41">61</reflink>]) analyze data across 117 countries and find economic development, improvement in women's status and global inter-connectedness to be significant the determinants of early childhood development.</p> <p>Despite these policy considerations, there remains a limited body of literature examining parental engagement at the preschool level. Existing studies focusing on primary and later stages of education indicate that various forms of parental engagement often act as substitutes for school inputs in the learning process (Datar & Mason, [<reflink idref="bib17" id="ref42">17</reflink>]; Fredriksson et al., [<reflink idref="bib23" id="ref43">23</reflink>]; Kim, [<reflink idref="bib36" id="ref44">36</reflink>]). Similarly, Cunha ([<reflink idref="bib16" id="ref45">16</reflink>]) recognized this substitutability, highlighting that parental time investment serves as a replacement for school inputs, particularly in the higher grades of primary education. Researchers have also suggested that external care may adversely affect the quality of at-home parental engagement, yet again, evidencing substitutability between at-home and external ECEC options (van den Berg & Siflinger, [<reflink idref="bib59" id="ref46">59</reflink>]). Based on the discussions thus far, this study examines whether such 'substitutability' exists within the ECEC context, while controlling for country and school level factors. Specifically, this study aims to assess whether preschooling and parental engagement function as substitutes or complements and to examine their joint impact on children's learning outcomes globally. To this effect, we have analyzed student data from 52 countries using the Trends in International Mathematics and Science Study (TIMSS) 2019 dataset. Using the TIMSS parental engagement index {i.e. Early Literacy and Numeracy Task (ELNT) index} alongside years of preschool enrollment, we estimate their interaction effects on TIMSS test scores using a Hierarchical Linear Modeling (HLM) framework. Owing to a lack of relevant data on ECEC for Grade 8 students, our analysis focuses on the Grade 4 level. Given that students are nested within schools, which in turn are nested within their respective countries, heterogeneities at both levels may impact the estimated results. Accordingly, within the HLM framework, we employ a mixed-effects model incorporating random effects at both the country and school levels to account for such variations. Although prior research has predominantly focused on developed countries with a few focusing on developing contexts (Rao et al., [<reflink idref="bib46" id="ref47">46</reflink>], [<reflink idref="bib47" id="ref48">47</reflink>]), this study covers 52 developed as well as developing nations, yielding better external validity.</p> <p>This paper is structured as follows: Sect. "Conceptual framework" presents the conceptual framework, while Sect. "Data and methodology" details the data and methodological approach. Sect. "Results and discussion" presents the empirical results, followed by an in-depth discussion in Sect. "Conclusion".</p> <hd id="AN0185069215-3">Conceptual framework</hd> <p>The extant literature has examined the interaction between preschooling and the home learning environment (Anders et al., [<reflink idref="bib1" id="ref49">1</reflink>]; Melhuish, [<reflink idref="bib43" id="ref50">43</reflink>]). Evidence from these studies suggests that the process through which Early Childhood Education and Care (ECEC) translates into better child outcomes is complex and context-dependent, influenced by heterogeneities within institutions and educational policies (Melhuish et al., [<reflink idref="bib42" id="ref51">42</reflink>]). In addition, there is mixed evidence and ambiguity regarding the relative impact of parental care, nonparental care (i.e., preschooling), or their combination on children's developmental and educational outcomes.</p> <p>Research evidence on ECEC supports this complex dynamic; for instance, Brilli ([<reflink idref="bib9" id="ref52">9</reflink>]), utilizing data from the United States, demonstrates that a reduction in the time spent by mothers with their children has negative effects on child development, though such effects can be partially compensated with nonmaternal care. Conversely, given the limitations in terms of access and quality of preschooling, it must be complemented with parental engagement to improve educational outcomes in developing contexts (Crouch, King, Olefir, Saeki, Savrimootoo, [<reflink idref="bib13" id="ref53">13</reflink>]; Sammons, Anders, Sylva, Melhuish, Siraj-Blatchford, Taggart, and Barreau, [<reflink idref="bib51" id="ref54">51</reflink>]). Nevertheless, added complexities persist in developing countries. There may be high opportunity costs for low-income families as increasing parental engagement with their children would imply a loss of income. A higher parental engagement may then lead to fewer financial benefits and poorer educational resources, such as books, which may lead to adverse outcomes despite higher preschooling and parental engagement. Therefore, considering children situated in varied contexts, the interaction between parental engagement and preschooling remains unclear, particularly in determining whether parental engagement and preschooling act as substitutes or complements. This forms the key investigation undertaken in this study.</p> <p>In context of the above inquiry, Fig. 1 shows the conceptual framework of the child development process that includes four events (i.e., parents' engagement at home; market-purchased preschooling; parents' position; and preschooling status), amongst other things. In similar vein, Cunha ([<reflink idref="bib16" id="ref55">16</reflink>]) has stated that the process resembles a production process. Within this analytical framework, we seek to answer whether the nexus of parents' engagement at home and market-purchased preschooling is substitutionary or complementary.</p> <p>Graph: Fig. 1 Conceptual framework to model the relationship between preschooling and parental engagement</p> <p>In Fig. 1, we note that there are two types of indicators, i.e., the final and intermediate. The final indicators are further bifurcated into two groups, impact and outcome. The 'impact group' refers to the student's well-being and achievements, while the 'outcome group' includes environmental factors, such as the home environment, amount of family resources allocated to children, school enrollment, and school-level factors. Typically, rational parents aim to shape children's learning outcomes by providing resources strategically, and maximize their well-being, thus creating an impact. The intermediate indicators mentioned, in turn, can be categorized as outputs and inputs. In this context, we consider that the outcome at the preschool level is affected by two main decisions undertaken by parents (i.e., output) including (i) the amount of time and engagement provided to the children at home; and (ii) the amount and quality of market-purchased inputs, such as preschool enrollment availed for the children (Harju-Luukkainen et al., [<reflink idref="bib28" id="ref56">28</reflink>]).</p> <p>In this regard, the parental time at home (i.e., output) involves engagement in intellectually and emotionally stimulating activities (e.g., reading aloud) that play a crucial role in improving a child's cognitive and noncognitive abilities. The time and depth of the parents' engagement at home (i.e., output) hinges on two 'inputs', viz. (i) the parents' education, and (ii) their opportunity cost of time (Harju-Luukkainen et al., [<reflink idref="bib28" id="ref57">28</reflink>]; Mahadevan & Fan, [<reflink idref="bib39" id="ref58">39</reflink>]), keeping other things constant. On the other hand, the quantity of market-purchased preschooling as the other output may depend on a set of inputs: (i) access and availability to preschool within the vicinity, and (ii) affordability, particularly when preschooling is not subsidized by the government (Blanden et al., [<reflink idref="bib8" id="ref59">8</reflink>]; Ferguson et al., [<reflink idref="bib19" id="ref60">19</reflink>]). With this base model, we present the interaction between preschooling and parental engagement and the potential conditions under which it would be substitutable or complementary in nature.</p> <p>Let the output be an achievement ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> </ephtml> ), a function of parental engagement ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math> </ephtml> ), and the number of hours spent in preschool ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> </ephtml> ), a simple production function of a child's achievement, reflecting the two parental choices; it may be presented as in Eq. (<reflink idref="bib1" id="ref61">1</reflink>) below:</p> <olist> <item> <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mo>=</mo><mi>A</mi><mo stretchy="false">(</mo><mi>P</mi><mo>,</mo><mi>S</mi><mo stretchy="false">)</mo></mrow></math> </ephtml> </item> </olist> <p>Graph</p> <p>where <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>A</mi></mrow><mrow><mi>∂</mi><mi>P</mi></mrow></mfrac><mo>></mo><mn>0</mn></mrow></math> </ephtml> and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>A</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mo>></mo><mn>0</mn></mrow></math> </ephtml></p> <p>Notably, parental engagement depends on labor market factors. Suppose <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math> </ephtml> represents the existing market wage rate, and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> </ephtml> refers to the maximum time available for a parent; during this time <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> </ephtml> , a parent can choose <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> </ephtml> time to engage in labor market activities and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>-</mo><mi>L</mi><mo stretchy="false">)</mo></mrow></math> </ephtml> in early childhood activities with his/her child, ceteris paribus. Further, based on Cunha ([<reflink idref="bib16" id="ref62">16</reflink>]) study, parental engagement (P) depends on the number of hours spent by the child in preschool (S), mathematically shown through:</p> <p>2 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mo>=</mo><mi>P</mi><mo stretchy="false">[</mo><mfenced close=")" open="("><mi>T</mi><mo>-</mo><mi>L</mi></mfenced><mo>,</mo><mi>S</mi><mo stretchy="false">]</mo></mrow></math> </ephtml></p> <p>Graph</p> <p>In a model of dynamic complementarity or substitution, parents would determine their allocation to preschool education and parenting effort together with the amount of each depending on whether they are viewed as substitutes or complements to maximize their utility. Hence, the unconstrained maximization problem of the parent becomes:</p> <p> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> </ephtml> —utility of a parent from child engagement</p> <p>3 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi><mfenced close=")" open="("><mi>L</mi></mfenced><mo>=</mo><mi>A</mi><mfenced close=")" open="("><mi>P</mi><mfenced close="]" open="["><mfenced close=")" open="("><mi>T</mi><mo>-</mo><mi>L</mi></mfenced><mo>,</mo><mi>S</mi></mfenced><mo>,</mo><mi>S</mi></mfenced><mo>-</mo><mi>w</mi><mi>L</mi></mrow></math> </ephtml></p> <p>Graph</p> <p>where we assume that enrolling a child into preschool is costless, and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>S</mi></mrow><mrow><mi>∂</mi><mi>L</mi></mrow></mfrac><mo>></mo><mn>0</mn><mo>.</mo></mrow></math> </ephtml> This implies that as parents spend time in the labor market, they are more likely to send their children to preschool. This can be represented by Eq. (<reflink idref="bib4" id="ref63">4</reflink>):</p> <p>4 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mo>=</mo><mi>S</mi><mo stretchy="false">(</mo><mi>L</mi><mo stretchy="false">)</mo></mrow></math> </ephtml></p> <p>Graph</p> <p>The first-order condition for the maximization problem of Eq. (<reflink idref="bib3" id="ref64">3</reflink>) with respect to <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> </ephtml> is represented by Eq. (<reflink idref="bib5" id="ref65">5</reflink>) below:</p> <p>5 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>-</mo><mspace width="0.166667em" /><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>A</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>P</mi></mrow></mfrac><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>P</mi></mrow><mo>⏞</mo></mover><mo>-</mo></mover><mrow><mi>∂</mi><mi>L</mi></mrow></mfrac><mspace width="0.166667em" /><mo>+</mo><mspace width="0.166667em" /><munder><munder accentunder="true"><mrow><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>A</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>P</mi></mrow></mfrac><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>P</mi></mrow><mo>⏞</mo></mover><mo>?</mo></mover><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac></mrow><mo>⏟</mo></munder><mrow><mi mathvariant="italic">IE</mi></mrow></munder><mspace width="0.166667em" /><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>S</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>L</mi></mrow></mfrac><mspace width="0.166667em" /><mo>+</mo><mspace width="0.166667em" /><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>A</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mspace width="0.166667em" /><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>S</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>L</mi></mrow></mfrac><mspace width="0.166667em" /><mo>=</mo><mspace width="0.166667em" /><mi>w</mi><mspace width="0.166667em" /></mrow></math> </ephtml></p> <p>Graph</p> <p>where IE denotes the indirect effect of preschool hours on children's achievement. Nevertheless, it is unclear how preschool hours affect children's achievements, since these hours have two different effects (i.e., direct, and indirect effects), as described algebraically in Eq. (<reflink idref="bib6" id="ref66">6</reflink>), following Cunha ([<reflink idref="bib16" id="ref67">16</reflink>]).[<reflink idref="bib1" id="ref68">1</reflink>]</p> <p>6 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtable><mtr><mtd /><mtd columnalign="left"><mrow><mfrac><mrow><mi mathvariant="italic">dA</mi></mrow><mrow><mi mathvariant="italic">dS</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>∂</mi><mi>A</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>∂</mi><mi>A</mi></mrow><mrow><mi>∂</mi><mi>P</mi></mrow></mfrac><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd columnalign="right"><mrow /></mtd><mtd columnalign="left"><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi><mspace width="0.166667em" /><mi>e</mi><mi>f</mi><mi>f</mi><mi>e</mi><mi>c</mi><mi>t</mi><mo>=</mo><mi>d</mi><mi>i</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>t</mi><mspace width="0.166667em" /><mi>e</mi><mi>f</mi><mi>f</mi><mi>e</mi><mi>c</mi><mi>t</mi><mo>+</mo><mi>i</mi><mi>n</mi><mi>d</mi><mi>i</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>t</mi><mspace width="0.166667em" /><mi>e</mi><mi>f</mi><mi>f</mi><mi>e</mi><mi>c</mi><mi>t</mi></mrow></mtd></mtr></mtable></mrow></math> </ephtml></p> <p>Graph</p> <p>In the third part of Eq. (<reflink idref="bib5" id="ref69">5</reflink>), <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>∂</mi><mi>A</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac></math> </ephtml> describes the direct effect; the second part, <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>A</mi></mrow><mo>⏞</mo></mover><mo>+</mo></mover><mrow><mi>∂</mi><mi>P</mi></mrow></mfrac><mspace width="0.166667em" /><mfrac><mover><mover accent="true"><mrow><mi>∂</mi><mi>P</mi></mrow><mo>⏞</mo></mover><mo>?</mo></mover><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mspace width="0.166667em" /></mrow></math> </ephtml> represents the indirect effect, whose sign is vague and depends on <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac></math> </ephtml> .</p> <p>Now, we assume that the market wage rate remains unchanged[<reflink idref="bib2" id="ref70">2</reflink>] and consider the following alternative scenarios. The underlying mechanism is that the marginal product of parental engagement and preschooling hours either declines, or remains the same, or increases as the amount of the other changes.[<reflink idref="bib3" id="ref71">3</reflink>]</p> <p></p> <ulist> <item> In the case above, the marginal <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mo>></mo><mn>0</mn><mo stretchy="false">→</mo><mfrac><mrow><mi mathvariant="italic">dA</mi></mrow><mrow><mi mathvariant="italic">dS</mi></mrow></mfrac><mo>></mo><mn>0</mn></mrow></math> </ephtml> (complementary case)</item> </ulist> <p>In this case, the marginal increase in preschool hours not only improves a child's achievement, but also enhances parental engagement. Hence, direct, indirect, and total effects are positive, implying thereby complementarity of parental engagement activities and preschooling to each other under the following condition:</p> <p></p> <ulist> <item> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mo><</mo><mn>0</mn><mspace width="0.166667em" /><mi>a</mi><mi>n</mi><mi>d</mi><mspace width="0.166667em" /><mfrac><mrow><mi mathvariant="italic">dA</mi></mrow><mrow><mi mathvariant="italic">dS</mi></mrow></mfrac><mo stretchy="false">→</mo><mn>0</mn></mrow></math> </ephtml> (neutral case)</item> </ulist> <p>In the case above, the marginal increase in achievement due to additional preschooling is infinitesimally small. Thus, the direct effect is positive, while the indirect effect is negative; interestingly, their absolute values are relatively equal, resulting in a near-zero total effect. This can occur when parents consider an additional year at preschool as a substitute, and therein reduce parental engagement to some extent as a result. Overall, the fall in a child's achievement due to lower parental engagement is offset by positive returns from preschool attendance, which leads to a neutral outcome.</p> <p></p> <ulist> <item> <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mo><</mo><mn>0</mn><mspace width="0.166667em" /><mi>a</mi><mi>n</mi><mi>d</mi><mspace width="0.166667em" /><mfrac><mrow><mi mathvariant="italic">dA</mi></mrow><mrow><mi mathvariant="italic">dS</mi></mrow></mfrac><mo><</mo><mn>0</mn></mrow></math> </ephtml> (substitutionary case)</item> </ulist> <p>In such a scenario, the indirect effect ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mi>∂</mi><mi>P</mi></mrow><mrow><mi>∂</mi><mi>S</mi></mrow></mfrac><mrow><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml> is negative and more than the direct positive effect. This is because the increase in achievement due to an increase in S following an increase in <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math> </ephtml> would imply that parents devote lesser time towards the child's education. In this substitutionary case, the loss of parental engagement is bigger than the preschool benefit, leading to a net decline in achievement. From another perspective, the preschool hours may be insufficient to fully compensate for the decline in achievement due to fewer hours of parental engagement.</p> <p>The model, as described above, motivates an empirical exercise we carry out in this paper. Moreover, this conceptual framework also alludes to the key purpose of this paper of examining whether preschooling and parental engagement can act as complements or substitutes for improving the learning outcomes, after controlling for cross-country variation. Hence, we are interested in the joint effect of parental engagement and levels of preschool enrollment on the test scores of math and science at the Grade 4 level.</p> <hd id="AN0185069215-4">Data and methodology</hd> <p></p> <hd id="AN0185069215-5">Data</hd> <p>We have employed the Trends in International Mathematics and Science Study (TIMSS) 2019 survey data that monitors global trends in mathematics and science learning for Grade 4 and Grade 8 students. In this study, we analyze the data of 52 countries,[<reflink idref="bib4" id="ref72">4</reflink>] where the math and science scores of Grade 4 students are the two dependent variables of interest. The main explanatory variables include the extent of parents' engagement during early childhood, measured using TIMSS Early Literacy and Numeracy Tasks (ELNT) scale, years of pre-primary education, and the interaction term between them.</p> <p>In large-scale time-constrained assessments like TIMSS, students may respond to a subset of the total question, introducing measurement errors. To eliminate uncertainties, plausible values are generated using Item Response Theory (IRT) based on students' responses to the question subset, along with contextual information from both the students' and parents' questionnaires. We have used IEA (International Association for the Evaluation of Educational Achievement) guidelines to determine scores using plausible values for the two subjects separately.</p> <p>The TIMSS, [<reflink idref="bib56" id="ref73">56</reflink>] survey provides an Early Literacy and Numeracy Tasks (ELNT) scale to account for the extent of parents' engagement and their frequency of undertaking 18 activities related to literacy and numeracy development of their children in their early years.[<reflink idref="bib5" id="ref74">5</reflink>] These activities include reading books, narrating stories, singing songs, playing with number toys, counting, writing numbers, and drawing shapes, among others (Martin et al., [<reflink idref="bib38" id="ref75">38</reflink>]). All these items are rated on a three-point Likert-type scale, ranging from 1 (never or rarely) to 3 (often). Importantly, this scale is developed after considering the highest education and occupation of either of the parents. For our study sample, the internal consistency reliability of this scale (determined by Cronbach's α) was 0.86. TIMSS, [<reflink idref="bib56" id="ref76">56</reflink>] includes data on the duration of preschool attendance, categorizing students into those who attended for less than a year, two years, and three or more years.</p> <p>To ensure that omitted variables do not bias the main coefficients of interest, we include a rich set of covariates in the regression equation. These variables are summarized in Table 1. To account for student background characteristics, we have incorporated control variables such as student gender, student age, and the TIMSS Home Resources Index for Grade 4, which captures the availability of educational resources at home (including the number of books, internet access, and a designated study space). Furthermore, we control for whether the student was born in the country of assessment and whether the student participated in supplementary math and science lessons aimed at academic enhancement. We also controlled for parental characteristics that include whether the parents were born in the current country of residence, the highest level of parental education, along with the parent's primary occupation. Since the students are nested within schools, the model controlled for school-level factors too, including the school's location, availability of school resources for math and science education, and school discipline and safety. We used country dummy variables to account for unobserved heterogeneity across different national contexts.</p> <p>Table 1 Summary statistics</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left"><p>Mean</p></th><th align="left"><p>Std. Dev</p></th></tr></thead><tbody><tr><td align="left"><p>Mathematics achievement score</p></td><td char="." align="char"><p>487.95</p></td><td char="." align="char"><p>103.56</p></td></tr><tr><td align="left"><p>Science achievement score</p></td><td char="." align="char"><p>479.51</p></td><td char="." align="char"><p>111.28</p></td></tr><tr><td align="left"><p>Parental engagement</p></td><td char="." align="char"><p>10.32</p></td><td char="." align="char"><p>2.11</p></td></tr><tr><td align="left"><p>Home resources</p></td><td char="." align="char"><p>9.97</p></td><td char="." align="char"><p>1.85</p></td></tr><tr><td align="left"><p>Math resources</p></td><td char="." align="char"><p>10.04</p></td><td char="." align="char"><p>2.42</p></td></tr><tr><td align="left"><p>Science resources</p></td><td char="." align="char"><p>10.05</p></td><td char="." align="char"><p>2.47</p></td></tr><tr><td align="left"><p>Age</p></td><td char="." align="char"><p>10.21</p></td><td char="." align="char"><p>0.67</p></td></tr><tr><td align="left"><p>School discipline</p></td><td char="." align="char"><p>9.90</p></td><td char="." align="char"><p>1.86</p></td></tr></tbody></table> </ephtml> </p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left"><p>Percentage of sample</p></th></tr></thead><tbody><tr><td align="left"><p>Female students</p></td><td align="left"><p>49.2</p></td></tr><tr><td align="left" colspan="2"><p><italic>Enrolment in preschool</italic></p></td></tr><tr><td align="left"><p> Not enrolled</p></td><td align="left"><p>12.1</p></td></tr><tr><td align="left"><p> Enrolled for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">≤</mo></math><inline-graphic mime-subtype="GIF" href="40723_2025_141_Article_IEq45.gif" /> 1 year</p></td><td align="left"><p>17</p></td></tr><tr><td align="left"><p> Enrolled for 2 years</p></td><td align="left"><p>18.1</p></td></tr><tr><td align="left"><p> Enrolled for <math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">≥</mo></math><inline-graphic mime-subtype="GIF" href="40723_2025_141_Article_IEq46.gif" /> 3 years</p></td><td align="left"><p>52.7</p></td></tr><tr><td align="left" colspan="2"><p><italic>Location of school</italic></p></td></tr><tr><td align="left"><p> Urban</p></td><td align="left"><p>32.4</p></td></tr><tr><td align="left"><p> Suburban</p></td><td align="left"><p>18.1</p></td></tr><tr><td align="left"><p> Medium city</p></td><td align="left"><p>22</p></td></tr><tr><td align="left"><p> Small Town/Village</p></td><td align="left"><p>21.4</p></td></tr><tr><td align="left"><p> Remote Rural</p></td><td align="left"><p>6.1</p></td></tr><tr><td align="left" colspan="2"><p><italic>Percentage of students in a school from an economically affluent background</italic></p></td></tr><tr><td align="left"><p> < 10 percent</p></td><td align="left"><p>29.6</p></td></tr><tr><td align="left"><p> 10–25 percent</p></td><td align="left"><p>18.9</p></td></tr><tr><td align="left"><p> 26–50 percent</p></td><td align="left"><p>22.2</p></td></tr><tr><td align="left"><p> > 50 percent</p></td><td align="left"><p>29.3</p></td></tr><tr><td align="left"><p> Parent 1 born in current country</p></td><td align="left"><p>75.0</p></td></tr><tr><td align="left"><p> Parent 2 born in current country</p></td><td align="left"><p>73.0</p></td></tr><tr><td align="left"><p> Parent education: University</p></td><td align="left"><p>41.2</p></td></tr><tr><td align="left"><p> Parent education: Post secondary</p></td><td align="left"><p>18.9</p></td></tr><tr><td align="left"><p> Parent education: Upper secondary</p></td><td align="left"><p>0.243</p></td></tr><tr><td align="left"><p> Parent education: Lower secondary</p></td><td align="left"><p>0.079</p></td></tr><tr><td align="left"><p> Parent education: Primary</p></td><td align="left"><p>0.070</p></td></tr><tr><td align="left"><p> Parent Occupation: Professional</p></td><td align="left"><p>41.5</p></td></tr><tr><td align="left"><p> Parent Occupation: Small business</p></td><td align="left"><p>12.1</p></td></tr><tr><td align="left"><p> Parent Occupation: Clerical</p></td><td align="left"><p>19.8</p></td></tr><tr><td align="left"><p> Parent Occupation: Skilled Worker</p></td><td align="left"><p>11.3</p></td></tr><tr><td align="left"><p> Parent Occupation: General labour</p></td><td align="left"><p>0.5</p></td></tr><tr><td align="left"><p> Student 1 born in current country</p></td><td align="left"><p>89.2</p></td></tr><tr><td align="left"><p> Extra lessons in Math for excelling</p></td><td align="left"><p>11.7</p></td></tr><tr><td align="left"><p> Extra lessons in Math for keeping up</p></td><td align="left"><p>11.3</p></td></tr><tr><td align="left"><p> Extra lessons in science for excelling</p></td><td align="left"><p>6.7</p></td></tr><tr><td align="left"><p> Extra lessons in science for keeping up</p></td><td align="left"><p>7.0</p></td></tr></tbody></table> </ephtml> </p> <p>The sample considered in this paper comprised of 280,925 observations from students in 756 schools across 52 countries</p> <hd id="AN0185069215-6">Methodology</hd> <p>Estimating the impact of preschools on future learning outcomes is challenging due to the potential self-selection of parents and students based on their 'types'. For instance, several unobservable factors like parental preference, motivation, and family background may influence school choice. The observed achievement scores may be influenced by country and school-level factors. Furthermore, due to the shared variance of outcomes at each level, applying the Ordinary Least Squares (OLS) may provide inaccurate results. We employed a three-level HLM, along with a linear mixed model with random effects, both at school and country levels. These random effects may be interpreted as residual differentials.</p> <p>Regression equations of the three-level HLM:</p> <p>Level 1:</p> <p>7 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>y</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>=</mo><msub><mi>π</mi><mrow><mn>0</mn><mi>j</mi><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>θ</mi><mrow><mn>1</mn><mi>j</mi><mi>k</mi></mrow></msub><msub><mi>P</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>+</mo><msub><mi>θ</mi><mrow><mn>2</mn><mi>j</mi><mi>k</mi></mrow></msub><msub><mi>S</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>+</mo><msub><mi>θ</mi><mrow><mn>3</mn><mi>j</mi><mi>k</mi></mrow></msub><mfenced close=")" open="("><msub><mi>P</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>×</mo><msub><mi>S</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></mfenced><mo>+</mo><munderover><mo>∑</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mi>P</mi></munderover><msub><mi>π</mi><mrow><mi mathvariant="italic">pjk</mi></mrow></msub><msub><mi>X</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>+</mo><msub><mi>e</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></mrow></math> </ephtml></p> <p>Graph</p> <p>where <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>y</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></math> </ephtml> is the dependent variable, <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></math> </ephtml> is parental engagement, <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>S</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></math> </ephtml> is preschool participation, <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mi mathvariant="italic">ipjk</mi></mrow></msub></math> </ephtml> is the vector of explanatory variables <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>e</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub></math> </ephtml> is the error term with:</p> <p> <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>e</mi><mrow><mi mathvariant="italic">ijk</mi></mrow></msub><mo>∼</mo><mi>N</mi><mrow><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><msup><mrow><mi>σ</mi></mrow><mn>2</mn></msup><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml> </p> <p>Graph</p> <p>The sign and significance of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>θ</mi><mn>3</mn></msub></math> </ephtml> would indicate whether the inputs are substitutes ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>θ</mi><mn>3</mn></msub><mrow><mo><</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml> or complements ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>θ</mi><mn>3</mn></msub><mrow><mo>></mo><mn>0</mn><mo stretchy="false">)</mo></mrow></mrow></math> </ephtml> , thus allowing us to assess which marginal productivity is declining. At level 2, the coefficients <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> </ephtml> and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> </ephtml> obtained from level 1 are considered outcome variables to be predicted. Let <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ρ</mi><mo>=</mo><mo stretchy="false">[</mo><mi>θ</mi><mi>π</mi><mo stretchy="false">]</mo></mrow></math> </ephtml> Hence, we have eqs. (<reflink idref="bib8" id="ref77">8</reflink>) and (<reflink idref="bib9" id="ref78">9</reflink>):</p> <p>8 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>ρ</mi><mrow><mi mathvariant="italic">jk</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mi mathvariant="italic">pjk</mi></mrow></msub><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>q</mi><mo>=</mo><mn>1</mn></mrow><mi>Q</mi></msubsup><msub><mi>β</mi><mrow><mi mathvariant="italic">pqk</mi></mrow></msub><msub><mi>W</mi><mrow><mi mathvariant="italic">qjk</mi></mrow></msub><mo>+</mo><msub><mi>r</mi><mrow><mi mathvariant="italic">pjk</mi></mrow></msub></mrow></math> </ephtml></p> <p>Graph</p> <p>9 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>π</mi><mrow><mn>0</mn><mi>j</mi><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>β</mi><mrow><mn>0</mn><mi>j</mi><mi>k</mi></mrow></msub><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>q</mi><mo>=</mo><mn>1</mn></mrow><mi>Q</mi></msubsup><msub><mi>β</mi><mrow><mn>0</mn><mi>q</mi><mi>k</mi></mrow></msub><msub><mi>W</mi><mrow><mi mathvariant="italic">qjk</mi></mrow></msub><mo>+</mo><msub><mi>r</mi><mrow><mn>0</mn><mi>j</mi><mi>k</mi></mrow></msub></mrow></math> </ephtml></p> <p>Graph</p> <p>where <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>β</mi><mrow><mi mathvariant="italic">pqk</mi></mrow></msub></math> </ephtml> are level 2 coefficients and <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>W</mi><mrow><mi mathvariant="italic">qjk</mi></mrow></msub></math> </ephtml> are the random explanatory variables. <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mrow><mi mathvariant="italic">pjk</mi></mrow></msub></math> </ephtml> represents the error term. The vectors of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>r</mi><mo>′</mo><mi>s</mi></mrow></math> </ephtml> are assumed to have a multivariate normal distribution with a mean vector of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn></mrow></math> </ephtml> , covariance matrix <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>π</mi></msub></math> </ephtml> and the dimension <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="false">(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> </ephtml> . Further, in level 3, the coefficient <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math> </ephtml> obtained from level 2 is considered outcome variable.</p> <p>Equations (<reflink idref="bib10" id="ref79">10</reflink>) and (<reflink idref="bib11" id="ref80">11</reflink>) are predicted:</p> <p>10 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>β</mi><mrow><mi mathvariant="italic">pqk</mi></mrow></msub><mo>=</mo><msub><mi>γ</mi><mrow><mi mathvariant="italic">pq</mi></mrow></msub><mo>+</mo><msub><mi>u</mi><mrow><mi mathvariant="italic">pqk</mi></mrow></msub></mrow></math> </ephtml></p> <p>Graph</p> <p>11 <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>β</mi><mrow><mn>0</mn><mi>j</mi><mi>k</mi></mrow></msub><mo>=</mo><msub><mi>γ</mi><mrow><mn>0</mn><mi>P</mi><mi>q</mi></mrow></msub><mo>+</mo><msub><mi>u</mi><mrow><mn>0</mn><mi>q</mi><mi>k</mi></mrow></msub></mrow></math> </ephtml></p> <p>Graph</p> <p>Herein, the vector of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> </ephtml> 's is assumed to have a multivariate normal distribution with a mean vector <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn></mrow></math> </ephtml> , covariance matrix <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>β</mi></msub></math> </ephtml> and the dimension of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="false">(</mo><mi>Q</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mi>Q</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> </ephtml> .</p> <p>where q = 1...Q.</p> <p>Following Rutkowski et al. ([<reflink idref="bib49" id="ref81">49</reflink>]), we selected one plausible value of math and science scores at random, and used it for the subjects. Plausible values are imputed values and not direct scores (Foy et al., [<reflink idref="bib22" id="ref82">22</reflink>]). Ignoring imputation variance, borderline statistically significant results should be carefully interpreted.</p> <hd id="AN0185069215-7">Descriptive analysis</hd> <p>The sample considered in this paper comprised 280925 observations from students in 756 schools across 52 countries. Almost half (49.2%) of the sample is female, as seen in Table 1. Although most schools are in urban areas, there is economic diversity among these attendees. Significant variation is seen in the average subject-wise scores (for details, please see Table A1); for instance, the Philippines had the lowest achievement scores in both mathematics and science at 298.97 and 252.72, while Singapore had the highest (622.16 and 591.14 respectively). Other top performers include South Korea, Hong Kong, and Russia, while Pakistan, South Africa, and Morocco perform poorly (317.53, 370.44, and 372.14 respectively).</p> <p>The data suggests that preschool enrollment is not a universal choice, and the degree of parental engagement also varies across countries and cultural contexts. Notably, parental engagement is lowest in Morocco, followed by Pakistan and Turkey, whereas it is highest in Russia, followed by Albania and Ireland.</p> <hd id="AN0185069215-8">Results and discussion</hd> <p>We initially used the base HLM model, incorporating preschool enrollment and parental engagement (ELNT Index) as explanatory variables. The analysis reveals a statistically significant and positive effect of both preschool enrollment and parental engagement on student achievement. Notably, students with over three years of preschool experience exhibited significantly higher scores in mathematics and science as compared to their counterparts who do not attend preschool (for details, <emph>please see</emph> Table A2). Similarly, higher levels of parental engagement, as reflected by the ELNT Index, are associated with improved achievement scores in both subjects. Furthermore, a positive and statistically significant effect is observed for science achievement in students who attended preschool for two years. This effectively validates previous findings of positive association between attending preschool and student achievement, across several countries.</p> <hd id="AN0185069215-9">Parental engagement and preschooling: substitutes or complements?</hd> <p>Table 2 explores the interaction effects between parental engagement (ELNT) and years of preschool attendance on TIMSS mathematics test scores.</p> <p>Table 2 HLM regression results for student achievement scores in mathematics</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left" colspan="4"><p>Dependent variable: TIMSS Student Achievement Scores (Mathematics)</p></th></tr><tr><th align="left"><p>Fixed effects</p></th><th align="left"><p>(1)</p></th><th align="left"><p>(2)</p></th><th align="left"><p>(3)</p></th><th align="left"><p>(4)</p></th></tr></thead><tbody><tr><td align="left"><p>(a) Parental engagement (ELNT Index)</p></td><td align="left"><p>4.374*** (0.187)</p></td><td align="left"><p>1.207*** (0.176)</p></td><td align="left"><p>1.414*** (0.175)</p></td><td align="left"><p>1.273*** (0.175)</p></td></tr><tr><td align="left" colspan="5"><p>(b) Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) Preschool enrollment up-to 1 year</p></td><td align="left"><p>4.273 (2.599)</p></td><td align="left"><p>− 1.185 (2.431)</p></td><td align="left"><p>− 0.842 (2.421)</p></td><td align="left"><p>− 2.427 (2.413)</p></td></tr><tr><td align="left"><p> (ii) Preschool enrollment for 2 years</p></td><td align="left"><p>11.066*** (2.585)</p></td><td align="left"><p>1.679 (2.418)</p></td><td align="left"><p>0.547 (2.411)</p></td><td align="left"><p>− 1.662 (2.404)</p></td></tr><tr><td align="left"><p> (iii) Preschool enrollment for 3 years and more</p></td><td align="left"><p>28.641*** (2.167)</p></td><td align="left"><p>13.051*** (2.032)</p></td><td align="left"><p>11.767*** (2.032)</p></td><td align="left"><p>9.643*** (2.028)</p></td></tr><tr><td align="left" colspan="5"><p>(c) Parental engagement X Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) ELNT X preschool enrollment up-to 1 year</p></td><td align="left"><p>0.695** (0.257)</p></td><td align="left"><p>0.613** (0.240)</p></td><td align="left"><p>0.480** (0.239)</p></td><td align="left"><p>0.583*** (0.238)</p></td></tr><tr><td align="left"><p> (ii) ELNT X preschool enrollment for 2 years</p></td><td align="left"><p>0.916*** (0.253)</p></td><td align="left"><p>0.753*** (0.237)</p></td><td align="left"><p>0.685*** (0.236)</p></td><td align="left"><p>0.845*** (0.235)</p></td></tr><tr><td align="left"><p> (iii) ELNT X preschool enrollment for 3 years or more</p></td><td align="left"><p>0.295 (0.214)</p></td><td align="left"><p>0.101 (0.200)</p></td><td align="left"><p>0.027 (0.200)</p></td><td align="left"><p>0.161 (0.199)</p></td></tr><tr><td align="left"><p> Student characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> Parent characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> School characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left" colspan="5"><p> Random effects</p></td></tr><tr><td align="left" /><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td></tr><tr><td align="left"><p> School</p></td><td align="left"><p>1146</p></td><td align="left"><p>837.8</p></td><td align="left"><p>819.7</p></td><td align="left"><p>774</p></td></tr><tr><td align="left"><p> Country</p></td><td align="left"><p>3852</p></td><td align="left"><p>2816.5</p></td><td align="left"><p>2870.7</p></td><td align="left"><p>2729</p></td></tr><tr><td align="left"><p> Residual</p></td><td align="left"><p>6635</p></td><td align="left"><p>5793.2</p></td><td align="left"><p>5731.9</p></td><td align="left"><p>5691</p></td></tr><tr><td align="left"><p> Observations</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td></tr></tbody></table> </ephtml> </p> <p>p < 0.1; <sups>**</sups>p < 0.05; <sups>***</sups>p < 0.01 Standard errors are reported in brackets For: Preschool enrolment and "Parental engagement X Preschool enrollment", the reference category is: "No preschool enrolment". Student characteristics include the gender of students being female (reference group is male students), age of the student, whether the student was born in the present country, whether the student takes extra lessons in mathematics and science to excel or to keep up, TIMSS index of home resources. Parental characteristics include whether the parents were born in the current country of residence, the highest level of parental education, and the parents' primary occupation group. School characteristics include the location of the school in the suburban area, medium city, small-town/village, and remote area, with a location in the urban area as the reference group. Other school variables are the TIMSS index on the availability of subject-specific teaching resources and school discipline. Each column includes a different set of control variables. The term "Yes" indicates that the specific group of control variables have been included in estimating the regression coefficients. The term "No" indicates that the group of variables have not been included in estimating the regression equation</p> <p>Column (<reflink idref="bib1" id="ref83">1</reflink>) of Table 2 reports the most parsimonious regression results that do not include any control variables. The subsequent columns report the regression results after including the student characteristics, parental characteristics, and school characteristics, respectively. The analysis reveals a positive and statistically significant joint effect for mathematics scores when attending preschool for a year. Notably, after the inclusion of all the variables, as compared to nonpreschoolers, a one-unit increase in the TIMSS parental engagement scale translates to test score gains of 0.58 units in math for those who complete one year of preschooling. This positive effect persists for math scores with two years of preschool attendance (with a test score increase of 0.84 units) as well. The results indicate that while the magnitude of the coefficients exhibits only marginal variations with the inclusion of different sets of control variables, the direction and statistical significance of the estimates remain largely stable, suggesting robustness to model specifications.</p> <p>Table 3 reports the corresponding results for TIMSS science test scores. For the science test scores too, we report the estimated coefficients of the most parsimonious model with no control variables and then include student characteristics, parental characteristics, and school characteristics subsequently. The findings indicate that while the inclusion of control variables alters the magnitudes of the main coefficients of interest, their direction and statistical significance remain unchanged. This may suggest potential endogeneity at the country level. In general, selection bias is not a primary concern in International Large-Scale Assessments (ILSAs) due to their robust, country-representative sampling methods. However, some selection bias may arise from nonresponse rates and sample replacement. Nevertheless, at the country level, TIMSS data remains broadly representative. Further, to ascertain that our results are robust, we estimate the same relationship using a fixed effects model (for details, <emph>please see</emph> Table A3). The results remain consistent in terms of sign and statistical significance, reinforcing the reliability of our estimates.</p> <p>Table 3 HLM regression results for student achievement scores in science</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left" colspan="4"><p>Dependent variable: TIMSS Student Achievement Scores (Science)</p></th></tr><tr><th align="left"><p>Fixed Effects</p></th><th align="left"><p>(1)</p></th><th align="left"><p>(2)</p></th><th align="left"><p>(3)</p></th><th align="left"><p>(4)</p></th></tr></thead><tbody><tr><td align="left"><p>(a) Parental Engagement (ELNT Index)</p></td><td align="left"><p>5.830*** (0.197)</p></td><td align="left"><p>2.434*** (0.185)</p></td><td align="left"><p>2.561*** (0.185)</p></td><td align="left"><p>2.095*** (0.175)</p></td></tr><tr><td align="left" colspan="5"><p>(b) Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) Preschool enrollment up-to 1 year</p></td><td align="left"><p>7.755*** (2.751)</p></td><td align="left"><p>2.954 (2.564)</p></td><td align="left"><p>2.668 (2.553)</p></td><td align="left"><p>− 0.349 (2.424)</p></td></tr><tr><td align="left"><p> (ii) Preschool enrollment for 2 years</p></td><td align="left"><p>20.753*** (2.735)</p></td><td align="left"><p>11.255*** (2.550)</p></td><td align="left"><p>9.113*** (2.542)</p></td><td align="left"><p>4.901*** (2.397)</p></td></tr><tr><td align="left"><p> (iii) Preschool enrollment for 3 years and more</p></td><td align="left"><p>39.201*** (2.300)</p></td><td align="left"><p>23.204*** (2.153)</p></td><td align="left"><p>20.886*** (2.142)</p></td><td align="left"><p>17.247*** (2.039)</p></td></tr><tr><td align="left" colspan="5"><p>(c) Parental Engagement X Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) ELNT X Preschool enrollment up-to 1 year</p></td><td align="left"><p>0.491* (0.273)</p></td><td align="left"><p>0.342 (0.254)</p></td><td align="left"><p>0.156 (0.252)</p></td><td align="left"><p>0.458*** (0.239)</p></td></tr><tr><td align="left"><p> (ii) ELNT X Preschool enrollment for 2 years</p></td><td align="left"><p>0.391 (0.269)</p></td><td align="left"><p>0.116 (0.251)</p></td><td align="left"><p>0.037 (0.249)</p></td><td align="left"><p>0.390 (0.234)</p></td></tr><tr><td align="left"><p> (iii) ELNT X Preschool enrollment for 3 years or more</p></td><td align="left"><p>− 0.695*** (0.227)</p></td><td align="left"><p>− 0.927*** (0.212)</p></td><td align="left"><p>− 0.951*** (0.210)</p></td><td align="left"><p>− 0.668*** (0.119)</p></td></tr><tr><td align="left"><p> Student characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> Parent characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> School characteristics</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>No</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left" colspan="5"><p>Random effects</p></td></tr><tr><td align="left" /><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td></tr><tr><td align="left"><p>School</p></td><td align="left"><p>1428</p></td><td align="left"><p>1076</p></td><td align="left"><p>1060</p></td><td align="left"><p>992.5</p></td></tr><tr><td align="left"><p>Country</p></td><td align="left"><p>4269</p></td><td align="left"><p>2941</p></td><td align="left"><p>2976</p></td><td align="left"><p>2624.1</p></td></tr><tr><td align="left"><p>Residual</p></td><td align="left"><p>7425</p></td><td align="left"><p>6461</p></td><td align="left"><p>6396</p></td><td align="left"><p>6259.2</p></td></tr><tr><td align="left"><p>Observations</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td><td align="left"><p>280925</p></td></tr></tbody></table> </ephtml> </p> <p>p < 0.1; <sups>**</sups>p < 0.05; <sups>***</sups>p < 0.01 Standard errors are reported in brackets For: Preschool enrolment and "Parental engagement X Preschool enrollment", the reference category is: "No preschool enrolment". Student characteristics include the gender of students being female (reference group is male students), age of the student, whether the student was born in the present country, whether the student takes extra lessons in mathematics and science to excel or to keep up, TIMSS index of home resources. Parental characteristics include whether the parents were born in the current country of residence, the highest level of parental education, and the parents' primary occupation group. School characteristics include the location of the school in the suburban area, medium city, small-town/village, and remote area, with a location in the urban area as the reference group. Other school variables are the TIMSS index on the availability of subject-specific teaching resources and school discipline. The term "Yes" indicates that the specific group of control variables have been included in estimating the regression coefficients. The term "No" indicates that the group of variables have not been included in estimating the regression equation</p> <p>The estimated coefficients from both the multilevel HLM model as well as fixed effects OLS estimation suggest a potential complementary effect between parental engagement and preschooling, with benefits observed for up to two years in math. However, the science score increments due to increased parental engagement become insignificant for up to two years of preschooling, and interestingly, turn negative for three or more years of preschooling. For the third year of preschooling or more, the interaction effect between preschooling and parental engagement turns negative and significant, only for science. Importantly, both insignificant and negative results indicate potential substitutability between preschooling and parental engagement above two years of attendance, given that preschooling till 3 years does have a significant effect on science scores itself, as derived from our conceptual framework.</p> <hd id="AN0185069215-10">Types of parental engagement</hd> <p>The ELNT variable, a measure of parental engagement, includes at-home literacy and numeracy activities. Literacy tasks include reading books, singing songs, playing different word games, etc.; while numeracy tasks include counting rhymes, playing with number toys, card games, etc. To understand heterogeneous returns to parenting, we run the same regression as in eqs. (i)–(v) twice, once with the literacy scale and numeracy scale using the TIMSS indices, as depicted in Table 4.</p> <p>Table 4 HLM regression results for student achievement scores by early literacy and numeracy tasks</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left" colspan="2"><p>Early Literacy Task</p></th><th align="left" colspan="2"><p>Early Numeracy Task</p></th></tr><tr><th align="left" /><th align="left"><p>Math</p></th><th align="left"><p>Science</p></th><th align="left"><p>Math</p></th><th align="left"><p>Science</p></th></tr><tr><th align="left"><p>Fixed effects</p></th><th align="left"><p>(1)</p></th><th align="left"><p>(2)</p></th><th align="left"><p>(3)</p></th><th align="left"><p>(4)</p></th></tr></thead><tbody><tr><td align="left"><p>(a) Parental engagement (ELNT Index)</p></td><td align="left"><p>0.77*** (0.16)</p></td><td align="left"><p>1.84*** (0.17)</p></td><td align="left"><p>1.38*** (0.17)</p></td><td align="left"><p>2.81*** (0.18)</p></td></tr><tr><td align="left" colspan="5"><p>(b) Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) Preschool enrollment up-to 1 year</p></td><td align="left"><p>− 1.82*** (2.20)</p></td><td align="left"><p>0.21 (2.32)</p></td><td align="left"><p>− 1.70 (2.41)</p></td><td align="left"><p>2.47 (2.54)</p></td></tr><tr><td align="left"><p> (ii) Preschool enrollment for 2 years</p></td><td align="left"><p>1.15 (2.20)</p></td><td align="left"><p>7.06*** (2.32)</p></td><td align="left"><p>− 1.66 (2.40)</p></td><td align="left"><p>7.03*** (2.53)</p></td></tr><tr><td align="left"><p> (iii) Preschool enrollment for 3 years and more</p></td><td align="left"><p>9.73*** (1.86)</p></td><td align="left"><p>15.08*** (1.96)</p></td><td align="left"><p>9.84 (2.03)</p></td><td align="left"><p>19.46*** (2.14)</p></td></tr><tr><td align="left" colspan="5"><p>(c) Parental engagement X Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) ELNT X Preschool enrollment up-to 1 year</p></td><td align="left"><p>0.55*** (0.22)</p></td><td align="left"><p>0.37 (0.23)</p></td><td align="left"><p>0.50*** (0.23)</p></td><td align="left"><p>0.12*** (0.24)</p></td></tr><tr><td align="left"><p> (ii) ELNT X Preschool enrollment for 2 years</p></td><td align="left"><p>0.60*** (0.22)</p></td><td align="left"><p>0.20 (0.23)</p></td><td align="left"><p>0.83*** (0.23)</p></td><td align="left"><p>0.19*** (0.24)</p></td></tr><tr><td align="left"><p> (iii) ELNT X Preschool enrollment for 3 years or more</p></td><td align="left"><p>0.18 (0.18)</p></td><td align="left"><p>-0.46** (0.19)</p></td><td align="left"><p>0.14*** (0.19)</p></td><td align="left"><p>-0.86*** (0.21)</p></td></tr><tr><td align="left"><p> Student characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> School characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> Parent characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left" colspan="5"><p>Random effects</p></td></tr><tr><td align="left" /><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td></tr><tr><td align="left"><p>School</p></td><td align="left"><p>773.8</p></td><td align="left"><p>992.7</p></td><td align="left"><p>775.9</p></td><td align="left"><p>995.5</p></td></tr><tr><td align="left"><p>Country</p></td><td align="left"><p>2729</p></td><td align="left"><p>2816.7</p></td><td align="left"><p>2721.6</p></td><td align="left"><p>2799.3</p></td></tr><tr><td align="left"><p>Residual</p></td><td align="left"><p>5695</p></td><td align="left"><p>6320.2</p></td><td align="left"><p>5689</p></td><td align="left"><p>6319.4</p></td></tr></tbody></table> </ephtml> </p> <p>p < 0.1; <sups>**</sups>p < 0.05; <sups>***</sups>p < 0.01 Standard errors are reported in brackets For: Preschool enrolment and "Parental engagement X Preschool enrollment", the reference category is: "No preschool enrolment". Student characteristics include the gender of students being female (reference group is male students), age of the student, whether the student was born in the present country, whether the student takes extra lessons in mathematics and science for excelling or for keeping up, TIMSS index of home resources. Parental characteristics include whether the parents were born in the current country of residence, the highest level of parental education, parents' primary occupation group. School characteristics include the location of the school in the suburban area, medium city, small-town/village, and remote area, with a location in the urban area as the reference group. Other school variables are the TIMSS index on the availability of subject-specific teaching resources and school discipline. The term "Yes" indicates that the specific group of control variables have been included in estimating the regression coefficients</p> <p>Home literacy and numeracy activities influence both math and science scores differently. For math, parental engagement complements preschooling for children with <emph>less than three years</emph> of attendance while enhancing outcomes. However, the results indicate substitutability between preschooling and parental engagement for 3 years or more, where higher parental engagement does not translate into a significant increase in student achievement. Moreover, the parents' engagement in neither task further improves science learning outcomes for children with ≥ 3 years of preschooling experience.</p> <hd id="AN0185069215-11">Cross-country heterogeneities</hd> <p>The objective of pre-primary schooling and early childhood parental engagement is to equip students with the foundational skills to excel later in life. We observed heterogeneities across countries (for details, <emph>please see</emph> Table A1). Even though enrolment in formal preschooling has increased over the years, there exists inequalities both across and within countries (Raikes et al., 2023, Kamerman, [<reflink idref="bib35" id="ref84">35</reflink>]; Ünver et al., [<reflink idref="bib58" id="ref85">58</reflink>]). As discussed earlier, the differences in ECEC enrolment could be due to self-selection issues, but also due to country-wise differences in institutional features and policies associated with ECEC structures. However, due to paucity of data on institutional features of the ECEC structure across all the countries included in our study, we focus on the heterogeneous effect on test scores across countries based on varying preschool enrolment.</p> <p>Tables 5 and 6 present the heterogeneity of the interaction effects of early childhood parental engagement vis-à-vis preschool enrollment, across different countries, grouped based on the extent of the proportion of students with no preschooling in the country. We classified countries into three groups based on the proportion of students without preschooling: (i) Group 1: countries with less than 5% of students lacking preschooling, (ii) Group 2: countries where 5% to 15% of students have no preschooling, and (iii) Group 3: countries with more than 15% of students not attending preschool. For each group, the reference category for the interaction terms between parental engagement and preschooling consists of students who did not attend preschool.</p> <p>Table 5 HLM regression results for student achievement scores in mathematics by nation-wise preschooling status</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left"><p>Group 1: No Preschooling up to 5%</p></th><th align="left"><p>Group 2: No Preschooling (> 5%-15%)</p></th><th align="left"><p>Group 3: No Preschooling (> 15%)</p></th></tr><tr><th align="left"><p>Fixed effects</p></th><th align="left"><p>(1)</p></th><th align="left"><p>(2)</p></th><th align="left"><p>(3)</p></th></tr></thead><tbody><tr><td align="left"><p>(a) Parental engagement (ELNT Index)</p></td><td align="left"><p>− 0.192 (0.567)</p></td><td align="left"><p>0.364 (0.389)</p></td><td align="left"><p>2.287*** (0.220)</p></td></tr><tr><td align="left" colspan="4"><p>(b) Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) Preschool enrollment up-to 1 year</p></td><td align="left"><p>− 9.833 (6.680)</p></td><td align="left"><p>− 4.047 (5.071)</p></td><td align="left"><p>2.815 (3.216)</p></td></tr><tr><td align="left"><p> (ii) Preschool enrollment for 2 years</p></td><td align="left"><p>3.478 (6.407)</p></td><td align="left"><p>− 12.721*** (4.886)</p></td><td align="left"><p>7.451*** (3.422)</p></td></tr><tr><td align="left"><p> (iii) Preschool enrollment for 3 years and more</p></td><td align="left"><p>6.325 (5.764)</p></td><td align="left"><p>− 1.789 (4.372)</p></td><td align="left"><p>20.618*** (3.141)</p></td></tr><tr><td align="left" colspan="4"><p>(c) Parental engagement X Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) ELNT X Preschool enrollment up-to 1 year</p></td><td align="left"><p>2.009*** (0.664)</p></td><td align="left"><p>0.716 (0.498)</p></td><td align="left"><p>0.105 (0.318)</p></td></tr><tr><td align="left"><p> (ii) ELNT X Preschool enrollment for 2 years</p></td><td align="left"><p>1.153** (0.639)</p></td><td align="left"><p>1.854*** (0.476)</p></td><td align="left"><p>0.049 (0.334)</p></td></tr><tr><td align="left"><p> (iii) ELNT X Preschool enrollment for 3 years or more</p></td><td align="left"><p>1.561** (0.580)</p></td><td align="left"><p>1.213** (0.425)</p></td><td align="left"><p>-1.194*** (0.303)</p></td></tr><tr><td align="left"><p> Student characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> School characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left" colspan="4"><p>Random effects</p></td></tr><tr><td align="left" /><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td></tr><tr><td align="left"><p>School</p></td><td align="left"><p>31.61</p></td><td align="left"><p>362</p></td><td align="left"><p>2293</p></td></tr><tr><td align="left"><p>Country</p></td><td align="left"><p>1190.5</p></td><td align="left"><p>3481</p></td><td align="left"><p>2597</p></td></tr><tr><td align="left"><p>Residual</p></td><td align="left"><p>4164.69</p></td><td align="left"><p>5868</p></td><td align="left"><p>6243</p></td></tr><tr><td align="left"><p>Observation</p></td><td align="left"><p>90417</p></td><td align="left"><p>87817</p></td><td align="left"><p>102691</p></td></tr></tbody></table> </ephtml> </p> <p>p < 0.1; <sups>**</sups>p < 0.05; <sups>***</sups>p < 0.01 Standard errors are reported in brackets For: Preschool enrolment and "Parental engagement X Preschool enrollment", the reference category is: "No preschool enrolment". Student characteristics include the gender of students being female (reference group is male students), the age of the student, whether the student was born in the present country, whether the student takes extra lessons in mathematics and science to excel or to keep up, TIMSS index of home resources. Parental characteristics include whether the parents were born in the current country of residence, the highest level of parental education, and the parents' primary occupation group. School characteristics include the location of the school in a suburban area, medium city, small-town/village, and remote area, with the location in an urban area as the reference group. Other school variables are the TIMSS index on the availability of subject-specific teaching resources and school discipline. The term "Yes" indicates that the specific group of control variables have been included in estimating the regression coefficients</p> <p>Table 6 HLM regression results for student achievement scores in science by nation-wise preschooling status</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Variables</p></th><th align="left"><p>Group 1: No preschooling up to 5%</p></th><th align="left"><p>Group 2: No preschooling (> 5%-15%)</p></th><th align="left"><p>Group 3: No preschooling (> 15%)</p></th></tr><tr><th align="left"><p>Fixed effects</p></th><th align="left"><p>(1)</p></th><th align="left"><p>(2)</p></th><th align="left"><p>(3)</p></th></tr></thead><tbody><tr><td align="left"><p>(a) Parental engagement (ELNT Index)</p></td><td align="left"><p>1.107** (0.548)</p></td><td align="left"><p>0.853** (0.408)</p></td><td align="left"><p>3.457*** (0.241)</p></td></tr><tr><td align="left" colspan="4"><p>(b) Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) Preschool enrollment up-to 1 year</p></td><td align="left"><p>− 5.022 (6.452)</p></td><td align="left"><p>− 9.494* (5.323)</p></td><td align="left"><p>8.838*** (3.525)</p></td></tr><tr><td align="left"><p> (ii) Preschool enrollment for 2 years</p></td><td align="left"><p>14.306** (6.189)</p></td><td align="left"><p>− 8.966* (5.128)</p></td><td align="left"><p>13.982*** (3.752)</p></td></tr><tr><td align="left"><p> (iii) Preschool enrollment for 3 years and more</p></td><td align="left"><p>19.811** (5.567)</p></td><td align="left"><p>− 1.114 (4.557)</p></td><td align="left"><p>24.938*** (3.443)</p></td></tr><tr><td align="left" colspan="4"><p>(c) Parental engagement X Preschool enrollment</p></td></tr><tr><td align="left"><p> (i) ELNT X Preschool enrollment up-to 1 year</p></td><td align="left"><p>1.600** (0.641)</p></td><td align="left"><p>1.150** (0.522)</p></td><td align="left"><p>-0.478 (0.349)</p></td></tr><tr><td align="left"><p> (ii) ELNT X Preschool enrollment for 2 years</p></td><td align="left"><p>0.337 (0.618)</p></td><td align="left"><p>1.490*** (0.499)</p></td><td align="left"><p>-0.422 (0.366)</p></td></tr><tr><td align="left"><p> (iii) ELNT X Preschool enrollment for 3 years or more</p></td><td align="left"><p>0.169 (0.560)</p></td><td align="left"><p>0.938** (0.446)</p></td><td align="left"><p>-1.728*** (0.332)</p></td></tr><tr><td align="left"><p> Student characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p> School characteristics</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left" colspan="4"><p>Random effects:</p></td></tr><tr><td align="left" /><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td><td align="left"><p>Variance</p></td></tr><tr><td align="left"><p>School</p></td><td align="left"><p>29.64</p></td><td align="left"><p>356.6</p></td><td align="left"><p>2988</p></td></tr><tr><td align="left"><p>Country</p></td><td align="left"><p>550.71</p></td><td align="left"><p>3886.1</p></td><td align="left"><p>2539</p></td></tr><tr><td align="left"><p>Residual</p></td><td align="left"><p>3885.82</p></td><td align="left"><p>6464.4</p></td><td align="left"><p>7503</p></td></tr><tr><td align="left"><p>Observation</p></td><td align="left"><p>90417</p></td><td align="left"><p>87817</p></td><td align="left"><p>102691</p></td></tr></tbody></table> </ephtml> </p> <p>p < 0.1; <sups>**</sups>p < 0.05; <sups>***</sups>p < 0.01 Standard errors are reported in brackets For: Preschool enrolment and "Parental engagement X Preschool enrollment" the reference category is: "No preschool enrolment". Student characteristics include the gender of students being female (reference group is male students), age of the student, whether the student was born in the present country, whether the student takes extra lessons in mathematics and science to excel or to keep up, TIMSS index of home resources. Parental characteristics include whether the parents were born in the current country of residence, the highest level of parental education, and the parents' primary occupation group. School characteristics include the location of the school in a suburban area, medium city, small-town/village, and remote area, with a location in an urban area as the reference group. Other school variables are the TIMSS index on the availability of subject-specific teaching resources and school discipline. The term "Yes" indicates that the specific group of control variables have been included in estimating the regression coefficients</p> <p>Table 5, focusing on TIMSS mathematics scores, indicates that in Group 1, there is evidence of complementarity between preschooling and parental engagement to some extent. The interaction terms for parental engagement with preschool attendance of up to one year, two years, and three or more years are statistically significant and positive as compared to no preschooling. In contrast, this effect becomes evident for students attending preschool for at least two years in Group 2. However, in Group 3—where a higher proportion of students lack preschooling—the interaction effect is insignificant for up to one and two years of preschooling. Additionally, there is indication of substitutability for students with more than three years of preschooling. Figure 2 provides a visual summary of these findings.</p> <p>Graph: Fig. 2 Heterogenous effects of parental engagement and preschooling on TIMSS mathematics test scores</p> <p>Increased parental engagement is likely to lead to improvement in science test scores across all country groups, as depicted in Table 6.</p> <p>However, the interaction effect is positive and significant only for those with preschooling up to 1 year in Group 1. Importantly, the interaction effect is significant and positive across all levels of preschooling for Group 2. For However, in Group 3, similar to the results in Table 5, the interaction effect is insignificant for up to one and two years of preschooling. Additionally, there is indication of substitutability for students with more than three years of preschooling. Here, either preschool enrolment or parental engagement leads to higher test scores relative to the interaction effects Fig. 3 provides a visual summary of these findings.</p> <p>Graph: Fig. 3 Heterogenous effects of parental engagement and preschooling on TIMSS science test scores</p> <p>In summary, the findings indicate that the interaction effect becomes smaller as the proportion of preschool enrolment reduces across countries. Preschooling is likely to complement parental engagement in countries where a larger number of children are in preschools, as compared to countries with lower enrolment rates.</p> <hd id="AN0185069215-12">Conclusion</hd> <p>Broadly, the HLM analysis indicates that both parental engagement and preschool enrollment are important, working as facilitators. The findings confirm that parental engagement and preschooling are complementary, with subject-specific variations. A unit increase in the scale of TIMSS parental engagement increases mathematics scores by 0.58–0.84 units with varying preschool duration, while the estimates are considerably lower for science. Globally, policymakers prioritize universal pre-primary education due to scalability, while often overlooking aspects like parental engagement. As governments expand preschooling to develop human capital, effective ECEC policies should integrate both aspects. Without quality parental engagement, preschooling may be insufficient. Previous research supports the idea that better information dissemination and hand-holding support to parents could improve learning (Napoli et al., [<reflink idref="bib45" id="ref86">45</reflink>]).</p> <p>Since the effect of preschool enrollment and parental engagement is high for students in countries with a higher proportion of preschooling, policy interventions to boost aggregate preschool enrollment along with parental engagement are essential. Moreover, our results show that early numeracy activities have a higher effect than literacy activities on the eventual cognitive gains. Generally, numeracy activities increase the math and science scores by 0.5 and 0.12 units, respectively, when coupled with preschooling of up to 1 year. This difference may be utilized by practitioners for designing and incentivizing domain-specific parental engagement.</p> <p>However, the limitations of this study must be acknowledged. Firstly, pinpointing the exact source of parental engagement remains challenging. This study attempts to address this by using the Early Literacy and Numeracy Tasks (ELNT) scale provided by TIMSS, which uses Likert's scale and attempts to measure both the frequency of engagement and extent of engagement in different activities. This does not holistically capture quality of parental engagement and richer data on engagement can be further explored to delve deeper into this topic.</p> <p>Secondly, while the use of multilevel linear modeling helps to account for interclass clustering effects at the student, school, and country levels, it does not address endogeneity arising from omitted variable bias. To ascertain that our results are robust, we estimated the same relationship using a fixed effects model, where the results remained consistent in terms of sign and statistical significance. However, the possibility of omitted variable persists, which cannot be fully accounted for due to the limitations of data and the secondary nature of the study.</p> <p>Further, due to the data unavailability, our model simplifies the allocation of time between work and childcare because we lack data on family structure, which has been found to significantly influence the time parents spend with their children (Harris & Goodall, [<reflink idref="bib29" id="ref87">29</reflink>]). In addition, influences on learning outcomes through neighborhood disadvantage during early years (Sammons et al., [<reflink idref="bib50" id="ref88">50</reflink>]), preschool quality (Muttaqin, [<reflink idref="bib44" id="ref89">44</reflink>]), the number of children per couple and the involvement of family members beyond parents (Bryson & Casper, [<reflink idref="bib11" id="ref90">11</reflink>]) could not be explored in detail due to data unavailability. Future research could address these gaps by incorporating additional nuances of the caregiving and learning environment. In addition, such questions and indicators could be added to existing ILSAs such as TIMSS to facilitate varied large-scale and cross-country investigation in this regard. This study contributes to unravelling the influence of responsive early childhood parenting and preschool enrollment on eventual student learning outcomes using global evidence, notwithstanding.</p> <hd id="AN0185069215-13">Acknowledgements</hd> <p>We thank Saee Hatwalne and Utkarsh Choudhary for their timely and exceptional assistance rendered for this project. We are grateful to the editor, anonymous referees, and seminar participants at the 9th IEA International Research Conference for their immensely useful comments. We appreciate the continuous support extended by Dr. Khaleel Harbi in organizing and managing the project. We thank the Education and Training Evaluation Commission (ETEC) Kingdom of Saudi Arabia for funding support.</p> <hd id="AN0185069215-14">Author contributions</hd> <p>Not applicable.</p> <hd id="AN0185069215-15">Data availability</hd> <p>The dataset analyzed in this paper is available online: https://<ulink href="http://www.iea.nl/news-events/news/iea-timss-2019-international-database-released">www.iea.nl/news-events/news/iea-timss-2019-international-database-released</ulink></p> <hd id="AN0185069215-16">Declarations</hd> <p></p> <hd id="AN0185069215-17">Competing interests</hd> <p>Not applicable.</p> <hd id="AN0185069215-18">Supplementary Information</hd> <p>Graph: Additional file 1.</p> <hd id="AN0185069215-19">Publisher's Note</hd> <p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p> <ref id="AN0185069215-20"> <title> References </title> <blist> <bibl id="bib1" idref="ref49" type="bt">1</bibl> <bibtext> Anders Y, Rossbach HG, Weinert S, Ebert S, Kuger S, Lehrl S, Von Maurice J. Home and pre-school learning environments and their relations to the development of early numeracy skills. Early Childhood Research Quarterly. 2012; 27; 2: 231-244. 10.1016/j.ecresq.2011.08.003</bibtext> </blist> <blist> <bibl id="bib2" idref="ref16" type="bt">2</bibl> <bibtext> Baker M, Gruber J, Milligan K. Universal Child Care, Maternal Labor Supply, and Family Well-Being. Journal of Political Economy. 2008; 116; 4: 709-745. 10.1086/591908</bibtext> </blist> <blist> <bibl id="bib3" idref="ref12" type="bt">3</bibl> <bibtext> Barnett, W. (2008). Pre-school Education and Its Lasting Effects: Research and Policy Implications Education and the Public Interest Center. https://nepc.colorado.edu/sites/default/files/PB-Barnett-EARLY-ED_FINAL.pdf</bibtext> </blist> <blist> <bibl id="bib4" idref="ref4" type="bt">4</bibl> <bibtext> Barnett, W. S, & Nores, M. (2012). Investing in Early Childhood Education: A Global Perspective. National Institute for Early Education Research.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref6" type="bt">5</bibl> <bibtext> Barnett WS. Effectiveness of early educational intervention. Science. 2011; 333; 6045: 975-978. 10.1126/science.1204534</bibtext> </blist> <blist> <bibl id="bib6" idref="ref7" type="bt">6</bibl> <bibtext> Barnett W, Masse LN. Comparative benefit–cost analysis of the Abecedarian program and its policy implications. Economics of Education Review. 2007; 26; 1: 113-125. 10.1016/j.econedurev.2005.10.007</bibtext> </blist> <blist> <bibl id="bib7" idref="ref10" type="bt">7</bibl> <bibtext> Blanden J, Bono ED, Hansen K, Rabe B. The Impact of Free Early Childhood Education and Care on Educational Achievement: a Discontinuity Approach Investigating Both Quantity and Quality of Provision. 2017: School of Economics; University of Surrey</bibtext> </blist> <blist> <bibl id="bib8" idref="ref59" type="bt">8</bibl> <bibtext> Blanden J, Bono ED, Hansen K, Rabe B. Quantity and quality of childcare and children's educational outcomes. Journal of Population Economics. 2022; 35: 785-828. 10.1007/s00148-021-00835-4</bibtext> </blist> <blist> <bibl id="bib9" idref="ref52" type="bt">9</bibl> <bibtext> Brilli, Y. (2013). Mother or Market care? A structural estimation of child care impacts on child development. Unpublished manuscript, Collegio Carlo Alberto, CHILD, and Catholic University of Milan.</bibtext> </blist> <blist> <bibtext> Bronfenbrenner U. Toward an experimental ecology of human development. American Psychologist. 1977; 32; 7: 513-531. 10.1037/0003-066x.32.7.513</bibtext> </blist> <blist> <bibtext> Bryson KR, Casper LM. Coresident Grandparents and Grandchildren. 1999: Census Bureau; Suitland</bibtext> </blist> <blist> <bibtext> Carneiro P, Ginja R. Long-term impacts of compensatory pre-school on health and behavior: Evidence from Head Start. American Economic Journal: Economic Policy. 2014; 6; 4: 135-173. 10.1257/pol.6.4.135</bibtext> </blist> <blist> <bibtext> Crouch L, King K, Olefir A, Saeki H, Savrimootoo T. Taking preprimary programs to scale in developing countries: Multi-source evidence to improve primary school completion rates. International Journal of Early Childhood. 2020; 52: 159-174. 10.1007/s13158-020-00271-7</bibtext> </blist> <blist> <bibtext> Cunha F, Heckman JJ. The Technology of Skill Formation. American Economic Review. 2007; 97; 2: 31-47. 10.1257/aer.97.2.31</bibtext> </blist> <blist> <bibtext> Cunha F, Heckman JJ, Lochner L, Masterov DV. Interpreting the evidence on life cycle skill formation. Handbook of the Economics of Education. 2006; 1: 697-812. 10.1016/s1574-0692(06)01012-9</bibtext> </blist> <blist> <bibtext> Cunha NM. Parents: substitutes or complements to the school environment?. 2018: Stanford; Stanford University</bibtext> </blist> <blist> <bibtext> Datar A, Mason B. Do reductions in class size "crowd out" parental investment in education?. Economics of Education Review. 2008; 27; 6: 712-723. 10.1016/j.econedurev.2007.10.006</bibtext> </blist> <blist> <bibtext> Desforges C, Abouchaar A. The impact of parental involvement, parental support and family education on pupil achievement and adjustment: A literature review. 2003: London; DfES.Chicago</bibtext> </blist> <blist> <bibtext> Ferguson HB, Bovaird S, Mueller MP. The impact of poverty on educational outcomes for children. Paediatrics & Child Health. 2007; 12; 8: 701-706. 10.1093/pch/12.8.701</bibtext> </blist> <blist> <bibtext> Fitzpatrick M. Starting school at four: the effect of universal pre-kindergarten on children's academic achievement. The B.e. Journal of Economic Analysis & Policy. 2008; 8; 2: 1-40. 10.2202/1935-1682.1897</bibtext> </blist> <blist> <bibtext> Flouri E, Buchanan A. Early father's and mother's involvement and child's later educational outcomes. British Journal of Educational Psychology. 2004; 74; 2: 141-153. 10.1348/000709904773839806</bibtext> </blist> <blist> <bibtext> Foy P, Fishbein B, Von Davier M, Yin L. (2019). Implementing the TIMSS 2019 Scaling Methodology. https://timssandpirls.bc.edu/timss2019/methods/pdf/T19_MP_Ch12-scaling-implementation.pdf</bibtext> </blist> <blist> <bibtext> Fredriksson P, Ockert B, Oosterbeek H. Inside the black box of class size: Mechanisms, behavioral responses, and social background. SSRN Electronic Journal. 2014. 10.2139/ssrn.2409541</bibtext> </blist> <blist> <bibtext> Ghosh S. Does attending pre-school benefit Indian children at a later stage? (Blog). 2019: The Hague; Bliss</bibtext> </blist> <blist> <bibtext> Ghosh S, Dey S. Public or private? Determinants of parents' pre-school choice in India. International Journal of Child Care and Education Policy. 2020; 14; 1: 3. 10.1186/s40723-020-00068-0</bibtext> </blist> <blist> <bibtext> Grolnick WS, Slowiaczek ML. Parents' involvement in children's schooling: A multidimensional conceptualization and motivational model. Child Development. 1994; 65; 1: 237. 10.2307/1131378</bibtext> </blist> <blist> <bibtext> Haeck C, Lefebvre P, Merrigan P. Canadian evidence on ten years of universal pre-school policies: The good and the bad. Labour Economics. 2015; 36: 137-157. 10.1016/j.labeco.2015.05.002</bibtext> </blist> <blist> <bibtext> Harju-Luukkainen H, Vettenranta J, Wang J, Garvis S. Family related variables effect on later educational outcome: A further geospatial analysis on TIMSS 2015 Finland. Large-Scale Assessments in Education. 2020; 8; 1: 3. 10.1186/s40536-020-00081-2</bibtext> </blist> <blist> <bibtext> Harris A, Goodall J. Do parents know they matter? Engaging All parents in learning. Educational Research. 2008; 50; 3: 277-289. 10.1080/00131880802309424</bibtext> </blist> <blist> <bibtext> Heckman JJ. schools skills and synapses. Economic Inquiry. 2008. 10.3386/w14064</bibtext> </blist> <blist> <bibtext> Heckman JJ, Moon SH, Pinto R, Savelyev PA, Yavitz A. The rate of return to the High Scope Perry Pre-school Program. Journal of Public Economics. 2010; 94; 1–2: 114-128. 10.1016/j.jpubeco.2009.11.001</bibtext> </blist> <blist> <bibtext> Hill NE, Tyson DF. Parental involvement in middle school: A meta-analytic assessment of the strategies that promote achievement. Developmental Psychology. 2009; 45; 3: 740-763. 10.1037/a0015362</bibtext> </blist> <blist> <bibtext> Janssen J, Vandenbroeck M. (De)constructing parental involvement in early childhood curricular frameworks. European Early Childhood Education Research Journal. 2018; 26; 6: 813-832. 10.1080/1350293x.2018.1533703</bibtext> </blist> <blist> <bibtext> Kalil A, Ryan R. Parenting practices and socioeconomic gaps in childhood outcomes. The Future of Children. 2020; 30; 1: 29-54. 10.1353/foc.2020.0004</bibtext> </blist> <blist> <bibtext> Kamerman SB. Early childhood education and care: An overview of developments in the OECD countries. International Journal of Educational Research. 2000; 33; 1: 7-29. 10.1016/S0883-0355(99)00041-5</bibtext> </blist> <blist> <bibtext> Kim H. Is there a crowding-out effect between school expenditure and mother's child care time?. Economics of Education Review. 2001; 20; 1: 71-80. 10.1016/s0272-7757(99)00038-2</bibtext> </blist> <blist> <bibtext> Kim Y. Minority parental involvement and school barriers: moving the focus away from deficiencies of parents. Educational Research Review. 2009; 4; 2: 80-102. 10.1016/j.edurev.2009.02.003</bibtext> </blist> <blist> <bibtext> Ma X, Shen J, Krenn HY, Hu S, Yuan J. A meta analysis of the relationship between learning outcomes and parental involvement during early childhood education and early elementary education. Educational Psychology Review. 2016; 28; 4: 771-801. 10.2307/44955364</bibtext> </blist> <blist> <bibtext> Mahadevan R, Fan S. Differential Effects of Parents' Education on Adolescent Well-being Outcomes. Child Indicators Research. 2021; 14; 6: 2495-2516. 10.1007/s12187-021-09856-7</bibtext> </blist> <blist> <bibtext> Manolitsis G, Georgiou GK, Tziraki N. Examining the effects of home literacy and numeracy environment on early reading and math acquisition. Early Childhood Research Quarterly. 2013; 28; 4: 692-703. 10.1016/j.ecresq.2013.05.004</bibtext> </blist> <blist> <bibtext> Mayer SE, Kalil A, Oreopoulos P, Gallegos S. Using Behavioral insights to increase parental engagement: The parents and children together intervention. The Journal of Human Resources. 2019; 54; 4: 900-925. 10.3368/jhr.54.4.0617.8835R</bibtext> </blist> <blist> <bibtext> Melhuish, E. C, Ereky-Stevens, K, Petrogiannis, K, Ariescu, A, Penderi, E, Rentzou, K, Leseman, P. (2015). A review of research on the effects of early childhood Education and Care (ECEC) upon child development. CARE project; Curriculum Quality Analysis and Impact Review of European Early Childhood Education and Care (ECEC).</bibtext> </blist> <blist> <bibtext> Melhuish E. Why children, parents and home learning are important. 2010: London; Routledge</bibtext> </blist> <blist> <bibtext> Muttaqin T. Determinants of unequal access to and quality of education in Indonesia. Jurnal Perencanaan Pembangunan the Indonesian Journal of Development Planning. 2018. 10.36574/jpp.v2i1.27</bibtext> </blist> <blist> <bibtext> Napoli AR, Korucu I, Lin J, Schmitt SA, Purpura DJ. Characteristics related to parent-child literacy and numeracy practices in preschool. Frontiers in Education. 2021; 6. 10.3389/feduc.2021.535832535832</bibtext> </blist> <blist> <bibtext> Rao N, Richards B, Sun J, Weber A, Sincovich A. Early childhood education and child development in four countries in East Asia and the Pacific. Early Childhood Research Quarterly. 2019; 47: 169-181. 10.1016/j.ecresq.2018.08.011</bibtext> </blist> <blist> <bibtext> Rao N, Umayahara M, Yang Y, Ranganathan N. Ensuring access, equity and quality in early childhood education in Bangladesh, China, India and Myanmar: Challenges for nations in a populous economic corridor. International Journal of Educational Development. 2021; 82. 10.1016/j.ijedudev.2021.102380102380</bibtext> </blist> <blist> <bibtext> Rose E, Lehrl S, Ebert S, Weinert S. Long-term relations between children's language, the home literacy environment, and socioemotional development from ages 3 to 8. Early Education and Development. 2018; 29; 3: 342-356. 10.1080/10409289.2017.1409096</bibtext> </blist> <blist> <bibtext> Rutkowski L, Gonzalez E, Joncas M, von Davier M. International large-scale assessment data: Issues in secondary analysis and reporting. Educational Researcher. 2010; 39; 2: 142-151. 10.3102/0013189X10363170</bibtext> </blist> <blist> <bibtext> Sammons, P, Sylva, K, Melhuish, E, Siraj-Blatchford, I, Taggart, B. and Hunt, S. (2008a). Effective Pre-school and Primary Education 3–11 Project (EPPE 3–11): Influences on Children's Attainment and Progress in Key Stage 2: Cognitive Outcomes in Year 6. Nottingham: DCSF Publications</bibtext> </blist> <blist> <bibtext> Sammons P, Anders Y, Sylva K, Melhuish E, Siraj-Blatchford I, Taggart B, Barreau S. Children's cognitive attainment and progress in english primary schools during key stage 2: Investigating the potential continuing influences of pre-school education. Frühpädagogische Förderung in Institutionen: Zeitschrift Für Erziehungswissenschaft. 2009; 179: 198</bibtext> </blist> <blist> <bibtext> Singh R, Mukherjee, P. (2017). Comparison of the effects of government and private pre-school education on the developmental outcomes of children: Evidence from young lives India. Working Paper 167.</bibtext> </blist> <blist> <bibtext> Singh K, Bickley PG, Keith TZ, Keith PB, Trivette P, Anderson E. The effects of four components of parental involvement on eighth-grade student achievement: structural analysis of NELS-88 data. School Psychology Review. 1995; 24; 2: 299-317. 10.1080/02796015.1995.12085769</bibtext> </blist> <blist> <bibtext> Sylva K, Meluish E, Sammons P, Siraj-Blatchford I, Taggart B. Early Childhood Matters: evidence from the Effective Pre-school and Primary Education project. 2010: London; Routledge. 10.4324/9780203862063</bibtext> </blist> <blist> <bibtext> Tan CY, Lyu M, Peng B. Academic benefits from parental involvement are stratified by parental socioeconomic status: A meta-analysis. Parenting. 2020; 20; 4: 1-47. 10.1080/15295192.2019.1694836</bibtext> </blist> <blist> <bibtext> TIMSS 2019. (2019). TIMSS 2019 International Reports Home & School Contexts. IEA TIMSS & PIRLS. https://timss2019.org/reports/wp-content/themes/timssandpirls/download-center/home-school/T19_Ch5-home-environment.pdf</bibtext> </blist> <blist> <bibtext> Topor DR, Keane SP, Shelton TL, Calkins SD. Parent involvement and student academic performance: A multiple mediational analysis. Journal of Prevention & Intervention in the Community. 2010; 38; 3: 183-197. 10.1080/10852352.2010.486297</bibtext> </blist> <blist> <bibtext> Ünver Ö, Bircan T, Nicaise I. Perceived accessibility of childcare in Europe: A cross-country multilevel study. International Journal of Child Care and Education Policy. 2018; 12: 1-30. 10.1186/s40723-018-0044-3</bibtext> </blist> <blist> <bibtext> van den Berg GJ, Siflinger BM. The effects of a daycare reform on health in childhood—Evidence from Sweden. Journal of Health Economics. 2022; 81. 10.1016/j.jhealeco.2021.102577102577</bibtext> </blist> <blist> <bibtext> Villena-Roldan B, Ríos-Aguilar C. Causal effects of maternal time-investment on children's cognitive outcomes. 2012: Center for Applied Economics; New Delhi. 10.2139/ssrn.2255809</bibtext> </blist> <blist> <bibtext> Wotipka CM, Rabling BJ, Sugawara M, Tongliemnak P. The worldwide expansion of early childhood care and education, 1985–2010. American Journal of Education. 2016; 123; 2: 307-339. 10.1086/689931</bibtext> </blist> <blist> <bibtext> Yizengaw JY, Tessega M. The implementation of early childhood care and education (ECCE) in Bahir Dar city administration: A comparative study between private and public pre-primary schools. Social Sciences & Humanities Open. 2020. 10.1016/j.ssaho.2020.100013</bibtext> </blist> <blist> <bibtext> Yoshikawa, H, & Kabay, S. (2015). The evidence base on early childhood care and education in global contexts. Background paper prepared for the Education for All Global Monitoring Report 2015: Education for All 2000–2015: Achievements and Challenges, 54. https://unesdoc.unesco.org/ark:/48223/pf0000232459.</bibtext> </blist> <blist> <bibtext> Yoshikawa H, Weiland C, Brooks-Gunn J. When does pre-school matter?. The Future of Children. 2016; 26; 2: 21-35. 10.1353/foc.2016.0010</bibtext> </blist> </ref> <ref id="AN0185069215-21"> <title> Footnotes </title> <blist> <bibtext> We use an arrow in the first case since if ∂P∂S is positive, dAdS is absolutely positive. However, we use "and" in the second and third statement, since if ∂P∂S negative it is unclear that dAdS is positive, zero, or negative.</bibtext> </blist> <blist> <bibtext> https://timssandpirls.bc.edu/timss2019/methods/pdf/T19%5fMP%5fCh11-scaling-methodology.pdf; Computers in education: the association between computer use and test scores in primary school (tandfonline.com).</bibtext> </blist> <blist> <bibtext> The choice of whether the marginal product of parental activity or that of the preschool program declines depends on the functional form of the production function for child learning outcomes. Empirically, both can be measured depending on the specification of the model. Our approach is to estimate interaction effects in a hierarchical or fixed-effects framework, where the marginal effect of parental engagement on learning outcomes is conditional on preschool participation. Without an explicit empirical test, it remains ambiguous whether the diminishing returns apply more strongly to parental engagement or preschooling, and the results may vary by context.</bibtext> </blist> <blist> <bibtext> We include all the countries which provide information on ECEC and parental engagement in early literacy and numeracy tasks. The countries for which these data are not available are excluded from our analysis. These countries are Austria, England, Netherlands, USA, Japan, and Northern Ireland.</bibtext> </blist> <blist> <bibtext> The ELNT scale is based on nine literacy activities and nine numeracy activities.</bibtext> </blist> </ref> <aug> <p>By Aditi Bhutoria; Nayyaf Aljabri and Saheli Bose</p> <p>Reported by Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib30" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib15" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib14" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib63" firstref="ref5"></nolink> <nolink nlid="nl5" bibid="bib12" firstref="ref8"></nolink> <nolink nlid="nl6" bibid="bib31" firstref="ref9"></nolink> <nolink nlid="nl7" bibid="bib20" firstref="ref11"></nolink> <nolink nlid="nl8" bibid="bib54" firstref="ref13"></nolink> <nolink nlid="nl9" bibid="bib43" firstref="ref14"></nolink> <nolink nlid="nl10" bibid="bib27" firstref="ref15"></nolink> <nolink nlid="nl11" bibid="bib64" firstref="ref17"></nolink> <nolink nlid="nl12" bibid="bib59" firstref="ref18"></nolink> <nolink nlid="nl13" bibid="bib62" firstref="ref19"></nolink> <nolink nlid="nl14" bibid="bib52" firstref="ref20"></nolink> <nolink nlid="nl15" bibid="bib24" firstref="ref21"></nolink> <nolink nlid="nl16" bibid="bib25" firstref="ref22"></nolink> <nolink nlid="nl17" bibid="bib41" firstref="ref23"></nolink> <nolink nlid="nl18" bibid="bib37" firstref="ref24"></nolink> <nolink nlid="nl19" bibid="bib40" firstref="ref25"></nolink> <nolink nlid="nl20" bibid="bib48" firstref="ref26"></nolink> <nolink nlid="nl21" bibid="bib60" firstref="ref27"></nolink> <nolink nlid="nl22" bibid="bib18" firstref="ref28"></nolink> <nolink nlid="nl23" bibid="bib38" firstref="ref29"></nolink> <nolink nlid="nl24" bibid="bib55" firstref="ref30"></nolink> <nolink nlid="nl25" bibid="bib32" firstref="ref31"></nolink> <nolink nlid="nl26" bibid="bib57" firstref="ref32"></nolink> <nolink nlid="nl27" bibid="bib10" firstref="ref33"></nolink> <nolink nlid="nl28" bibid="bib26" firstref="ref34"></nolink> <nolink nlid="nl29" bibid="bib53" firstref="ref35"></nolink> <nolink nlid="nl30" bibid="bib34" firstref="ref36"></nolink> <nolink nlid="nl31" bibid="bib21" firstref="ref37"></nolink> <nolink nlid="nl32" bibid="bib33" firstref="ref38"></nolink> <nolink nlid="nl33" bibid="bib35" firstref="ref39"></nolink> <nolink nlid="nl34" bibid="bib58" firstref="ref40"></nolink> <nolink nlid="nl35" bibid="bib61" firstref="ref41"></nolink> <nolink nlid="nl36" bibid="bib17" firstref="ref42"></nolink> <nolink nlid="nl37" bibid="bib23" firstref="ref43"></nolink> <nolink nlid="nl38" bibid="bib36" firstref="ref44"></nolink> <nolink nlid="nl39" bibid="bib16" firstref="ref45"></nolink> <nolink nlid="nl40" bibid="bib46" firstref="ref47"></nolink> <nolink nlid="nl41" bibid="bib47" firstref="ref48"></nolink> <nolink nlid="nl42" bibid="bib42" firstref="ref51"></nolink> <nolink nlid="nl43" bibid="bib13" firstref="ref53"></nolink> <nolink nlid="nl44" bibid="bib51" firstref="ref54"></nolink> <nolink nlid="nl45" bibid="bib28" firstref="ref56"></nolink> <nolink nlid="nl46" bibid="bib39" firstref="ref58"></nolink> <nolink nlid="nl47" bibid="bib19" firstref="ref60"></nolink> <nolink nlid="nl48" bibid="bib56" firstref="ref73"></nolink> <nolink nlid="nl49" bibid="bib11" firstref="ref80"></nolink> <nolink nlid="nl50" bibid="bib49" firstref="ref81"></nolink> <nolink nlid="nl51" bibid="bib22" firstref="ref82"></nolink> <nolink nlid="nl52" bibid="bib45" firstref="ref86"></nolink> <nolink nlid="nl53" bibid="bib29" firstref="ref87"></nolink> <nolink nlid="nl54" bibid="bib50" firstref="ref88"></nolink> <nolink nlid="nl55" bibid="bib44" firstref="ref89"></nolink>
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  Label: DOI
  Group: ID
  Data: 10.1186/s40723-025-00141-6
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1976-5681<br />2288-6729
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper examines whether parental engagement in early childhood and preschooling act as substitutes, or whether their joint effect enhances students' learning outcomes. We utilize the TIMSS 2019 dataset and employ a hierarchical linear modeling (HLM) approach to analyze data from 52 countries, ensuring a robust examination of cross-national variations. Although extant literature proposes that parental engagement and preschooling are likely to function as substitutes, our analysis reveals that they can also serve as complements. For instance, a one-unit increase in the TIMSS ECEC parental engagement index is associated with an estimated increase of 0.58 and 0.85 units in math test scores for students with up to one and two years of preschooling, respectively. In the case of science, for students with three or more years of preschooling, our findings suggest a substitutive relationship between parental engagement and preschool participation. In addition, we find that home literacy and numeracy activities undertaken by parents influence both math and science scores, albeit differently. Furthermore, we observe that a higher degree of parental engagement, combined with preschooling, yields the largest test score gains in countries with a greater proportion of children already enrolled in preschool, thereby making a case for expanding preschool access.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1470797
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1470797
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1186/s40723-025-00141-6
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 22
    Subjects:
      – SubjectFull: Early Childhood Education
        Type: general
      – SubjectFull: Parenting Skills
        Type: general
      – SubjectFull: Child Rearing
        Type: general
      – SubjectFull: Preschool Children
        Type: general
      – SubjectFull: Enrollment
        Type: general
      – SubjectFull: Outcomes of Education
        Type: general
      – SubjectFull: Comparative Education
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Hierarchical Linear Modeling
        Type: general
      – SubjectFull: Achievement Tests
        Type: general
      – SubjectFull: International Assessment
        Type: general
      – SubjectFull: Mathematics Tests
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Science Achievement
        Type: general
      – SubjectFull: Science Tests
        Type: general
      – SubjectFull: Trends in International Mathematics and Science Study
        Type: general
    Titles:
      – TitleFull: Responsive Early Childhood Parenting, Preschool Enrollment, and Eventual Student Learning Outcomes: A Cross-Country Analysis Using Hierarchical Linear Modeling with TIMSS 2019 Data
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Aditi Bhutoria
      – PersonEntity:
          Name:
            NameFull: Nayyaf Aljabri
      – PersonEntity:
          Name:
            NameFull: Saheli Bose
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 1976-5681
            – Type: issn-electronic
              Value: 2288-6729
          Numbering:
            – Type: volume
              Value: 19
          Titles:
            – TitleFull: International Journal of Child Care and Education Policy
              Type: main
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