numeracy skills research paper

Literacy and numeracy: Global and comparative perspectives

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• Published: 12 August 2020
• Volume 66 , pages 127–137, ( 2020 )

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• Anke Grotlüschen   ORCID: orcid.org/0000-0003-3072-1741 1 ,
• Richard Desjardins   ORCID: orcid.org/0000-0002-4179-2791 2 &
• Huacong Liu   ORCID: orcid.org/0000-0002-6219-2795 1  

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The overall aim of this special issue is to contribute to the international discourse around literacy, numeracy, adult education and basic education. It engages with numeracy and mathematical literacy, New Literacy Studies, adult education, and lifelong learning in the context of the United Nations Sustainable Development Goals (SDGs), both from theoretical perspectives and from an empirical viewpoint.

Education affects people’s lives in ways that go far beyond what can be measured by labour market earnings and economic growth. Education contributes to a wide range of social outcomes such as better health, higher levels of civic and social engagement, as well as addressing other socially relevant domains of concern, such as crime, anti-social behaviour and poverty (Schuller and Desjardins 2007). Footnote 1 In the midst of the ongoing global pandemic, individuals who suffer the most, economically, psychologically and socially, are those who are the most disadvantaged in accessing quality education. The COVID-19 pandemic has amplified the need to take a more holistic approach towards education and learning than merely emphasising skills for employability.

The broader approach towards education and learning and the concept of sustainability are already embedded in the history of the United Nations Educational, Scientific and Cultural Organization (UNESCO). They are reflected in the instrumental role UNESCO has played since the end of the Second World War in expanding the right to education to include adults. The call within the fourth Sustainable Development Goal (SDG 4) to “ensure inclusive and equitable quality education and promote lifelong learning opportunities for all” (UN 2015) Footnote 2 has awakened hope among many for a stronger role for adult education in global education agendas and policies (Elfert 2019). Footnote 3 Among the targets within SDG 4, Footnote 4 the one which is of particular relevance to this special issue is SDG target 4.6:

By 2030, ensure that all youth and a substantial proportion of adults, both men and women, achieve literacy and numeracy (UN 2015, SDG target 4.6).

Despite the collective efforts among various stakeholders to achieve progress in working towards the targets of SDG 4, several problematic issues remain, even as we are already five years into implementing the United Nations 2030 Agenda for Sustainable Development. The current pandemic arrived on top of these. The challenges involved in developing indicators to monitor progress were already well-acknowledged at the start of the SDG agenda in 2015. In 2016, led by the UNESCO Institute for Statistics (UIS), the Global Alliance to Monitor Learning (GAML) was established (UIS 2017). Footnote 5 Its mandate is to support national strategies for learning assessments and develop internationally comparable indicators related to SDG 4. GAML set up thematic task forces Footnote 6 which hold expert meetings in order to collect and evaluate existing tests and findings and discuss adequate testing instruments. However, most of the challenges facing GAML and its associated task forces have not yet been resolved and were actively debated at the last GAML meeting in August 2019. Footnote 7

The challenges pertaining to SDG target 4.6 include the complexity of measuring functional literacy and numeracy, the feasibility of reporting adults’ literacy and numeracy against a global common measurement scale, and the difficulty of increasing data coverage among those UNESCO Member States that do not currently have direct assessments in place. GAML’s task force on SDG target 4.6, chaired by the UNESCO Institute for Lifelong Learning (UIL) and the Organisation for Economic Co-operation and Development (OECD), recommended the use of specific skills levels associated with the OECD Programme for the International Assessment of Adult Competencies (PIAAC) as benchmarks. Footnote 8 Specifically, the task force recommended that the minimum proficiency level that should be achieved – and thus count as progress towards SDG indicator 4.6.1 – should be the literacy and numeracy skills level associated with PIAAC Level 1 for high-income countries, and below PIAAC Level 1 (at the sentence-processing level) for middle- and low-income countries (UIS 2018). Footnote 9

These recommendations were based on results of a global consultation as well as analyses of existing population data on skills such as PIAAC and the World Bank’s Skills Towards Employment and Productivity (STEP) study. Empirical data have revealed that approximately 50 per cent of adult populations living in middle-income countries, such as, for example, Turkey and Chile, are at or below PIAAC Level 1 on the literacy scale (OECD 2017). Footnote 10 Therefore, a common benchmark for global reporting purposes could lead to a majority of countries having a large percentage of their adult population classified as being below target levels of literacy proficiency. Arguably, this would make it difficult to assess progress for a large number of countries. However, the Technical Cooperation Group (TCG) on the Indicators for SDG 4 Footnote 11 – another committee established in 2016 – recommended using the PIAAC Level 2 descriptor as a reference point for global reporting of SDG indicator 4.6.1 (UIS 2019). Footnote 12

Notwithstanding these challenges, five years into the SDG agenda, the research community has produced methodological advancements that can help measure adult literacy and numeracy at the lower end of the proficiency scale. It has also produced useful knowledge towards understanding literacy and numeracy competences and practices among men and women, albeit mostly in high-income countries. Moreover, scholars have provided important critical perspectives for better understanding the diversity and contextualisation of literacy and numeracy practices. With ten years remaining until the deadline of the United Nations 2030 Agenda for Sustainable Development, it is timely for the International Review of Education – Journal of Lifelong Learning ( IRE ) to take stock and gather perspectives from various research fields in order to support a more comprehensive understanding of key issues and challenges surrounding SDG target 4.6 on adult literacy and numeracy.

Part 1: critiques of the monitoring and measurement of adult literacy and numeracy

The first part of this special issue contains two articles that provide critiques of the monitoring and measurement of adult literacy and numeracy as well as three others that add to the critiques by discussing methodological advancements.

Several scholars have warned that the time pressure and lack of scientific reflection associated with large-scale assessments bear the potential danger of leading to monopolist effects of a handful of education assessment companies or institutions on low- and middle-income countries (Hamilton et al. 2015). Footnote 13 Monitoring the SDGs effectively probably requires a diversity of approaches that exceed what can be achieved by an international and comparative survey like the OECD PIAAC study (Addey 2017). Footnote 14 Unfortunately, other major measurement instruments such as UNESCO’s Literacy Assessment and Monitoring Programme (LAMP) and the World Bank’s STEP study, are closely related to PIAAC and its predecessors, namely the International Assessment of Literacy Skills (IALS) conducted in the 1990s and the Adult Literacy and Lifeskills (ALL) Survey carried out in the early 2000s.

In particular, the test items developed for IALS Footnote 15 and ALL Footnote 16 were designed for contexts derived from high-income OECD countries and were conceptualised exclusively in European languages written in the Roman alphabet. While the LAMP Footnote 17 and the STEP Footnote 18 studies focused on middle- and low-income countries with a wider array of language families and scripts, there is still a lack of sound empirical evidence on how one set of reading components can be used to compare proficiencies across languages and writing systems. Even in cases where such comparability can be arguably established, merely comparing the averages of countries’ literacy and numeracy scores against a common scale or an OECD average risks overlooking the myriad of micro (individual-level), meso (group-level), and macro (government-level) factors contributing to high- versus low- performances (Boeren 2019). Footnote 19 Researchers commented in a recently published article (Grotlüschen and Buddeberg 2020) Footnote 20 that in this kind of global benchmarking, measurements developed in and for countries sharing basic commonalities, such as those belonging to the Western world, are understood and projected as normality .

Even though the SDGs explicitly try to overcome the Brandt Line Footnote 21 and its North-South division (Singh 2019), Footnote 22 there is a danger that this general application of “normality” to all contexts might become a reality. Therefore, it seems necessary to revisit some underlying theoretical assumptions of measurement and monitoring on a sociological level and from the perspective of educational sciences.

The first article we present in this special issue is entitled “Prophets, saviours and saints: Symbolic governance and the rise of a transnational metrological field”. Arguing from the Bourdieusian perspective of a “sociology of numbers”, Sotiria Grek investigates the SDG 4-related monitoring procedures carried out by supranational organisations. Her purpose is to offer insights into the labour and infrastructure involved in the joint production of metrics. Drawing on declarations, agreements and reports as well as empirical findings from a series of interviews she conducted with key actors from major international organisations and civil society, Grek suggests that quantification has facilitated symbolic governance of the education policy field. As a result, the joint effort towards achieving the targets of SDG 4 represents the rise, and to a large degree the dominance, of the influence of the transnational field of measurement in education.

In our second article, entitled “Doing competence: On the performativity of literacy and numeracy from a post-structural viewpoint”, Lisanne Heilmann looks at literacy and numeracy from a post-structuralist perspective. This perspective relies on theories of a relational subject , as introduced by Judith Butler from a feminist standpoint (Butler 2004). Footnote 23 Heilmann questions the individualised understanding of literacy and numeracy as abstract competences which people simply “have” and explores the possibility of viewing these basic competences as constructed through how they are actively performed (e.g. when someone engages in reading, writing or calculating for a particular purpose in a particular context) and referred to (e.g. when someone is pronounced “literate” or “competent”). She points out that measuring competences implies an individual that “has” competences. What if we are “doing competences”? Emphasising discourse analysis, e.g. by Michel Foucault and Judith Butler, Heilmann elaborates a shift from the New Literacy Studies, which questioned the individualised understanding of literacy as an abstract competence, to a post-structuralist literacy theory.

Challenges from discourse theory and sociology of numbers do not only apply to literacy research, but also to numeracy. Slowly, but steadily, numeracy research is becoming more visible, but adult numeracy can still be seen as a neglected field (Gal et al. 2020). Footnote 24 Being numerate means being critical (Geiger et al. 2015) Footnote 25 – this is especially empowering in the era of “fake news”, when data literacy has become more important than ever. The theoretical concept of numeracy shifts towards a more holistic approach and asks for criticality. This seems highly relevant in times of infection statistics and disastrous financial markets, and thus in times where statistics and infection rates inform policymakers and the public on whether to cut back fundamental rights. Therefore, it is most important to discuss how we conceptualise “numeracy” in large scale assessments.

The next article, “Evolution of adult numeracy from quantitative literacy to numeracy: Lessons learned from international assessments” by Dave Tout, explains the most recent concept underpinning the ongoing PIAAC cycle, in which relevant changes include the aforementioned critical approach. Data collection is scheduled for 2021–2022 and the results are due to be published in 2023. Tout points out that the development and ongoing refinement of the theoretical frameworks and constructs that shape programmes such as PIAAC and the assessments themselves, alongside the research based on the rich data of empirical and background information emerging from these surveys, have contributed significantly to our knowledge and understanding of numeracy in people’s lives.

However, measurement and monitoring on a global level produce a need for scholarly knowledge on testing especially at the lower end of the hierarchically arranged skills levels. Even if many consider a hierarchical model as problematic (Duckworth and Tett 2019; Thériault 2019), Footnote 26 in the absence of any alternatives, these levels will probably still be used for some time around the globe for comparison. However, testing at the lower end of hierarchical scales is problematic due to a lack of testable items and needs competence descriptions. This is addressed in our fourth article, entitled “Proficiency level descriptors for low reading proficiency: An integrative process model”. Tabea Durda, Cordula Artelt, Clemens M. Lechner, Beatrice Rammstedt and Alexandra Wicht provide a process model based on reader-related, text-related and task-related factors along different stages of the reading process that can cause reading difficulties. Their model enables the identification of difficulty-generating factors , in particular task and text characteristics. This model is also suitable for developing proficiency level descriptors by differentiating between a low reading proficiency level and a functional reading proficiency level among adolescents and adults.

PIAAC has five hierarchically organised proficiency levels for literacy. A sixth category, labelled “below Level 1”, lumps together low proficiencies at the bottom end of the proficiency continuum. While PIAAC Levels are already broadly suitable for international comparison, the in-depth assessment of “Level 1” and “below Level 1” has so far only been focused on by individual countries (e.g. Canada, the United States, the United Kingdom, France and Germany) using instruments developed nationally. Focusing on the reading aspect of literacy, the article which concludes the first part of this special issue investigates how these nationally developed low proficiency assessment instruments might be adjusted to facilitate international comparability.

In “International assessment of low reading proficiency in the adult population: A question of components or lower rungs?”, Anke Grotlüschen, Barbara Nienkemper and Caroline Duncker-Euringer discuss two competing approaches. One is the reading components approach, and the other is the lower-rungs approach . Reading components test sets are well-known and widespread. Some of them have been administered in national surveys, some were applied under LAMP in several languages, and many countries opt to run the reading components module of the PIAAC programme. However, starting from IALS in the 1990s, the concept of a hierarchical ladder of proficiency levels has emerged and since been applied with a focus on the lower rungs in the Skills for Life surveys (conducted by the UK Department for Business, Innovation and Skills) and the two German Level-One (LEO) surveys conducted by the University of Hamburg. Based on the German PIAAC Reading Components dataset, Grotlüschen et al. investigate whether the existing component items can be arranged hierarchically (as lower rungs of the ladder) in a similar way as PIAAC and LAMP items to facilitate global reporting and comparison. They conclude that that it is indeed technically possible to integrate the full set of PIAAC reading component test items into hierarchical “rungs”.

Part 2: findings from qualitative and quantitative literacy and numeracy research

In the second part of this special issue, we present five articles that relate to findings from qualitative and quantitative literacy and numeracy research, and help to reveal several insights and nuances relevant to measurement and monitoring of literacy and numeracy.

Several major theoretical approaches have shown that the discussion of “competences” is shifting towards the notion of “practices”. Social anthropologist Jean Lave, grande dame of numeracy research, showed the importance of practices in 1988 with her work on “cognition in practice” (Lave 1988). Footnote 27 Later PIAAC theoretical framework, led by Iddo Gal, built on Lave’s work (Gal et al. 2009). Footnote 28 Most recently, results from longitudinal studies show the impact of practices on competences (Reder 2017). Footnote 29

We begin this second part with an article entitled “Practice makes perfect: Practice engagement theory and the development of adult literacy and numeracy proficiency”. Stephen Reder, Britta Gauly and Clemens Lechner present more recent findings generated by PIAAC-L, a longitudinal national follow-up survey conducted in Germany, and discuss the influences of practices on competences and vice versa. Footnote 30 Based on practice engagement theory (PET) Reder et al. suggest that literacy training which increases engagement in meaningful practices might generate proficiency growth. The authors’ comparisons of how various practice engagement indexes predict growth of literacy and numeracy proficiencies indicate that reading engagement is the strongest predictor of literacy growth, and maths engagement is the strongest predictor of numeracy growth. They conclude their article by considering their findings’ implications for sustainable development, lifelong learning policy and future research into the development of adult literacy and numeracy proficiency.

In our next article, entitled “Micro and macro drivers affecting adult literacy proficiency profiles across countries”, Richard Desjardins offers a retrospective of thirty years of assessment with a particular focus on the trend data made available from IALS and PIAAC. The aim of his research is to understand the determinants of literacy proficiency in terms of (1) how they may be affecting the development of literacy from an individual lifecycle (micro-level) perspective, and (2) how they may be affecting the development of national (macro-level) profiles of literacy proficiency as countries’ sociodemographic compositions, sociocultural practices and economies change over time. He discerns an interesting decline of literacy practices in work-related contexts. Possible reasons for this may be that early measurement parameters do not fit any more, or that earlier practices (like looking up something in a printed dictionary) no longer apply in a digital world, but it may also be due to less practical use of skills in everyday contexts, which in the long run can affect skills levels as well. Overall, the decline of literacy practices may be a reason for stagnation in literacy competences (Desjardins 2017). Footnote 31

The eighth article we present in this special issue is entitled “It’s not what you know but where you come from: Cognitive skills, job autonomy and latent discrimination of ethnic minorities in Israel”. Based on PIAAC data, Sabina Lissitsa and Svetlana Chachashvili-Bolotin investigated the association between cognitive skills and job autonomy among Israeli-born Jews, Arabs and immigrants from the former Soviet Union (FSU) living in Israel. Job autonomy – employees’ freedom to schedule and organise their work independently according to their own experience and preferences – is a major factor in job satisfaction. However, it is not granted to many employees in Israel, and the authors’ close examination of the Israeli labour market reveals that while cognitive skills are positively correlated with job autonomy among Israeli-born Jews and partially among Arabs, these effects are insignificant among FSU immigrants. Lissitsa and Chachasvili-Bolotin analyse their findings through social homophily theory, which explains bonding tendencies among socially and culturally similar people.

Outside the PIAAC measurement industry, questions and findings on literacy and numeracy research extend beyond the question of predictors and outcomes of competences. Based on her narrative interviews with vulnerable adult learners, Doria Daniels looks at how adult education and training (AET) learners navigate second-chance education. In her article entitled “Exploring adult education and training as a transformative learning space for alienated out-of-school youth in South Africa”, she investigates what facilitates these learners’ educational success. Education policies in South Africa recently introduced a shift in the function of AET from providing opportunities for the acquisition of literacy to offering a formal qualification. This changed status of AET created a second-chance educational opportunity for youthful, non-traditional “new-generation” adult learners with a troubled history of formal schooling both to complete their general education and/or to further their education and their chances of entering the workforce. Daniels shows how vulnerable second-chance learners slowly, but steadily find ways to advance their quest for an education as energies within AET contexts and their personal worlds come together. Daniels’ narrative interviews also demonstrate how desperate the situation is in South Africa for adults with low literacy skills. Moreover, migration and globalisation call for basic education and pathways to vocational education for immigrants and people with learning disabilities. Adults with learning disabilities – a problematic terminology anyway – are often excluded and overlooked by large-scale assessments and by educational policies.

We conclude this special issue with an article by Wiebke Curdt and Silke Schreiber-Barsch entitled “Abilities in the blind spot of testing regimes: Eliciting the benefits and the limitations of participatory research approaches for numeracy in adult basic education”. The article argues that adults with learning difficulties (also referred to by some as intellectual disabilities ) and their numeracy-related abilities are still hidden in the blind spot of large-scale testing regimes. Based on rich qualitative data, Curdt and Schreiber-Barsch discuss how participatory research designs can work out in exploring how these learners apply numeracy practices in everyday life contexts, and what challenges occur. This allows both a methodological perspective as well as a focus on vulnerable subpopulations (Grotlüschen et al. 2019) Footnote 32 in the field of adult numeracy research. Curdt and Schreiber-Barsch aim to demonstrate benefits and limitations of using participatory research approaches and give evidence why they consider them to be useful for diminishing blind spots of testing regimes.

In sum, the authors who have contributed to this special issue reflect on the complexity of literacy and numeracy assessments, focus on the need for a contextualisation of literacy and numeracy practices, and present us with the knowledge that we can gain from analysing existing data generated through large-scale skills assessments over the past 30 years. In particular, they provide critical considerations regarding monitoring and measuring literacy and numeracy, and remind us of those learners who might have been excluded in the policy debates around literacy and numeracy improvement. Between them, these ten articles cover a rich and controversial set of approaches, a set that avoids easy answers or recipes, and instead offers a critical discourse that matches the aims of the United Nations Agenda 2030 SDGs.

Yet, as editors and authors, we are aware of many gaps we could not possibly fill. In particular, it is worth noting that these articles were written before the outbreak of the COVID-19 pandemic. Thus, the timing of this special issue did not allow us to reflect upon the impact of the pandemic on adult learning and education in general, and the monitoring and reporting for SDG target 4.6 in particular. For instance, the short-term impact of school closures when it comes to the ability to read and write, may, in the long run, have a more severe impact on lifelong learning. As commented by Per Magnusson in his blog post published by UIL on 22 May 2020,

Children who do not learn to read early enough often fail later in school or when they enter the labour market: Close a school today and you will end up with an increased share of illiterate adults (Magnusson 2020). Footnote 33

As countries and the international community are joining efforts to fight the pandemic and ensure that learning does not stop for children, young people and adults alike, we are hoping to see sound research on the impacts on adult learning and basic education. We would do well to advance the common goal set by SDG target 4.6.

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Grotlüschen, A., Desjardins, R. & Liu, H. Literacy and numeracy: Global and comparative perspectives. Int Rev Educ 66 , 127–137 (2020). https://doi.org/10.1007/s11159-020-09854-x

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This study explored the influence of early literacy and numeracy skills on fourth-grade math achievement using the Trends in International Mathematics and Science Study (TIMSS). The study utilized valuable information collected by TIMSS about context related questionnaires such as home resources for learning, early literacy and numeracy development, readiness for school, and students’ home and school lives in a cross cultural and linguistic framework. The main purpose of this study was aligned with those of TIMSS to improve math learning and performance and strengthen future employees’ skills in the global workplace. Participants were comprised of mostly Asian and European students. Results show that (1) early literacy skills have a stronger effect on G4 math scores than early numeracy skills; (2) Home resources for learning impact more on children’s early literacy skills than early numeracy skills; (3) both early literacy and numeracy activities have progressed to early literacy skills but demonstrated limited advancement to early numeracy skills, a missing link; (4) students’ confidence in math emerged as the strongest predictor of G4 math scores; (5) students with stronger early literacy skills and early numeracy skills are more confident in math; and (6) The moderated mediation analysis revealed that (a) early literacy skills have stronger direct effects on G4 math achievement than early numeracy skills; (b) the effects of early numeracy skills on G4 math scores become more pronounced for children with weaker early literacy skills (i.e., conditional effects); and (c) the effect of early numeracy skills on G4 math achievement is transmitted through students’ confidence (i.e., mediator) and the effect is more prominent for those who had more proficient early literacy skills (i.e., conditional indirect effects). Findings from the conditional direct and indirect effects of early numeracy skills on G4 math achievement suggest that children who had more proficient early literacy skills utilize strategies beyond just early numeracy skills to solve G4 math problems and that children’s strategies to solve math problems may be enhanced by the proficiency of their literacy skills.

Introduction

A prolific body of literature has identified the family as the key dynamic influencing the early development of children’s academic skills including literacy and numeracy (e.g., Liu et al., 2019 ; Manolitsis et al., 2013 ; McCormick et al., 2020 ; Munro et al., 2021 ; Van Voorhis et al., 2013 ). To further understanding of the influence of early literacy skills (ELS) and early numeracy skills (ENS) stemming from the home learning environment on children’s academic achievement, many researchers have focused on identifying the specific skills which may predominantly impact later math performance. Considerable research has confirmed ENS are the strongest predictor for later math achievement (e.g.,Duncan et al., 2007 ; Kiss et al., 2019 ; Nelson & McMaster, 2019 ; Nguyen et al., 2016 ; Scalise & Ramani, 2021 ). In contrast, other studies have found that ELS were the foremost predictor in later math achievement (e.g., Aragón et al., 2016 ; Birgisdottir et al., 2020 ; Purpura et al., 2011 ; Yang et al., 2021 ). In addition, topics related to children’s family resources and confidence in math have also received research attention seeking to identify factors that might affect the gaps in math achievement observed among various ethnic groups in the United States and among countries in the international comparisons.

Additionally, multiple studies have utilized mediation models to illustrate the indirect effects of ENS on later math achievement. For example, the effect of ENS on later math achievement has been found to transmit through a third variable which is math language skills (King & Purpura, 2021 ). However, the extant studies have rarely, if ever, examined whether the effect of ENS on later math achievement becomes more (or less) pronounced for children with different levels of ELS (i.e., moderation effect). Likewise, few if any studies have been initiated utilizing a moderated mediation model to explore whether the effects of ENS on later math achievement transmitted through a mediator differs depending upon the levels of a moderator (e.g., ELS). The present study will address these gaps by constructing a moderated mediation model utilizing the Trends in International Mathematics and Science Study (TIMSS, 2019 ) data to explore the conditional direct and indirect effects of ENS on G4 math achievement.

Early literacy and numeracy activities

There is substantial literature demonstrating that home learning environments with parent–child early literacy activities (ELA) and early numeracy activities (ENA) encouraged children’s learning and enhanced their school achievement. Respective studies found differences in children’s outcomes resulted from distinct approaches in which parents interact with their children and have consistently confirmed home numeracy environment predicted ENS (e.g., Clerkin & Gilligan, 2018 ; Fazio et al., 2014 ; Segers et al., 2015 ; Siegler, 2016 ; Susperreguy et al., 2020 ). Parent–child activities in basic addition and subtraction lead to improved academic ability (Munro et al., 2021 ) and the home numeracy environment was predictive of numeracy (Napoli & Purpura, 2018 ). Children engaged in ELA and ENA became more confident and curious about math at age 10 (Clerkin & Gilligan, 2018 ) and later school academic achievement benefitted (Lehrl et al., 2020 ; Niklas & Schneider, 2017 ). Mothers who shared picture books with their children enhanced their math and literacy skills (Ribner et al., 2020 ) whereas fathers in Hong Kong reported higher frequencies of engagement in more real-life number game activities than mothers (Liu et al., 2019 ). Parents posed more complex questions about numbers to their sons than daughters (Uscianowski et al., 2020 ) while maternal use of relevant math facts during games were associated with their daughters’ later addition accuracy (Casey et al., 2020 ). Parent–child letter–sound interactions predicted growth in counting skills (Soto-Calvo et al., 2020 ) and formal home ENA (e.g., comparing numerals) predicted children’s symbolic number system knowledge (Skwarchuk et al., 2014 ). Moreover, symbolic knowledge was found to relate to broader mathematical competence (Chen & Li, 2014 ; Scalise & Ramani, 2021 ; Schneider et al., 2017 , 2018 ). Parents reported engaging in more literacy than numeracy practices as they considered literacy development more important than numeracy development (Napoli et al., 2021 ). Other parents reported prioritizing early numeracy and providing more math activities at home (Zippert & Rittle-Johnson, 2020 ).

McCormick et al. ( 2020 ) affirmed that unconstrained language and math activities predicted gains in children’s language and math skills. Examples of unconstrained skills are vocabulary and problem solving, while constrained skills would include competencies like letter knowledge and counting. Constrained skills are directly teachable and have a ceiling, while unconstrained skills are limitless and are acquired gradually through experience (Snow & Matthews, 2016 ). Everyday contexts such as shopping in grocery stores can promote math related conversations and potentially provide learning opportunities for children (Hanner et al., 2019 ). It appears that negligible research has been conducted exploring attainable ways for ELA to evolve to ELS or for ENA to advance to ENS much less how to develop curricula and remedial programs that help parents and teachers facilitate ELA and ENA to extend to ELS and ENS.

Early literacy and later math achievement

Studies on the influence of early literacy to later math achievement have largely focused on phonological awareness. Researchers have demonstrated the associations between phonological awareness and math achievement (De Smedt et al., 2010 ; Fuchs et al., 2006 ; Krajewski & Schneider, 2009 ) and fifth-grade computation skills (Hecht et al., 2001 ). Studies show that ENS and phonological processing influenced growth in math from kindergarten through third grade (Vukovic, 2012 ) and elementary school children with mild intellectual disabilities were found to profoundly rely on phonological awareness when solving math problems (Foster et al., 2015 ). However, other studies found early written language skills, but not phonological awareness, are unique predictors of Icelandic fourth graders’ (Birgisdottir et al., 2020 ) and Finnish third and fourth graders’ math achievement (). Verbal skills and visuomotor skills uniquely predicted fourth-grade math achievement (Kurdek & Sinclair, 2001 ) and reading skills significantly predicted Canadian children’s third-grade reading and math performance (Romano et al., 2010 ). Manfra et al. ( 2017 ) reported that writing and counting skills were consistently strong predictors of third-grade reading and math achievement among low-income, ethnically diverse children while Fuchs et al. ( 2016 ) found that second-grade language comprehension is more critical for fourth-grade word-problem solving than pre-algebraic knowledge. Furthermore, Kiss et al. ( 2019 ) affirmed that reading skills explained significant variations in third graders’ performance on number operations, algebra, data analysis, and geometry measurement. Third grade reading comprehension was related to a conceptual understanding and the application of math knowledge at eighth grade (Grimm, 2008 ). In addition, specific early literacy skills (e.g., vocabulary and print knowledge) were found to be influential in math development (e.g., Purpura & Napoli, 2015 ; Purpura et al., 2011 ). Purpura and Reid ( 2016 ) observed that math language (e.g., “more,” “many,” and “fewer”) is more proximal to numeracy skills than general language. Vanbinst et al. ( 2020 ) suggest that early reading and early arithmetic have a shared underlying cognitive basis for Flemish children. Furthermore, English literacy (second strongest to working memory) predicted Singaporean 11-year-olds’ algebraic word problem solving skills (Lee et al., 2009 ) and bilingualism is beneficial for children's math reasoning and problem-solving skills (Hartanto et al., 2018 ). Peng and colleagues’ (2020) meta-analysis results affirmed that more complicated language and math skills were associated with stronger relations between language and math.

Early numeracy and later math achievement

Early numeracy is a common term that is comprised of skills such as verbal counting, recognizing number patterns, comparing numerical magnitudes, manipulating quantities, and adding and subtracting objects. The associations between children’s ENS and their later math achievement have been well documented (e.g., Clerkin & Gilligan, 2018 ; Duncan et al., 2007 ; Raghubar & Barnes, 2017 ). While preliteracy skills were more strongly related to word reading, sensitivity to relative quantity was more strongly related to first-grade math (Chu et al., 2016 ). Basic numerical cognition was predictive of later procedural calculation skills and word problem development (Fuchs et al., 2010 ) and most strongly related to the ability to solve applied math problems (Jordan et al., 2010 ). Students who received early numeracy intervention improved their second-grade math performance (Bryant et al., 2021 ). Similarly, advanced counting competencies (Nguyen et al., 2016 ) and fluency in solving addition problems (Geary, 2010 ) were found to be strong predictors of fifth-grade math achievement. A meta-analysis of longitudinal studies revealed that number acuity may prospectively predict later math performance and is also retrospectively associated with early math performance (Chen & Li, 2014 ). Nevertheless, studies demonstrated that early math and reading skills positively influence each other in later school years (e.g., Cirino et al., 2018 ; Hooper et al., 2010 ) but when deficient also displayed comorbidities with each other.

Mediation effects

Some studies have employed more complex statistical techniques to identify and explain the mechanism or procedure that underlies an observed relation between ENS and math achievement via a third hypothetical variable (i.e., a mediator). For example, Purpura et al. ( 2017 ) detected that the relation between early math and literacy skills is mediated by children’s mathematical language skills and partially mediated by print knowledge (Purpura & Napoli, 2015 ). Math language mediates the relation between the direct home numeracy environment and numeracy skills (King & Purpura, 2021 ) and language abilities impact formal math skills partially through informal math skills (). In addition, verbal analogies were indirectly related to arithmetic knowledge through symbolic number skill (Vukovic & Lesaux, 2013 ) and reading comprehension skills may be partially mediating the relation between problem solving ability and growth in math (Vista, 2013 ).

It appears that the extant studies barely, if ever, explored how ELA and ENA directly or indirectly enhanced later math performance nor inquired into how ELA and ENA progress into ELS and ENS which in turn advance later math achievement. Furthermore, insufficient research has been undertaken examining whether a third variable influences the strength or direction of the relations between ENS and math achievement. For instance, if found to be significant, ELS can cause an amplifying or weakening effect between ENS and math achievement as the child’s ELS level increases (i.e., moderation). Hence, the question as to whether children with weaker ELS might rely more on ENS to solve math problems remains unexplored. This study will explore the moderation effect of ELS for ENS on G4M. For instance, whether the effect of ENS on G4M becomes less pronounced for children possessing stronger ELS.

HRL and math achievement

Many studies have confirmed the relation between home resources and children’s school achievement. Increases in school resources are consistently associated with improvements in math achievement for all groups, regardless of their individual resources (McConney & Perry, 2010 ). In China, increased levels of family and school resources were favorably related to student math achievement, and the association became more pronounced for levels of school resources in rural areas (Xue et al., 2020 ). In Japan, the student level of resources (i.e., number of books, computer access, paternal, and maternal educational levels) were positively related to student math achievement, whereas the school level of resources (i.e., rural and economically disadvantaged) were inversely related to student math achievement (Takashiro, 2017 ). In contrast, in Australia correlations between math performance and resources are far weaker in the nonmetropolitan schools than for those in the metropolitan areas (Murphy, 2019 ). In Tennessee, the higher the percentage of disadvantaged (determined by the percentage of students receiving federally subsidized free and reduced-priced lunches) the lower the achievement was. Hence, it appears there is a locale difference. Students with few resources in rural areas outperformed their economically disadvantaged nonrural peers. The author surmised that it is possible that support in the economically disadvantaged rural locales provides a sense of community not found in other economically disadvantaged areas which enables rural students to achieve higher in math than their nonrural peers (Hopkins, 2005 ). Furthermore, the effect of cognitive activation on math achievement was transmitted through self-efficacy which was moderated by resources at both the student level and the teacher level (Li et al., 2020 , 2021 ).

Researchers tested the Information Distortion Model (IDM) and hypothesized that in Australia children with a few resources would have higher academic interest compared to those with many resources and who were academically equally prepared. Results support the model and indicate that children with a few resources had higher numeracy interest than those who were equally prepared with many resources (Parker et al., 2021 ). In contrast, in China few family resources were shown to hamper middle school student math achievement, however high levels of subjective social mobility can buffer the adverse effects of low family resources on math achievement. Subjective social mobility reflects students’ personal beliefs in their ability to attain a higher social and economic status in the future and is regarded as a motivational resource (Zhang et al., 2020 ). Math and reading ability heightened future adult SES attainment (Ritchie & Bates, 2013 ). Further studies examining the underlying mechanism of family resources and its impact on academic achievement, as well as the varying influences on student achievement in different locales (e.g., rural vs. urban) in a cross-culture paradigm (e.g., European descents vs. Asian countries) are necessary. It appears that children with few resources in rural areas of mostly European descent countries (e.g., Australia and U.S.) outperformed their urban counterparts, whereas the reverse association was observed in Asian countries (e.g., China and Japan).

Confidence in math

Studies examining confidence and math achievement often focused on the reciprocal relations between the two. Typically, math self-efficacy improved math achievement and earlier math achievement was a consistent predictor of later confidence and interest, suggesting a reciprocal relation between confidence and math performance (e.g., Arens et al., 2017 ; Ganley & Lubienski, 2016 ; Grigg et al., 2018 ; Schöber et al., 2018 ; Sewasew et al., 2018 ). Nonetheless, Vogt et al. ( 2020 ) analyzed the NICHD SECCYD data and reported that children who scored higher on applied problems at 54 months had lower non-ability-based confidence (or overconfidence) at age 15 than those with a lower achievement. The associations between non-ability-based confidence and earlier development were similar for boys and girls. NICHD ( 2006 ) reported that the participants in SECCYD were comprised of “76.4% white, 12.7% African-American, 6.1% Hispanic…” (p. 30). Hence, caution is needed in generalization of the findings as the Hispanic group was underrepresented with whites overrepresented. In a cross-cultural study, self-rating in math and absence of disappointment with poor performance were associated with better performance in the English group, whereas no significant relationships between attitudes and performance were detected among Chinese first graders (Dowker et al., 2019 ). Fourth through sixth graders who perceived their classroom environments as more caring, challenging, and mastery oriented had significantly higher levels of math self-efficacy, which favorably impacted math performance. Note that the participants consisted of “Latino/a (62%) and Caucasian (31%) students” (Fast et al., 2010 , p. 731). Students from a sample of “5th grade to early college students (41% female, 80% white)” (Rice et al., 2013 , p. 1028) with greater social support for math and science from parents, teachers, and friends had more constructive attitudes and a higher sense of their own competence. Marked overconfidence was observed within the world regions that had lower scores on measures of cognitive ability whereas less inflated levels of overconfidence were noted among the high-achieving world regions based on samples from 33 nations (Stankov & Lee, 2014 ). Erickson and Heit ( 2015 ) cautioned that both overconfidence and anxiety can adversely affect metacognitive ability and can lead to math avoidance. Another cross-cultural study reported that teachers with greater self-efficacy in teaching math had higher job satisfaction and class levels of math achievement and interaction quality. At the student level, a higher individual self-concept advanced math achievement, and individual perceptions of interaction quality enhanced self-concept (Perera & John, 2020 ). It appears that the extant studies have given minimal attention as to whether the effect of ENS on later math achievement is transmitted through confidence (i.e., mediation). Furthermore, whether the effect of ENS on later math achievement becomes more pronounced for children with stronger ELS (i.e., moderation effect) is a topic deserving more comprehensive research.

The present study

The review of the existing studies on related topics has shown that complex relations among multiple variables influence students’ math achievement. However, few studies have explored moderators of ENS on later math performance and whether the effects might be inordinately impacted by the levels of the moderator (e.g., mean and ± 1SD). For example, the effect of ENS on math might become less pronounced as children’s ELS increased. In addition, whether the effect of ENS is transmitted through other variables (e.g., confidence) to enhance later math performance and if this effect may be stronger for children with stronger ELS (i.e., moderated mediation) deserves comprehensive study. This study uses the TIMSS 2019 data in a cross-linguistic and cross-cultural framework to examine the variables comprising (1) home environment support and (2) student engagement and attitudes that lead to the differing outcomes in students’ fourth-grade math achievement. Specifically, this study targeted the top eight performing countries on variables in home environment support including ELA, ENA, ELS, ENS, and HRL, as well as student engagement and attitudes (e.g., SCM), and fourth-grade math plausible values as the outcome variable. The hypotheses explored in this study are as follows:

Home environment support, student engagement, and attitudes are predictors of G4M. In particular, ELS are more effective than ENS in predicting G4M.

Home environment support and student engagement and attitudes are intercorrelated.

There are conditional direct effects of ENS on G4M.

ELS have a direct effect on G4M.

ENS have a direct effect on G4M.

ELS moderate the effect of ENS on G4M, and the effect of ENS on G4M is more prominent for children with weaker ELS

HRL (a covariate) have a direct effect on G4M.

There are conditional indirect effects of ENS on G4M (i.e., ENS → SCM → G4M).

ENS have a direct effect on SCM.

ELS have a direct effect on SCM.

ELS moderate the effect of ENS on SCM, and the effect of ENS on SCM is more pronounced for children with stronger ELS.

SCM have a direct effect on G4M.

SCM mediate the relation between ENS and G4M, and the effect is more evident for children with stronger ELS.

HRL (a covariate) have a direct effect on SCM.

Note that HRL serve as a covariate to control for ENS differences on SCM and G4M. The conceptual and statistical moderated mediation model diagrams are exhibited in Fig.  1 .

Moderated Mediation Diagrams. Predictor: ENS Early numeracy tasks (skills) beginning school/SCL, Moderator: ELS Early literacy tasks (skills) beginning school/SCL, Mediator: SCM Students confident in mathematics/SCL, Covariate: HRL Home Resources for Learning/SCL, Outcome variable: G4M Fourth-grade mathematics

Participants

UNESCO’s International Standard Classification of Education (ISCED) 2011 (UNESCO, 2012 ) provides an internationally accepted classification scheme for describing levels of schooling across countries. All students enrolled in the grade that represents 4 years of schooling counting from the first year of ISCED Level 1 (providing the mean age at the time of testing is at least 9.5 years) are eligible to participate in TIMSS. Approximately 600,000 students from 64 countries and 8 benchmarking systems (e.g., Hong Kong Special Administrative Region, SAR) participated in TIMSS, 2019 . Approximately 32,000 participants from the top eight performing countries were included in the present study and their mean PVs are shown in Fig.  2 .

TIMSS 2019 Top Eight Fourth Grade Average Math Scale Scores. SGP Singapore, HKG Hong Kong, KOR Korea, TWN Taiwan, JPN Japan, RUS Russia, IRL Ireland, LAT Latvia

Assessments

The TIMSS, 2019 assessment migrated to eTIMSS, a digital version of the assessment administered to students on computers and tablets. eTIMSS also included a novel section consisting of problem solving and inquiry tasks (PSIs) designed to exploit the digital environment to its fullest. About half the participating countries chose to transition to eTIMSS. The eTIMSS participating countries also administered the paper version of their trend items to a sample of schools, providing a bridge that helped link the two test-taking modes. For TIMSS, 2019 , comparing the item statistics for eTIMSS and paperTIMSS was integral in identifying items that were psychometrically equivalent under the IRT scaling. This process enabled the eTIMSS and paperTIMSS achievement results to be reported on the same achievement scale (i.e., fourth-grade math). The TIMSS assessment was categorized into content and cognitive domains. The content domains were comprised of (1) numbers, (2) geometric shapes and measures, and (3) data display, while the cognitive domains consisted of (1) knowing, (2) applying, and (3) reasoning. Constructed response items were scored independently by two trained scorers and TIMSS, 2019 trend scoring reliability for human scored items was 97%. The agreement across items was 98% or higher across countries, whereas within-country scoring reliability was 98% (Fishbein et al., 2020 ).

TIMSS utilized Item Response Theory (IRT) models to compute proficiency scores to provide valid comparisons across student populations based on broad coverage of the achievement domain. These test items were arranged in blocks that were assembled into student booklets that contained different (but systematically overlapping) sets of item blocks. Because each student received only a fraction of the achievement items for 72 min test time, statistical and psychometric methods were required to link these different booklets together so that student proficiency could be reported on a comparable numerical scale even though no student answered all the tasks. IRT was well suited to handle such data collection designs in which not all students were tested with all items. In addition, TIMSS used the three-parameter logistic (3PL) for multiple-choice items, the 2PL IRT model for constructed response items worth 1 score point, and the generalized partial credit model for constructed response items worth up to 2 score points (von Davier, 2020 ).

Home Environment Support

Participating countries (except U.S. and England) administered an early learning survey to the parents/guardians and a questionnaire to students, both of which were linked to the achievement booklet. The scales were constructed using the partial credit model IRT scaling methods. Each context scale separated students into regions corresponding to high, middle, and low values on the construct using the combinations of responses. Partial credit IRT scaling was based on a statistical model that related the probability that a student would respond to an item to that student’s math ability on the underlying construct. The average Cronbach’s alpha reliability coefficients for countries with data is approximately 0.88 for the early literacy and numeracy activities and the early literacy and numeracy tasks scales, and 0.70 for the home resources for learning scale (Yin & Fishbein, 2020 ).

Early literacy activities scale (9 items).

This survey asked parents, “ Before your child began elementary school, how often did you or someone else in your home do the following activities with him/her? ” Such an item included in this scale is “ Play with alphabet toys (e.g., blocks with letters of the alphabet) .” Students whose parents “ often ” engaged in five activities with them while “ sometimes ” doing the other four activities scored 10.8 or higher. Those whose parents “ never or almost never ” did five activities with them while “ sometimes ” doing the other four activities scored 6.2 or lower. All others sometimes engaged them in early literacy activities.

Early numeracy activities scale (9 items)

This survey asked parents, “ Before your child began elementary school, how often did you or someone else in your home do the following activities with him/her? ” Such an item included in this scale is “ Play games involving shapes (e.g., shape sorting toys, puzzles) .” Students whose parents “ often ” engaged in five activities with them while “ sometimes ” doing the other four activities scored 11.0 or higher. Those whose parents “ never or almost never ” did five activities with them while “ sometimes ” doing the other four activities scored 6.6 or lower. All others sometimes engaged them in early numeracy activities.

Early Literacy tasks scale (7 items)

This survey asked parents, “ How well could your child do the following when s/he began the first grade of elementary school? ” Such an item included in this scale is “ Write words other than his/her name .” Students whose parents rated “ very well ” to four tasks and “ moderately well ” to the other three tasks scored 11.2 or higher. Those whose parents rated “ not very well ” to four tasks while “ moderately well ” to three tasks scored 8.8 or lower.

Early numeracy tasks scale (5 items)

This survey asked parents, “ Could your child do the following when s/he began the first grade of elementary school? ” Such an item included in this scale is “ Recognize written numbers .” Students whose parents’ responses were “ very well ” to two tasks and “ moderately well ” to one task and “ yes ” to two tasks scored 11.7 or higher. Those whose parents’ responses were “ not very well ” to two tasks and “ moderately well ” to one task and “ no ” to two tasks scored 8.1 or lower (P. Foy, Personal Communication, July 26, 2021).

Home resources for learning scale (5 resources, 22 items)

One of the five resource questions comprised of this scale asked parents, “ Highest level of occupation of either parent (parents) .” Such an item included in this resource subscale was “ Professional (corporate manager or senior official, professional, or technician or associate professional). ” Students with many resources scored 11.8 or higher, having more than 100 books at home and both home study supports, more than 25 children’s books at home, at least one parent having finished university, and at least one parent having a professional occupation. Students with few resources scored 7.4 or lower, having 25 or fewer books at home and neither of the home study supports, 10 or fewer children’s books at home, neither parent having achieved beyond upper-secondary education, and neither parent owning a small business or holding a clerical or professional occupation. All others had some resources.

Student engagement and attitudes

Confidence in mathematics scale (9 items).

This scale asked students, “ How much do you agree with these statements about mathematics? ” Such an item included in this scale is “ I am good at working out difficult mathematics problems .” Those very confident in mathematics scored 10.7 or higher reporting “ agree a lot ” with five statements and “ agree a little ” with the other four. Students not confident in mathematics scored 8.5 or lower reporting “ disagree a little ” with five statements and “ agree a little ” with the other four. All others were somewhat confident in mathematics (Yin & Fishbein, 2020 ). The average Cronbach’s alpha reliability coefficients for the students confident in math scale for these eight countries is 0.87.

Data analysis

The present study employed the IEA IDB Analyzer (Version 4.0.42, IEA, 2021 ) and PROCESS Macro (v4.0, 2022) (Hayes, 2022 ) in conjunction with IBM SPSS 28 ( 2022 ) to test on the public-use version of the TIMSS, 2019 data. The proportions of the sample are approximately 8% from Hong Kong, 18% from Singapore, and 12% from each of the remaining six countries with relatively similar contributions. IDB Analyzer was utilized to compute descriptive statistics and bivariate correlations. A moderated mediation model (Hayes, 2017 , model 8) was constructed to estimate the conditional effect of ENS on SCM (mediator) varied as a function of ELS (moderator). In addition, the conditional direct effect of ENS on G4M is also dependent upon the levels of ELS. An index of moderated mediation was used to test the significance of the moderated mediation. Confidence intervals did not contain zero between the lower and upper limits of the 95% confidence intervals indicating that the direct and indirect effects were conditional on the level of the moderator (ELS). The number of bootstrap samples for percentile bootstrap confidence intervals was 5,000.

Descriptive statistics and correlations

The average bivariate correlations comprised of mostly Asian and European students showed that ELS ( r  = 0.36) were effective than ENS ( r  = 0.21) in predicting G4M and ELA and ENA were inadequate indicators of G4M ( r s = 0.16 and 0.15). SCM dominated with the highest impact in G4M ( r  = 0.44) with HRL also prominent ( r  = 0.39). Hypothesis 1 has been supported.

Bivariate correlations between home learning environment and student attitudes showed that children who were proficient in ELS were also likely to be proficient in ENS ( r  = 0.30). ELS benefitted from both ELA ( r  = 0.34) and ENA ( r  = 0.32) while ENS were facilitated ineffectively from ELA and ENA ( r s = 0.09 and 0.11), and ENA evolved more to ELS ( r  = . 32) than ENS ( r  = 0.11). Parents with many HRL engaged in more early literacy ( r  = 0.30) and numeracy ( r  = 0.25) activities with their children than their counterparts who possessed fewer HRL, and parents engaged both activities with their children in proportional amounts ( r  = 0.77). HRL enriched children’s ELS ( r  = 0.34) more than ENS ( r  = 0.16), and inadequately boosted SCM ( r  = 0.19). Children who engaged in more ELA and ENA with their parents were not much more confident in math ( r s = 0.14 and 0.15). In a similar vein, students with more HRL, and who entered school with higher levels of ELS and ENS, were not more confident in math with r s = 0.17, 0.11, and 0.19 respectively. A correlation matrix with home environment support, student attitudes, and plausible values (PVs) is exhibited in Table 1 . Hypothesis 2 has been supported. Note that ELA and ENA were not included in further analysis mostly due to the weak correlation coefficients with G4M.

• Moderated mediation

A moderated mediation model was tested using the PROCESS macro (Hayes, 2022 ) in SPSS to estimate the conditional direct and indirect effects of ENS on G4M through SCM (i.e., mediator) as moderated by ELS. All variables were standardized prior to entering the analysis to facilitate interpretation of any effects resulting in the estimation of standardized coefficients (β). Betas are comparable in magnitude within a model as well as between studies with higher absolute β coefficients presenting stronger effects. Results from the present study exhibited that ENS and ELS both had direct effects on SCM (βs = 0.05 and 0.10 ps < 0.001, respectively) signifying that ELS had a stronger influence on SCM than ENS. Moreover, ELS moderated the relations between ENS and SCM (β = 0.02, p  < 0.001) suggesting that the effect of ENS on SCM became more pronounced for students with stronger ELS (β = 0.07, p  < 0.001) than those with lower ELS (i.e., mean and -1SD) (βs = 0.05 and 0.03, respectively, p s < 0.001). The results suggested that there were conditional effects of the focal predictor (ENS) at different levels of the moderator (i.e., ± 1SD and mean ELS) on SCM. Furthermore, HRL was significantly associated with SCM (β = 0.13, p  < 0.001).

ENS → SCM → G4M

ENS, SCM, and ELS had direct effects on G4M (βs = 0.09, 0.28, and 0.16, respectively, p s < 0.001) indicating that ELS was a much more prominent predictor of G4M than ENS despite SCM having the strongest effect on G4M. ELS moderated the relations between ENS and G4M (β = -0.04, p  < 0.001) suggesting that the effect of ENS on G4M was more evident for those with weaker ELS (βs = 0.13 and 0.09, respectively, p s < 0.001) than those with stronger ELS (β = 0.06, p  < 0.001). The results suggested that there were conditional direct effects of the focal predictor (ENS) varying with different levels of the moderator (ELS) on G4M implying that students who possessed stronger ELS utilized strategies more than ENS to solve fourth grade math problems. Further, HRL had a strong direct effect on G4M (β = 0.20, p  < 0.001). Sub-hypotheses ( a ) through ( d ) of H3 have been supported, suggesting that there are conditional direct effects of ENS at different levels of ELS on G4M.

The estimation of the moderated mediation models suggested that SCM was a mediator of the relation between ENS and G4M and had significant direct effects on G4M (ENS → SCM → G4M: Index of moderated mediation = 0.0056, BootSE  = 0.0013, BootLLCI  = 0.0030, BootULCI  = 0.0081). That is, the effect of ENS on G4M was transmitted through SCM. This denotes that (1) children who have stronger ENS had higher math achievement at fourth grade, (2) this relationship was explained by stronger SCM, and (3) this effect was stronger for children with stronger ELS. Sub-hypotheses ( a ) through ( f ) of H4 have been supported suggesting that there are conditional indirect effects of ENS on G4M transmitted through SCM at different levels of ELS.

In summary, the results indicate that (1) the mechanism linking ENS to G4M through a mediator SCM is related to ELS, and (2) the conditional direct effects of ENS on G4M vary at different levels of ELS suggesting that literacy skills might enhance students’ approaches in analyzing, interpreting, and solving math problems. The findings suggest that students with lower ELS benefitted more from ENS whereas those with higher ELS relied less on ENS to solve fourth-grade math problems. The full moderated mediation model with estimations of conditional direct and indirect effects are presented in Table 2 . The hypotheses that have been explored and supported are summarized in Table 3 .

IEA TIMSS has employed advanced techniques in methodology to derive the scale scores of home environment support and student engagement and attitudes and sub-categories in cognitive and content domains. This has provided data for researchers to explore multifaceted relations among variables using advanced statistical techniques to test models with moderated and mediated relations with the intent of improving math teaching and learning around the world. This study adds greater understanding of math learning and how early literacy and numeracy skills influence G4 math performance. The participants were comprised of mostly Asian and European students with results showing that ELS were stronger than ENS in predicting G4M and lend support to extant studies including Aragón et al. ( 2016 ), Birgisdottir et al. ( 2020 ), Purpura et al. ( 2011 ), and Yang et al. ( 2021 ). In contrast, it appears that the results from this study did not confirm children’s early numeracy skills as the strongest predictor of their later math achievement that have been reported by others (e.g., Bryant et al., 2021 ; Duncan et al., 2007 ; Raghubar & Barnes, 2017 ). Parents reported engaging in higher frequencies of ELA than ENA before their children started school, which is coherent with recent findings by Napoli et al. ( 2021 ). Both parent–child ELA and ENA developed into ELS, while bafflingly neither ELA nor ENA advanced into ENS which did not confirm that home numeracy environment predicted ENS (e.g., Clerkin & Gilligan, 2018 ; Fazio et al., 2014 ; Segers et al., 2015 ; Siegler, 2016 ; Susperreguy et al., 2020 ). Parents with many HRL engaged in moderately more ELA than ENA with their children than those with fewer HRL. In addition, HRL contributed more to ELS than ENS although children’s proficiencies in ELS and ENS were correlated. The findings that HRL fostered G4 math achievement are consistent with previous studies (e.g., McConney & Perry, 2010 ; Xue et al., 2020 ). Moreover, higher individual SCM advanced math achievement, in agreement with existent studies (e.g., Perera & John, 2020 ).

The positive moderation effect of the ELS on the relations between ENS and SCM indicate that the effect of ENS on SCM becomes more pronounced for children possessing stronger ELS. The negative moderation effect of the ELS on the relations between ENS and G4M appears to be in line with results from Fuchs et al. ( 2016 ) and Peng et al. ( 2020 ). The results suggest that children with weaker ELS utilized more ENS to assist them when approaching math problems whereas those with stronger ELS employed strategies more than ENS to answer math problems. Findings from this study suggest that children’s strategies to solve math problems might be enhanced by their literacy skills. Future studies that explore the dynamics between ELS and ENS and their combined influences and strengths on math achievement are urgently needed. In addition, studies to uncover how ELS help children answer math problems deserve comprehensive examination. It is necessary to separate ELS into different levels (e.g., ± 1SD and mean) when examining relations between ENS and math attainment. Moderated mediation analysis is an informative technique for assessing whether direct and indirect effects are conditional on values of a moderating variable such as ELS.

Limitations

The limitations of this study include characteristics of design or methodology that impacted or influenced the interpretation of the findings. For instance, parents reported low percentages of early literacy and numeracy activities with their children before school in the top five performing East Asian countries. Intriguingly, how Asian children have mastered their early literacy and numeracy skills and excelled to the top in international assessments remain undetermined. Likewise, low percentages of East Asian students reported that they were confident in math, nevertheless their performance was exceptional. In addition, participating countries included in this study were comprised of mostly Asian and European students and as such the findings should not be generalized to black and Hispanic children’s math learning. Future studies should explore whether the conditional direct and indirect effects are equal or more evident in black and/or Hispanic children’s math learning. If so, parents and educators should try to strengthen children’s literacy skills in tandem with numeracy skills to enhance their later math achievement. It would also be beneficial if the results of this moderated mediation model can be replicated using large-scale U.S. data which often include participants from more diverse ethnic backgrounds.

Implications

Both ELA and ENA advanced to children’s ELS and ELS are stronger than ENS in predicting children’s math achievement. Moreover, HRL have a stronger association with ELS than ENS. This study seeks to prompt awareness among parents and educators and should foster children’s literacy skills in concert with numeracy skills thanks to the critical role of ELS in their later math achievement. Most critically, parents are urged to engage in comparable levels of early literacy and numeracy practices utilizing instantaneous everyday situations with their children before entering school to enhance their children’s literacy and numeracy skills regardless of the availability of learning resources they can provide. However, whether strengthening literacy skills for students from disadvantaged groups with few resources can narrow the achievement gap deserves comprehensive studies.

Results from this study suggest that children’s early literacy skills have a critical role in their later math achievement in a cross-linguistic and cross-cultural framework. The effect of ENS on SCM becomes more pronounced when the level of ELS increases whereas the effect of ENS on SCM diminishes for those with weaker ELS. In addition, the effect of ENS is transmitted through SCM, and confidence has a strong effect on G4M. In contrast, the effect of ENS on G4M diminishes when the level of ELS increases. It appears that children with weaker ELS employ ENS whereas those with stronger ELS utilize strategies more than ENS to tackle math problems. This suggests that children’s math problem solving strategies might be advanced by their early literacy skills. Furthermore, ELS are more effective than ENS in predicting children’s G4 math achievement. The main takeaways from this study are: (1) ELS have a stronger effect on G4M than ENS; (2) HRL impact more on children’s ELS than ENS; (3) both early literacy and numeracy activities have progressed to ELS but demonstrated limited advancement to ENS, a missing link; (4) SCM emerged as the strongest predictor of G4M; (5) students with stronger ELS and ENS are more confident in math; and (6) The moderated mediation analysis revealed that (a) ELS have stronger direct effects on G4 math achievement than ENS; (b) the effects of ENS on G4M become more pronounced for children with weaker ELS (i.e., conditional effects); and (c) the effect of ENS on G4 math achievement is transmitted through SCM (ENS → SCM → G4M) and the effect is more prominent for those who had more proficient ELS (i.e., conditional indirect effects). Findings from the conditional direct and indirect effects of ENS on G4M suggest that children who had more proficient ELS utilize strategies beyond just ENS to solve G4 math problems and that children’s strategies to solve math problems may be enhanced by the proficiency of their literacy skills. Parents and educators should facilitate children’s literacy skills and numeracy skills to enhance their later math achievement.

Availability data and materials

The datasets generated and/or analyzed during the current study are available in the TIMSS 2019 International Database repository, https://timss2019.org/international-database/.

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Chang, I. Early numeracy and literacy skills and their influences on fourth-grade mathematics achievement: a moderated mediation model. Large-scale Assess Educ 11 , 18 (2023). https://doi.org/10.1186/s40536-023-00168-6

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Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling

• Peera Wongupparaj   ORCID: orcid.org/0000-0001-8099-9157 1 &
• Roi Cohen Kadosh   ORCID: orcid.org/0000-0002-5564-5469 2  

BMC Psychology volume  10 , Article number:  27 ( 2022 ) Cite this article

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The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.

The current study recruited 6- and 7-year-old children ( N total  = 505, n 6yrs  = 238, and n 7yrs  = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.

The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.

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Introduction

Mathematical skills are regarded as an important tool and an integral part of effective functioning in everyday life [ 1 , 2 ]. These skills are the keys to analyzing and interpreting information and also making basic or complex decisions [ 3 ]. Meanwhile, several lines of evidence show that early mathematics achievement might predict a person’s professional success and economic growth [ 4 , 5 ]. Understanding these developmental trajectories and cognitive underpinnings is essential because of the promising predictability of later positive outcomes as a result of early numerical abilities.

Researchers from several disciplines have currently begun to reveal underlying cognitive and brain architectures of our numerical processing abilities (e.g., [ 6 , 7 , 8 , 9 , 10 , 11 ]). One theoretical perspective explains the diversity in early numerical ability by referring to the development of the domain-specific approach. The theory states that early numerical abilities and difficulties are closely related to numerical core systems (i.e., the approximate number system [ANS]; [ 12 , 13 ]). Typically, several studies on infants and young children suggested progressive acquisitions of numerical development [ 14 , 15 , 16 ], where the ANS nonsymbolic and symbolic numerical magnitude processing abilities (as indexed by dot–dot and dot–number comparison and a mental number line tests) were assumed to form the basis of numerical skills among preschoolers who had not yet been taught a formal mathematics lesson [ 12 ]. A more accurate ANS or symbolic magnitude comparison ability (e.g., a number comparison test) and symbolic magnitude estimation ability (e.g., the mental number line test) were later developed [ 17 , 18 ]. This continuing numerical ability uses the prenumerical ANS and is also being thought of as the numerical development from subitizing, counting, and estimating to arithmetic [ 16 ]. These early numerical systems have also been called the “core-systems of number” [ 12 ].

Other studies have also alternatively revealed the main roles of executive functions (EFs) [ 19 ] as a crucial predictor of early numerical abilities. This domain-general theoretical framework proposes that symbolic numerical magnitude estimation ability, as measured by the mental number line test, may need more than complete core systems of number [ 20 , 21 ]. It has been proposed that this process includes broad cognitive processes, such as EFs, that work together with numerical processing to influence numerical development throughout childhood [ 22 ]. EFs in early childhood show significant improvements after age 5, demonstrated in abilities such as shifting (cognitive flexibility), inhibition of dominant or prepotent responses, and updating of working memory [ 23 , 24 , 25 , 26 ]. The majority of the research suggests that domain-general skills contribute to early numerical development, especially during the transition from preschool to kindergarten [ 27 , 28 ]. Nonetheless, several contradictory results on the contribution of domain-general abilities to numerical development and the processes driving their integration remain uncertain. [ 29 ]. Specifically, the how, why, and what components of EFs in numerical context are essential and whether or not EFs are genuinely malleable to leverage early mathematical development from informal to formal schooling [ 30 , 31 ].

A multicomponent framework of mathematics highlighting the main role of EFs on domain-specific numerical skills and early numerical abilities as being an indirect and stable relationship from age 8 years through to young adults has been documented [ 31 ]. This study did not capture the early stage of informal mathematical growth. The unique contributions of either the general EFs or EFs in numerical contexts on domain-specific numerical skills and early numerical abilities across age groups are also unclear [ 32 ]. A recent study found that general EFs skills did not affect mathematics achievement across age and grade (preschool–fourth grade) [ 33 ], but a recent longitudinal finding suggested that only EFs in a numerical context were far more important than ANS or general EFs to predict developmental dyscalculia and numerical accomplishment [ 34 ]. This finding is consistent with prior research that discovered a significant contribution of EFs-related numerical, but not non-numerical, content to mathematical abilities in 93 children [ 35 ]. Further, only EFs in numerical context, beyond general EFs, could predict developmental dyscalculia and mathematics achievement from ages 4 to 13 [ 34 ].

More specifically, the general EFs or EFs in numerical contexts may consist of partially dissociable components in early childhood [ 36 , 37 , 38 , 39 , 40 ]. The numerical specific EFs or EFs in numerical contexts have a stronger link to children’s math growth over and above the general EFs [ 40 ] because children’s ability to attend to numerical and spatial magnitudes involving in mathematics achievement may differ from those of music activities or reading counting books [ 41 ].

Several studies demonstrated the significant connection among specific executive functioning, that is, working memory, inhibition and shifting abilities, and mathematical ability in children [ 35 , 42 ]. Inhibitory control is required to inhibit a dominant or irrelevant response [ 43 ]. Working memory refers to the ability to hold, update, and manipulate information within memory storage [ 25 , 43 ]. Shifting ability is the ability to switch attention between tasks, mental sets, and strategies or the ability to flexibly disengage or engage with specific parts within tasks [ 25 , 39 ]. Nonetheless, the relationship between EF components and mathematical competencies in early childhood may depend on some aspects of EF and specific mathematical concepts (i.e., early numeracy, counting, conceptual, and procedural skills) [ 44 , 45 ].

The developmental patterns for the relationship between inhibitory control and shifting/switching abilities with mathematics achievement differed depending on the academic outcomes examined [ 46 ]. That is, few developmental changes were shown in the connection between EF components and mathematical abilities across elementary schools [ 42 ]. The unique contribution of EF components on mathematics outcome has also not been fully understood because the key roles of EF components on mathematics achievement were discovered, particularly for older students [ 47 ]. There is little research that highlights the interface of emerging and specific EF components and early mathematical learning in preschool children beyond numeracy and counting to emergent and critical mathematical proficiency in primary school children [ 45 , 48 ]. These works have mainly relied on general EF assessment even though extensive research has been carried out in young children on the EF components and mathematics achievement in several contexts [ 42 , 49 , 50 ].

Although recent literature support transfer effects from EF interventions to mathematical abilities, the EF trainings have a larger effect in preschool than in school ages [ 51 , 52 , 53 ]. Further, some studies suggested ineffective transfers from EF trainings to mathematics outcomes [ 50 , 54 ]. It is possibly suggested that previous approaches might fail to consider the specific ways in which EF is related to mathematics [ 55 ]. The lack of training transfer could stem from the fact that number-specific EFs are more significantly correlated with mathematical abilities than EFs measured by tasks that do not involve numerically relevant stimuli [ 34 , 56 , 57 , 58 ]. Taken together, these pieces of information appear to imply that the heterogeneity of general EF measures may mask the relationship between EF components and mathematical achievement [ 46 , 56 ]. Therefore, the EFs-numerical contexts tasks should be emphasized and used to investigate the complex relationship between specific components of the EFs and mathematics achievement.

It can be concluded that several studies have focused on numerical and domain-general executive functioning skills [ 59 , 60 ]. The primary functions of the domain-specific early mathematical skills (i.e., ANS) and number-specific EFs (i.e., EFs in numerical contexts) from informal to formal schooling are relatively scarce. Such knowledge could shed light on the development of mathematical achievement in that the number-specific EF was conceptualized as the main underlying processes or mechanisms for driving the domain-specific early mathematics across the development of numerical cognition in children. The current investigation aimed to (a) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children and (b) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children. Structural equation modeling (SEM) was employed to test the direct and indirect effects of the domain-specific early mathematics and number-specific EFs on mathematical abilities among preschool [6 years old] and primary school (7 years old) children. Domain-specific early mathematics were categorized by the dot-dot comparison, the dot-number comparison, the number comparison, and the mental number line tests. Number-specific EFs were represented by the numerical inhibitory and the numerical shifting tests. Formal and informal mathematical abilities were measured by the number sets [ 61 ] and the numerical operation tests (Fig.  1 ).

Screenshots of the tests in the current study: A The dot-dot comparison test; B The dot-number comparison test; C The number comparison test; D The mental number line; E The numerical Stroop test; F The numerical shifting test; H The number sets test; G The numerical operation test

Participants

The current study included 511 6- to 7-year-old children (238 or 47.1% for 6-year-old preschoolers and 267 or 52.9% for 7-year-old first graders); six children were excluded because of missing values, thus leaving 505 children (50.2% female participants) for final analysis. All participants were native Thai and attended 12 public schools in Chonburi province, Thailand and a sample of 12 public schools was drawn using a stratified sampling technique. All public schools used the same set of subjects and standards under the national curriculum for Thailand. The preschoolers and first graders were studying at the same public schools with equal proportions. No participant was clinically referred for learning difficulties (LD) or attention-deficit/hyperactivity disorder (ADHD). The experimental protocols were approved by the Burapha University Research Ethics Committee (BUU 6200/01533). All methods were carried out in accordance with the Good Clinical Practice (GCP) guidelines and the Declaration of Helsinki. Written informed consent was obtained from parents of all participants prior to inclusion.

The domain-specific early mathematics is composed of eight paper-and-pencil tests (the dot-dot comparison test, the dot-number comparison test, the number comparison test [also termed symbolic magnitude processing test [ 1 ], and the mental number line], the number-specific EFs (numerical inhibitory and shifting tests), and the mathematical abilities (number sets and numerical operation tests). These domain-specific early mathematics assessments were developed to tap into distinct aspects of young children’s mathematics development that are considered to be essential in preschool and primary school mathematics [ 18 , 20 ]. The number-specific EFs measures were used to reflect common and specific aspects of EFs in numerical contexts [ 62 ]. These tests were chosen to fit best with the age range tested in the current study and fit the emerging literature on the structure of EFs in the preschool and primary school periods [ 56 , 58 , 63 ].

The number sets and numerical operation tests were selected to index the mathematical abilities because these measures were used to reflect different mathematical skills rather than mathematics achievement in a single multicomponent standardized test [ 61 , 64 ]. The number sets test was designed to assess a small area of early numeracy or “number sense” and fluency in identifying and processing quantities indexed by object sets and numerals [ 61 , 65 ], whereas the numerical operation test was used to measure basic arithmetic skills or “arithmetic fact” in line with the national curriculum for preschool and primary school levels. These tests were administered in quiet rooms that were provided by the schools, and a group-administered test was used for all children at their schools. All children were not allowed to count and/or take notes, and these behaviors were monitored by researchers. The constructs, tests, test lengths, and time spent are shown in Table 1 . All children were assessed across eight tests, and the test administration took approximately 33 min for each child.

The dot-dot comparison test

The dot-dot comparison test was used to assess the enumerating ability by comparing two sets of dots that reflect subitizing and counting systems of children’s early numerical abilities [ 66 ]. The dot-dot comparison test is composed of 30 items, and each item contains two sets of black dots with a pseudorandom arrangement on a white background (see Fig.  1 A). The average distance between the centers of the two black-dot sets was 2.93 cm (minimum = 2.80 cm and maximum = 3.0 cm). Each dot was equated in size (0.30 cm in diameter), each group of dots was also comparable in size (1.00 cm in diameter), and numerosity (several dots from 1 to 9) differed across items. All children were instructed to circle which set of dots contained more dots without counting as accurately and quickly as possible within 2.5 min. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 30. The correct answer for each item was counterbalanced, and no more than three consecutive right answers on the same side were shown [ 1 ]. The Kuder–Richardson (KR)-20 reliability coefficient of this test was 0.97.

The dot-number comparison test

The dot-number comparison test was used to assess the numerical ability in associating and comparing a perceived number of objects (dots) with Arabic numerals (nonsymbolic vs. symbolic numbers). An Arabic symbolization is required for the development of the mental number line as a representation of magnitude and ordinality to visual space [ 67 ]. The dot-number comparison test contained 30 items, and each item contains two different sets of black dots and a single digit presenting on a white background with a pseudorandom arrangement on the left side and the single digit on the right side (see Fig.  1 B). The mean distance between the centers of the dot-number pairs was 2.99 cm (minimum = 2.9 cm and maximum = 3.2 cm). All dots were equated in size (0.3 cm in diameter), each group of dots was also equal in size (1 cm), and several dots ranged from 1 to 9. All the single digits were displayed in 20-point Times New Roman font. All children were instructed to circle which of the two sets between the dot–number pair is larger without counting as accurately and quickly as possible within 2.5 min. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 30. The correct answer for each item was also counterbalanced, and no more than three successive correct answers on the same side were shown [ 1 ]. The KR-20 reliability coefficient of this test was 0.97.

The number comparison test

The number comparison test was used to examine symbolic numerical magnitudes [ 1 ]. The number comparison test is composed of two numerical magnitude comparison subtests: a single-digit subtest with digits ranging from 1 to 9 and a two-digit subtest with digits between 11 and 99. The 120-digit pairs (60 pairs for single and 60 pairs for two-digit subtests) were displayed in four columns of 15 pairs in a 12-point Verdana font for each subtest (see Fig.  1 C). The number pairs were randomly presented, and four factors were taken into account: (1) a counterbalance of the correct answer on the side in each column, (2) different numbers in subsequent or neighboring number pairs, (3) no more than three consecutive correct answers presenting on the same side, and (4) no similar or inverse number pairs (e.g., 6–2 vs. 2–6) presenting in the same row or column. All children were instructed to circle the larger of the single or two-number pairs as accurately and quickly as possible within 2 and 3 min for single- and two-digit subtests. A response was also scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 60 for both single- and two-digit subtests. The KR-20 reliability coefficient of this test was 0.99 for the single-digit subtest, 0.98 for the two-digit subtest, and 0.99 for the overall numerical comparison test.

The mental number line test

The mental number line test was used to assess proficiency in numerical magnitude processes and representations [ 68 ]. The mental number line test contained 10 items, and all children were instructed to estimate by crossing out a location of 10 target numbers on 13-cm number lines. Each horizontal number line started with a target number and a 0 at the left endpoint and numbers (i.e., 10, 20, 50, and 100) at the right endpoint (see Fig.  1 D). All digits were displayed in a 12-point and 16-point Times New Roman font for target numbers and anchored numbers at the left and right endpoints of the mental number line test, respectively. They were instructed to complete the test as accurately and quickly as possible within 5 min. A response was scored in line with the percent absolute error (PAE) formula [ 21 ] and was defined as the absolute difference between target number and children’s estimate divided by the scale of each item and expressed as a percentage (i.e., |target number − participant’s estimated number|]/numerical range) × 100. The PAE scores ranged from 0 to 100%, and a higher PAE score indicated a less accurate series of estimates. The internal consistency with Cronbach’s α was 0.77.

The numerical inhibition test

The numerical inhibition test was used to assess a cognitive inhibition or the ability to automatically inhibit irrelevant responses and adjust control [ 69 , 70 , 71 ] on physical and numerical pairs. The numerical inhibition test contained two subscales, that is, a one-digit subtest with digits ranging from 1 to 9 and a two-digit subtest with digits ranging from 11 to 99. The 60-digit pairs (30 pairs for single and 30 pairs for two-digit subtests) were displayed in three columns of 10 pairs in 22-point and 26-point Times New Roman font for smaller and larger physical sizes. The distances between two digits of each number pair were six, four, and two for the first, second, and third columns, respectively (e.g., 1 7, 2 6, and 3 5; see Fig.  1 E). The number pairs were randomly shown, and four factors were also taken into consideration: (1) a counterbalance of the right answer on the side in each column, (2) different numbers in subsequent or neighboring number pairs, (3) no more than three consecutive correct answers showing on the same side, and (4) no similar or inverse number pairs (e.g., 1 5 vs. 5 1) presenting in the same row or column. All children were instructed to compare the physical sizes of two numbers and circle the larger of the single or two-number pairs as accurately and quickly as possible within 2 and 3 min for single- and two-digit subtests. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 30 for both single- and two-digit subtests. The KR-20 reliability coefficient of this test was 0.98 for the single-digit subtest, 0.95 for the two-digit subtest, and 0.98 for the overall test.

The numerical shifting test

The numerical shifting test was used to assess children’s cognitive flexibility performance or the ability to shift attention on the basis of changing (numerical) condition demands [ 72 ]. The paper-and-pencil version for the children was adapted from the computerized switching task by modifying the procedures and stimuli [ 73 , 74 ]. The numerical shifting test contained 36 items with digit pairs ranging from 1 to 9. The 36-digit pairs were showed in three columns of 12 pairs in 26-point Times New Roman font for each column. The digit pairs were displayed in red or black: the red digit pairs signaled to the children that it was a greater-than-five condition and the black digit pairs indicated that it was an odd–even condition. Each column is composed of three-set shifts between greater-than-five and odd–even conditions (see Fig.  1 F). The number pairs were randomly displayed, and four factors were also taken into consideration: (1) a counterbalance of the correct answer on the side in each column, (2) different numbers in subsequent or neighboring number pairs, (3) no more than three consecutive correct answers showing on the same side, and (4) no similar or inverse number pairs (e.g., 5 2 vs. 2 5) presenting in the same row or column. All children were instructed to decide which red digit is greater than five and which black digit is odd or even as accurately and quickly as possible within 3 min. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 36. The KR-20 reliability coefficient of this test was 0.95.

The number sets test

The number sets test was used to assess mathematical abilities in young children [ 64 ]. The number sets test is composed of 32 items with 16 items for each target number: “five” and “nine.” Each item contained a pair or trio of Arabic numbers with an 18-point font in a half-inch square, object sets (stars, circles, diamonds, and triangles) in a half-inch square, or both of them, and the Arabic numbers and object sets were combined to create domino-like rectangles (see Fig.  1 G and further details in a previous study [ 61 ]). All children were instructed to circle any groups that can be put together to make the number at the top of the page, which could be 5 or 9, and to complete as quickly as possible within 2 and 3 min for the targets “5” and “9”, respectively. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 16 for the targets “5” and “9” and between 0 and 32 for both targets. The KR-20 reliability coefficient for the targets “5” and “9” were 0.94 and 0.95 and 0.96 for both targets.

The numerical operation test

The numerical operation test was adapted and used to assess children’s storage and manipulation of numerical operations [ 75 , 76 ]. This test was also called “arithmetic facts” in the literature, but it included only addition and subtraction in basic forms. The test items were reviewed, and all items were consistent with education and curriculum in preschool and primary school levels. The numerical operation test is composed of 20 items: 8 items for single-digit numerical operations and 12 items for double-digit numerical operations. The 20 items of numerical operations were shown in four columns in 22-point Times New Roman font for each column (see Fig.  1 H). All children were only asked to write down the answer as the outcome of numerical operations such as adding and carrying. A response was scored as correct (1 point) and incorrect (0 point) with a range of scores between 0 and 20. The KR-20 reliability coefficient of this test was 0.95.

Statistical analysis

MANOVA was used to evaluate the age group differences between preschool (6 years old) and primary school (7 years old) children across eight dependent variables to answer the research questions and test the research hypotheses. The partial η 2 was also calculated to represent the magnitude of difference between groups [ 77 , 78 ]. The first latent variable for domain-specific early mathematics was obtained from four observed variables, that is, dot-dot, dot-number, number comparison, and mental number line, and the second latent variable for number-specific EFs was generated from two observed variables, namely numerical inhibition and shifting, in measurement and structural models. The third variable for the mathematical abilities was also derived from two observed variables, that is, the number sets and the numerical operation. Finally, the direct paths among the first latent variable, the second latent variable, and the third latent variable were estimated.

No missing value was found for the current study. Data analyses were carried out using IBM SPSS statistics for Window, version 26 (IBM Corp., Armonk, NY, USA) and SPSS Amos version 26.0 [ 79 , 80 , 81 ]. The structural equation model (SEM) parameters were estimated by using the maximum likelihood procedure. The goodness-of-fit indices of the estimated models were evaluated using five indicators, that is, the p value of chi-square ( χ 2 ) above 0.05 and χ 2 / df smaller than 3 are preferred, the p value of root mean square error of approximation (RMSEA) lower than 0.07 indicates a well-fitting model, the comparative fit index (CFI), the goodness of fit index (GFI), and the adjusted GFI; the values over 0.90 suggest a good fit [ 82 , 83 ]. The models for the overall pooled, 6-year-old, and 7-year-old children supported the empirical data and provided good model fits, the p values of χ 2  = 0.93, 0.05, and 0.57; χ 2 / df  = 0.93, 1.97, and 0.83; RMSEA =  < 0.05, 0.06, and < 0.01; CFI = 1.00, 0.99, and 1.00; GFI = 1.00, 0.98, and 0.99; Adjusted GFI = 0.98, 0.93, and 0.97, respectively.

Descriptive statistics, group difference, and correlation coefficients among variables

Table 2 shows the domain-specific early mathematics represented by four variables, that is, dot-dot, dot-number, number comparison, and mental number line. The number-specific EFs were indexed by two variables, namely, numerical inhibition and shifting. The mathematical abilities were also represented by two variables, that is, the number sets and the numerical operation. In general, the domain-specific early mathematics of 6-year-old children was significantly lower than that of 7-year-old children, but it was clearly shown for the number comparison test that the 6-year-old children had a lower score on the number comparison test with a large effect size than that of the 7-year-old children. Similarly, the number-specific EFs for 7-year-old children were higher; however, the effect sizes for all variables in the number-specific EFs between two age groups were moderate. The mathematical abilities were better for 7-year-old children, and a strong effect size was observed.

The coefficient alpha ( α ) for all measures was generally excellent ( α  ≥ 0.90), but it was only acceptable for the mental numbe line test ( α  = 0.76). All variables were normally distributed, as measured by skewness and kurtosis (see Table 2 ). Table 3 shows the correlation coefficients among variables representing the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities for the overall pooled children ( N  = 505) broadly demonstrating a moderate relationship, that is, the correlations between variables in the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities ranged from − 0.43 to 0.64 for the number sets. Table 4 shows a moderate correlation between variables reflecting the domain-specific early mathematics, and the number-specific EFs and the number sets (− 0.30 to 0.51) and the numerical operation (− 0.31 to 0.51) were observed for 6-year-old children. A weak-to-moderate connection, on the other hand, was identified between variables indexing domain-specific early mathematics and number-specific EFs and the number sets (0.34 to 0.54) and the numerical operation (0.29 to 0.51) for 7-year-old children. The multicollinearity tests were performed using the value inflation factor (VIF), and all VIF scores for pooled children, for 6-year-old children, and for 7-year-old children were less than the threshold of 5, indicating that the multicollinearity is not a problem in current datasets [ 83 ].

SEM analyses to test the relationship among 6-year-old children (n = 238), 7-year-old children (n = 267), and the overall pooled children (N = 505)

For the SEM model of 6-year old children, the dot-dot, dot-number, and number comparison tests exerted comparable effects ( β  = 0.85, p  < 0.01; β  = 0.85, p  < 0.01; β  = 0.80, p  < 0.01, respectively) on the domain-specific early mathematics, but the mental number line showed the lowest factor loading ( β  =  − 0.30, p  < 0.01) on the given latent variable. Further, the numercal Stroop and the numerical shifting tests also showed similar effects ( β  = 0.79, p  < 0.01; β  = 0.75, p  < 0.01, respectively) on the number-specific EFs latent variable. Both latent variables significantly and positively related ( β  = 0.67, p  < 0.01; β  = 0.69, p  < 0.01) to the mathematical abilities factor as measured by the number sets and the numerical operation tests.

For the SEM model of 7-year old children, the number comparison test showed the strongest factor loading on the domain-specific early mathematics ( β  = 0.94, p  < 0.01), followed by the dot-number comparison ( β  = 0.67, p  < 0.01), and the dot-dot comparison tests ( β  = 0.51, p  < 0.01), respectively. However, the mental number line demonstrated the lowest factor loading ( β  =  − 0.37, p  < 0.01) on the given latent variable in comparison to other factor loadings in measurement model. Hence, the numerical inhibition and shifting showed comparable effects ( β  = 0.67, p  < 0.01; β  = 0.62 , p  < 0.01, respectively) on the number-specific EFs latent variable. Both latent variables also significantly and positively related ( β  = 0.76, p  < 0.01; β  = 0.77 , p  < 0.01) to the mathematical abilities factor as measured by the number sets and the numerical operation tests.

For the SEM model of the overall pooled children, the number comparison test showed the strongest factor loading ( β  = 0.97, p  < . 01) on the domain-specific early mathematics, followed by the dot-number comparison ( β  = 0.71, p  < 0.01), and the dot-dot comparison tests ( β  = 0.67, p  < 0.01), respectively. Nonetheless, the mental number line showed the weakest factor loading on the given latent variable ( β  =  − 0.41, p  < 0.01). Hence, the numerical inhibition and shifting showed comparable effects ( β  = 0.79, p  < 0.01; β  = 0.74, p  < 0.01) on the number-specific EFs latent variable. Both latent variables also significantly and positively related ( β  = 0.81, p  < 0.01; β  = 0.77, p  < 0.01) to the mathematical abilities factor as measured by the number sets and the numerical operation tests (see Fig.  2 ).

The relationships among the domain-specific early mathematics, the number-specific EF, and the mathematical abilities. Separate parameters of different age groups (6-year-old/ 7-year-old/6-and-7-year-old) and standardized coefficients ( β s) are reported. Note ** p  < .01

The current study aims to compare and examine the effects of the domain-specific early mathematics and the number-specific EFs on the mathematical abilities in a sample of 6- and 7-year-old children. Analyses were first carried out to test the age group differences across eight dependent variables and to examine the relationships between two latent variables (i.e., the domain-specific early mathematics and the number-specific EFs) and the latent mathematical abilities in a sample of 6- and 7-year-old children.

It can be inferred from the current results that 6- and 7-year-old children (informal schooling and formal schooling) were evident on the number comparison, the number sets, and the numerical operation differences. The finding in itself shows an integrative role of numerical development among numerical comparison, storage, and manipulation abilities on mathematical achievement from preschool to primary school students [ 75 ]. The distinctive competency for the number comparison, the numerical operation, and the number sets between two age groups also suggests numerical and developmental acquisitions from understanding precise magnitudes of nonsymbolic numbers, relating nonsymbolic to a foundation of symbolic numerical representations in six-year-olds [ 84 ], to expanding understanding the small symbolic numbers to larger whole numbers (i.e., single and double digits) in 7-year-olds [ 16 ].

The dot-dot and dot-number comparison tests were used to examine the process of attributing numerical magnitude to nonsymbolic numbers in both age groups. The effect sizes of both tests were somewhat small despite the significant differences between the two age groups on both dot-dot and dot-number observed in Table 2 . It is plausible that ANS acuity, nonsymbolic, and basic symbolic numerical knowledge fully reach the developmental milestone on numerical competence at younger ages [ 85 ]. This follows previous findings that demonstrated the specific effects of ANS acuity and mapping precision between numeral notations and their corresponding magnitudes that are dominant only in preschool children [ 86 ]. The performance on the mental number line test significantly differed between 6- and 7-year-old children but the extent of discrepancy was small following the literature. However, the performance in the mental number line test explained a relatively small amount of variance in the SEM model compared to the numerical comparison tasks. Although young children can count objects and understand relationships between objects and cardinal numbers, the number line further requires an understanding of lengths between the numbers written below the intervals on the number line. Thus, the number line seems to be a difficult tool to master for children who are younger than 7 and 8 years [ 87 ].

There is still a lack of agreement on the relative importance of domain-specific precursors in the development of mathematical abilities [ 76 ]. The unique contribution of the present SEM findings is the differential associations between specific indicators of the domain-specific early mathematics and the number-specific EFs and the mathematical abilities from kindergarten through primary school. The importance of subitizing, approximation, and comparison as indexed by the dot-dot and dot-number comparison tests for mathematical abilities decreased as preschool children progressed through formal schooling. Nonetheless, the symbolic and exact understanding of numerical concepts as measured by the number comparison and the mental number line tests was prioritized for the mathematical abilities with successive grades. Furthermore, the mathematical abilities were more dependent on both the domain-specific early mathematics (0.67 vs. 0.76) and the number-specific EFs (0.69 vs. 0.77) in older children. The mathematical problems will call upon a crucial process of detecting and assessing critical features of number sense [ 61 ] and involving inhibition and shifting of information [ 88 ]. A strong influence of both the domain-specific early mathematics and the number-specific EFs in older children may reflect the increasingly demanding role of shifting and inhibition capacities with age (e.g., [ 40 , 89 ]).

Another main finding is that the relative importance of the domain-specific early mathematics and the number-specific EFs that are similar in size in relation to the mathematical abilities of 6-year-old children. However, the number-specific EFs showed a stronger relationship with mathematical abilities than the domain-specific early mathematics for 7-year-old children. Indeed, children are required to map and combine the different Arabic numerals and symbols onto the corresponding quantities and then compare them with the target number of each item to master mathematical competencies as measured by the number sets and the numerical operation tests. Although the present study supports the previous findings that quantity representation or ability to map quantities and magnitudes with symbols was associated with the mathematical abilities (e.g., 1, 86, 91), our results highlight the stronger association among the domain-specific early mathematics, the EFs in a numerical context, and the mathematical abilities at the beginning of formal schooling. The older children may learn school-taught mathematics, providing them with knowledge on symbol systems and procedural tools. Accordingly, to achieve mathematical calculations, the performances of EFs in a numerical context were improved in older children.

Furthermore, a more efficient supporting system or the EFs may be required to encourage the acquisition of existing early mathematical abilities and arithmetical capabilities with cumulative knowledge of symbol systems and strategy choices and discoveries in older children [ 90 , 91 ]. In this view, apart from better knowledge on domain-specific early mathematics, primary school children have to rely directly on the EF subcomponents to some extent. In this case, solving mathematical problems allows the child to select relevant information or strategies, inhibiting numerical information already processed but no longer relevant. Cognitive flexibility also allows the child to switch from one strategy to another, transforming or substituting the no-longer relevant information with a new one [ 92 , 93 , 94 ].

Nonetheless, this study also possesses several noteworthy limitations. Given the strong link between working memory and IQ, although no children with LD and ADHD were found, the present study lacks control over children’s IQ scores. Accordingly, a cautious interpretation of the finding must be considered. In addition, working memory was found to be the second EF component to emerges, after inhibitory ability and before shifting ability, during preschool ages and it is also regarded as a tool of learning (e.g., [ 96 , 97 ]). Specifically, a weakness in working memory has been documented in children with dyscalculia (e.g., [ 98 , 99 ]). Thus, further study should investigate working memory as an EF component in numerical domain.

Moreover, the weak correlation among the mental number line and other variables in the same construct may additionally stem from the issues of the test format and the scoring method. A further limitation of this study is that children could have made their comparisons on the basis of continuous extent rather than the number for nonsymbolic stimuli [ 95 , 96 ]. Future work needs to consider this stimulus issue for children at this young age.

For practice reasons and practices, the paper-and-pencil based tests were suitable for our settings in terms of distribution and administration of the tests. However, the response time could reflect the automatization during numerical processing of both mathematical and executive functioning skills of the young age [ 99 ]. Thus, the selection of the computerized version of these mathematical cognition tasks should also be considered for further studies because the computer-based tasks may offer several sophisticated parameters (e.g., response accuracy, response time, and difference scores), standardized test administration procedures, automatic scoring, and instant feedback for children and teachers [ 97 , 98 , 99 , 100 ].

The current study did not compare the relative effects of the domain-specific early mathematics, the number-specific EFs, and the general EFs on mathematical abilities. Further studies should specifically compare common and unique roles of domain-general vs. domain-specific EF on mathematical development. The present findings provide a strong motivation to delineate these factors. Finally, a longitudinal study is needed to support the current findings in regards to the differential effects of the domain-specific early mathematics and the number-specific EFs on the mathematical abilities.

The present study yielded two key findings. First, 7-year-old children outperformed 6-year-old children in the overall measures of the domain-specific early mathematics and the number-specific EFs, especially for more sophisticated numerical knowledge and EF subcomponents, namely, symbolic numerical magnitude representations as indexed by the number comparison and the mental number line tests and the numerical inhibitory and shifting abilities as measured by the numerical inhibition and shifting tests. Second, both the domain-specific early mathematics and the number-specific EFs comparably and significantly related to the mathematical abilities for 6- and 7-year-old children, but the domain-specific early mathematics and the number-specific EFs were dominant concerning the mathematical abilities for 7-year-old children.

Availability of data and materials

The dataset for the current study is available from the corresponding author on reasonable request.

Abbreviations

Approximate Number System

Executive Functions

Learning Difficulties

Attention Deficit Hypoeractivity Disorder

Percent Absolute Error

Multiple Analysis of Variance

Structural Equation Modeling

Goodness of Fit Index

Value Inflation Factor

Long-Term Memory

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Acknowledgements

This work is part of the project entitled ‘A neuropsychological investigation and development of a cognitive-based screening tool in children at risk of mathematical learning disability’ and was supported by National Research Council of Thailand (NRCT54/2550) and Newton Mobility Grant 2017 RD1 (NG170110).

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Wongupparaj, P., Kadosh, R.C. Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling. BMC Psychol 10 , 27 (2022). https://doi.org/10.1186/s40359-022-00740-9

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Developing numeracy skills using interactive technology in a play-based learning environment

• Tess Miller   ORCID: orcid.org/0000-0001-6984-9326 1  

International Journal of STEM Education volume  5 , Article number:  39 ( 2018 ) Cite this article

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The purpose of this study was to measure the impact of interactive technology in the form of mathematical applications (apps) delivered using iPads on kindergarten children’s learning of number sense in a play-based learning environment. Secondly, factors influencing the use of interactive technology in a play-based environment were examined. This technology was introduced to a small ( n  = 13) rural kindergarten classroom using an experimental design embedded in a mixed methods approach.

The teacher was keen to introduce technology to her class but was self-described as a beginner in using iPads for personal or teaching tasks. Small gains were noted between the control and intervention groups but they were not significant. Further, children were observed collaborating which supported prior research. Another observation was related to attention span, when an app became too challenging children would abandon the app or use a trial and error method to move to the next level. Lastly, when given choice, children were drawn to creative and entertaining apps rather than apps that were more pedagogically accurate but less creative. Although there was not a large gain in achievement, using interactive technology promoted student collaboration and engagement in a play-based learning environment.

Conclusions

Small gains in mathematics achievement and high levels of engagement suggest that using interactive technology in the kindergarten classroom enhances learning of mathematics. Factors influencing the use of interactive technology included the quality of the app such that creative and fun apps promoted children’s engagement in learning mathematics. The level of difficulty of an app was a second factor influencing children’s use of interactive technology. If the difficulty level was too challenging, children became disengaged with the app.

In the next era of technological advancements, we can only envision futuristic developments such as no-touch interfaces and sensors that read and predict our movements (Loganathan 2013 ). However, for the current generation, we are enjoying the developments in technology that have focused on interactive tablets among a host of other interactive gadgets currently on the market. The intuitive design of iPads positions them for use in educational settings, including early years classrooms (Warmoth 2013 ). Their design was built on mental models of how we perceive an experience (Weinschenk 2011 ). For example, when reading a book, we turn pages by using the index finger to flip to the next page. This method of turning pages has been modeled on the iPad where the user also uses his/her index finger to flip to the next page. Interacting with an iPad in this manner facilitates data flow through the interface (i.e., what the user sees on the screen) linking the user and technology and is referred to as interactive technology (Large 2016 ). Page flipping and other interactive features (e.g., voice recognition) on an iPad make using this form of technology simple or intuitive even for the youngest of learners.

The introduction of iPads into early learning classrooms has revealed gains in student achievement (Bebell et al. 2012 ); however, measuring gains in achievement should not be the sole factor determining the merit of interactive technology. Leveraging student engagement in a discipline like mathematics also makes iPads a worthy investment for the classroom given that they can be used to gather information, read a book, take photos, record physical activity, make artistic drawings, and learn about literacy or numeracy through the use of stimulating and creative applications (apps). Given the abundance of apps currently available, examples of how iPads can be used to engage children and promote learning is much larger than what is posited here. In the next era of educational technology, we need to think of the iPad as a manipulative that children can choose from a host of other manipulatives to discover new concepts.

The purpose of this study is to measure the impact of interactive technology in the form of mathematical applications delivered using iPads on kindergarten children’s learning of numeracy in a play-based learning environment (Fesseha and Pyle 2016 ). In particular, numeracy concepts were focused on the number-sense strand (Department of Education, Early Learning and Culture of PE 2008 ). Secondly, factors influencing the use of interactive technology in a play-based environment were examined. The research questions posed in this study are as follows: To what extent does the use of mathematical apps using iPads enhance children’s learning of numeracy in kindergarten? What factors influence children’s use of interactive technology in a play-based learning environment?

Considering the relatively short evolution of iPads that were introduced in 2010 with Apple’s launch of iPad 1 (Ritchie 2014 ), a significant body of literature has been published on the use of iPads in education, building on literature reporting on the use of desktop computers in education. In a systematic review of what the authors described as mobile learning, Crompton et al. ( 2017 ) reviewed 113 studies of which four were at the pre- or kindergarten levels and these four studies were conducted in 2014 and 2015 suggesting interactive technology was slowly making its way into the early grades. Unfortunately, these authors did not cross list their review to identify the subject domains the four studies were conducted in.

Of the research focusing on technology in early learning, studies focused on children and teachers’ perceptions of technology (Knezek and Christensen 2002 ; Tsitouridou and Vryzas 2003 ) as well as the use of technology in literacy development (e.g., Chiong and Shuler 2010 ; Flewitt et al. 2015 ; Primavera et al. 2001 ). Fewer studies have been in the area of numeracy (Clements and Sarama 2007 ). This literature review begins with teachers’ perceptions towards using technology given that teachers’ comfort with technology, including the teacher in this study, has been shown to impact the use of technology in the classroom (Simon et al. 2013 ). The second part of this literature review focuses on literature exploring the effective use of iPads in the area of literacy and numeracy. This review concludes with a look at studies that advocated against the use of technology in early learning.

Teachers’ perceptions towards using technology

For many preschool teachers, their use of technology is less than teachers in higher grades and was limited to downloading images for instructional purposes and digital cameras (Public Broadcasting Service and Grunwald Associates 2009 , 2011 ). This absence of technological integration into early years classrooms is most likely due to limited opportunities for professional development on interactive technology as well as the lack of technology itself. Hence, to advance interactive technology in early years classrooms, it is important to recognize that teachers need professional development on the appropriate use of technology in the classroom (Simon et al. 2013 ), as well as opportunities to acquire technology. In a case study of four kindergarten teachers by Lu et al. ( 2017 ), teachers’ experiences using iPads in a literacy context was also found to be beneficial as it allowed teachers to meet the demands of creating individual assessments or work on lesson preparation as the iPads “functioned like an extra teaching assistant, providing feedback to students” (Lu et al. 2017 , p.19).

Studies employing interactive technology in the form of tablets reported improved motivation, supported learning in small groups, and independent work as well as gains in vocabulary and phonological awareness (Dobler 2012 ; Hutchison et al. 2012 ; Flewitt et al. 2015 ; Hutchison and Reinking 2011 ; Simon et al. 2013 ; Takac et al. 2015 ). For example, Simon et al. ( 2013 ) concluded that tablets in addition to desktop computers supported learning in small groups or individually. These researchers also noted a tendency for longer periods of use especially when children had choice in their activity. Similarly, Flewitt et al. ( 2015 ) introduced iPads in early learning for the purpose of literacy development, which included writing and video recording of stories for sharing with the class. One iPad was given to a classroom with 3- and 4-year-olds and another iPad to a class of 4- and 5-year-olds for 2 months. Each iPad contained a story-creation app as well as a number of other learning apps. Training was provided to both instructors and data collection consisted of surveys, observations, and conversations. These researchers reported increased motivation and use of iPads. This was especially noted among children who were not easily engaged in traditional writing tasks. Further, the touch screen interface was reported to be easier than a keyboard. Similar to findings reported by Simon et al. ( 2013 ), the iPads fostered small group and independent learning. At the same time, children were observed helping each other use the iPads which is aligned with the findings from Shifflet et al. ( 2012 ) who reported that pre-school children using tablets developed a collaborative approach to learning which enhanced their social skills.

In terms of academic gains, an experimental study revealed that kindergarten children in both the control and experimental groups (i.e., with iPads) showed gains as measured using the Rigby Benchmark Assessment and the Children’s Progress Academic Assessment but the differences between groups were not statistically significant (Bebell et al. 2012 ). However, on a third measure, the Observation Survey of Early Literacy Achievement assessment, a statistically significant difference in phonemic awareness was reported where children in the iPad group scored higher (Bebell et al. 2012 ). Based on this study, the introduction of iPads in early learning did not appear to hinder learning, and in some areas of literacy, they enhanced children’s understanding of the discipline.

Of the studies that examined early learning of mathematics using tablets, most studies reported gains in achievement or positive experiences (Alade et al. 2016 ; Dejonckheere et al. 2015 ; Hubber et al. 2016 ; Hung et al. 2015 ; Kosko and Ferdig 2016 ; Mattoon et al. 2015 ; Outhwaite et al. 2017 ; Presser et al. ( 2015 ); Reeves et al. 2017 ; Stubbe et al. 2016 ). However, Bebell and Pedulla’s ( 2015 ) longitudinal study examining the impact of mathematics apps on achievement in grades kindergarten (K) to 2 did not reveal any consistent gains. Despite different outcomes, each of these studies dispelled the argument that iPads and other digital manipulatives were not edutainment but rather effective learning aids (Baird and Henninger 2011 ).

A few studies narrowed their focus to a small number of apps or a specific mathematical skill, which provided insight on the connection between the app and student gains for young children. For example, Reeves et al. ( 2017 ) selected apps that focused on skills related to counting, sequencing, and early addition. In each area of skill development, gains were reported. Dejonckheere et al. ( 2015 ) also focused on a specific skill and reported a gain in achievement. These researchers used tablets to allow 4- to 6-year-olds to play on a digital number line exploring concepts related to estimation. This focus on one numeracy concept applying different strategies for estimation revealed a significant gain in accuracy of estimation for the two groups that were given strategies but not for the control group. Likewise, Presser et al. ( 2015 ) focused on skills related to subitizing (recognizing how many in a set without counting) and equi-partitioning (splitting an area or set into equal groups) using an app known as Next Generation Preschool . Gains in numeracy skills were also reported in their study.

Along the same focus, Kosko and Ferdig ( 2016 ) examined gains in achievement but approached their study from the perspective of selecting apps that were pedagogically accurate and aligned with curriculum. These researchers reported that well-designed mathematics apps improved achievement and concluded that well-designed mathematics apps can support student learning but more research was needed to explore the extent to which these apps improved learning. Given the number of mathematics apps available on the iPad, it is particularly important to consider characteristics of mathematics apps to better understand the impact, if any, an app has on student learning. Further, neither of these studies centered on a play-based learning environment that allowed for flexible and creative use of time and space or provided choice in selecting an app (Steglin 2005 ). Hence, the characteristics of apps that attracted children are largely unknown.

Advocates against interactive technology

Although Dinehart ( 2015 ) was an advocate against the use of technology in early learning, citing that it diminished children’s fine motor skills, she did not consider apps designed for early childhood education that fostered fine motor skills through writing letters and numbers. Other concerns against the use of technology in early learning focused on the amount of time spent viewing screens. Vanderloo ( 2014 ) reported that children between 4 and 7 years of age spent an average 1.5 to 7.0 h viewing screens each day. Unfortunately, there was no differentiation between viewing screens for different activities such as watching a movie, watching a lesson on the interactive whiteboard, or playing games on an iPad (Vanderloo 2014 ). The sedentary nature of viewing screens was the catalyst for Vanderloo’s work, which is undoubtedly a concern; however, moderation of screen viewing may better guide the use of technology in early learning rather than banning it all together. This position is more aligned with the National Association for Education of Young Children ( 2012 ) who differentiated between screen viewing for interactive activities (e.g., mathematical apps) and non-interactive activities (e.g., movies) to promote active learning using technology.

When drawing on the literature presented above, it is reasonable to conclude that young children experienced gains when using iPads to learn about literacy and numeracy, and in one study, gains were long term (Outhwaite et al. 2017 ). When these gains were compared to a control group, the gains were not always statistically significant. Concerns related to excessive screen viewing were tempered by differentiating between interactive learning versus non-interactive learning. Since most studies narrowed their focus to a few mathematical apps, there is much to learn about the characteristics of apps that children gravitate towards when left to their own accord in a play-based learning environment.

Theoretical framework

The Technological Pedagogical Content Knowledge (TPACK) framework was utilized to explore the implications of using mathematical apps installed on iPads in an early learning context. Integrating technology to enhance learning requires knowledge related to the subject content (i.e., numeracy), pedagogy, and technology (Mishra and Koehler 2006 ). Based on the TPACK framework, technology can be successfully integrated into learning when these three domains are successfully woven together. Hence, when apps were selected for this study on early numeracy concepts, the pedagogy had to be aligned with children’s level of cognitive development, and at the same time, the technology had to be simple and intuitive so that kindergarten children could be successful using it.

This research also builds on Naismith et al.’s ( 2004 ) theories in identifying six theory-based categories of activities for interactive technology: behaviorist, constructivist, situated, collaborative, internal and lifelong, and learning and teaching support. These researchers described behaviorist activities as those that primarily aim to change behavior through reinforcement of a stimulus such as feedback. For example, when a student responds correctly to a mathematics question, a pleasing sound or an animated character may appear in an app designed for kindergarten level students. In contrast, constructivist activities were described as activities that call on the student to apply what they know to new contexts and build new learning. The game, Environmental Detectives , was created for high school students who engage in the game as environmental engineers tasked with solving a problem is an example of a constructist activity/game. For a younger audience, Minecraft is similar in that students create and manipulate objects and engage in a task. When selecting apps for this study, there were no constructivist activities/games for the iPads that were aimed at the early learner.

In returning the focus to the theory-based categories, the remaining four theory-based categories of activities/games for interactive devices involved a higher cognitive engagement and advanced interactive software, which is appropriate for students in the senior grades. Subsequently, interactive activities designed for early learners appears to be founded on the behaviorist theory-based category which is similar to the finding in Bray and Tangney’s ( 2017 ) systematic review of literature focused on using technology in mathematics education. These researchers identified a wide range of technologies being used in different contexts within the middle and senior mathematics classrooms with a predominance of constructivist and social constructivist tasks. Such tasks appear to be aligned with higher grade levels where the curriculum calls for higher levels of inquiry-based, student-centered, and collaborative approaches to learning mathematics leaving the behaviorist types of activities/games for the younger students.

This study was implemented in a small rural Canadian primary school. The kindergarten teacher selected to be involved in the study was a veteran teacher with over 20 years of early years teaching experience. Although the teacher was not fluent with iPad technology, she was keen to learn and introduce the technology to her classroom. Funds to purchase four iPads with protective childproof cases and glass screen protectors, apps, stylus, and child safe headsets (control the volume such that the sound does not increase above 85 dB) were obtained through a small university grant. The agreement between the researcher and the primary school allowed the iPads and supporting technology to remain a property of the kindergarten class. Ethics permission was obtained through the university research ethics board as well as the local school board ethics authority.

A mixed methods design was applied using qualitative and quantitative data to explore the impact of mathematical apps on the learning of numeracy skills and the factors influencing the use of this technology in an early years setting. The qualitative data included field notes documenting conversations during the training session with the kindergarten teacher as well as observation notes of students using iPads. The experimental component provided the quantitative data. In this aspect of the study, the quantitative measures were the pre- and post-test measures for the experimental and control groups. The rationale for choosing a mixed methods design was to provide a wider perspectives of the context of using interactive technology in an early years setting as well as to have greater understanding of the research questions posed in this study (Johnson and Onwuegbuzie 2004 ; Almalki 2016 ). A mixed methods approach allows the researcher to compensate for the fundamental weaknesses that are associated with using only a quantitative or qualitative study (Almalki 2016 ).

Study design

The participating kindergarten teacher was selected for this study because she had demonstrated excellent knowledge about teaching mathematics to kindergarten children and was keen to engage in a research project. Prior to commencing the study, four iPads with several language arts and mathematics apps that were aligned with the curriculum were selected in collaboration with the teacher and researcher. The researcher and teacher met three times prior to commencing the study to select and experiment with the apps.

One week prior to commencing the study, one iPad was placed at each play station for approximately 20 min each day for 1 week. Children had the choice of using the iPads without receiving guided instructions. This pre-exposure to the iPads was intended to remove any novelty effects that might influence a gain in numeracy skills (Gravetter and Forzano 2011 ).

In the experimental phase, 13 children in the kindergarten class, aged four and five, were randomly selected to one of two groups. One group received a 2-week intervention involving the use of iPads to learn numeracy concepts each day and the other group followed the traditional play-based learning activities that focused on numeracy development, in particular, concepts of number sense. In a conversation with the teacher, she believed that students would be able to master the outcomes being learned in the 2-week period.

Children’s mathematical skills from both groups were measured at the beginning of the study (time 1) with 30 items that were aligned with the curriculum being taught and again following the 10-day intervention period (time 2). At the conclusion of the study, the control group was introduced to the iPads in the same manner as the experimental group (i.e., 10 days) for the purpose of ensuring equal opportunity to engage with the iPads.

The intervention consisted of using interactive technology in a play-based mathematics classroom in lieu of the teachers’ originally planned play-based lessons. A teacher-trained, research assistant removed Group 1 children to another classroom during the time designated for learning mathematics, which was approximately 20 min each day. This group of children was introduced to various mathematical apps while the control group, Group 2, children followed the play-based activities that fostered the same skill development that was in the apps. For example, one of the apps fostered the development of writing numerals and a play-based activity required students to trace numerals.

The intervention began using 10 apps for the first week and then a new app was introduced each day thereafter for a total of 15 apps. Children would receive instruction on how to use a particular app at the start of the lesson followed by time to play with the app. In the second part of the lesson, children could choose whatever app they preferred for the remainder of the lesson. The apps were downloaded from the Apple Store for free or for a nominal fee. The app icons used in this study are shown in Fig.  1 .

Apps used in study

Table  1 , below, summarizes the types of skill development in each of the apps.

The items used to measure children’s mathematics ability in the pre- and post-tests were created based on the concepts taught in the classroom, which were aligned with the curriculum outcomes as previously noted. A map of the curriculum outcome and corresponding items is shown in Table 4 in the Appendix . These items were modeled from the exemplars provided in the provincial curriculum document and in consultation with the teacher (Department of Education, Early Learning and Culture of PE 2008 ).

Data collection

Data in the form of children’s numeracy test scores was collected using an application called Explain Everything. This application is an interactive screen-casting whiteboard, which stored the test items and recorded children’s responses to each item. To capture children’s responses, the examiner would orally read instructions that were printed on the bottom of each test page and then the child would respond by speaking, writing, or manipulating objects on the screen; all of which were captured using Explain Everything simultaneous video and audio recording feature known as screen casting. Figure  2 shows an original test item as presented in Explain Everything and how a student manipulated the objects on the screen (on the right) to demonstrate their understanding.

Original test item and test item after answered by student

The researcher and a research assistant independently scored each child’s test by reviewing each screen-cast. When the scores did not match, we discussed our responses and agreed on a score. Each item was scored based on a 4-point rubric: (1) Do not know or responded incorrectly, (2) demonstrated some understanding of the concept but response was not correct, (3) provided a correct response but the strategy was not strategic or efficient, and (4) provided a correct response that was efficient. An example of a level 2 response would be a number written backwards or upside down and an example of a level 3 response is writing the number seven starting from the bottom and moving to the top (i.e., drawing the number from the finish position to the start position). The kindergarten teacher reviewed and agreed with the 4-point rubric. In the sample response shown in Fig.  2 , the child would receive a 4 for the first answer (i.e., 5) but a 3 for the second answer because the child orally indicated the set containing six elements but they had difficulty writing the digit 6.

The pre-test at time 1 and post-test at time 2 contained the same items except that the colors or the shape of objects were changed. Prior to implementing the study, the test was piloted with three children from another school and reviewed by the kindergarten teacher. Small changes to the printed instructions on each slide were made to better align the vocabulary with children’s understanding.

During the experimental phase, the research assistants recorded field notes documenting children’s behaviors and the apps that were most favored. Children’s feedback on what they liked about the apps (i.e., the characteristics of the apps) and other observations were also documented.

Mean scores were calculated for both groups on the pre-test. Due to the small sample size, it was not possible to conduct the stringent inferential analysis of covariance; therefore, group difference scores were analyzed. The observational field notes were conceptually analyzed to determine the presence of common words or phrases to make inferences about the observations. The coding began with predefined categories such as collaboration, level of engagement, and choice of apps but was flexible to allow for the addition of other unanticipated themes.

Cronbach’s alpha was used to measure the internal consistency of the scale. After removing poor performing items due to poor discrimination, 22 items remained. The items that discriminated poorly were due to all students receiving the top score on the item; subsequently, there was no discrimination between ability. Easy items were purposefully included on the assessment to ease students into the testing; hence, it was expected that a number of items would be removed from the test due to poor discrimination. Cronbach’s alpha for the remaining 22-item scale on the pre-test was 0.803 and 0.805 for the post-test. Thus, the coefficient exceeded the absolute minimum threshold of 0.7 but also met the ideal minimum threshold of 0.8 (Tabachnick and Fidell 2012 ), indicating a reliable set of test items.

Descriptive summary of items

Group 1 consisted of four females and three males, and group 2 had two females and four males. All children were 4 or 5 years old. Items ranged in difficulty with the hardest being items 1.7b (write the number 6; M  = 2.46, SD  = 1.27), 1.7c (write the number 5; M  = 2.92, SD  = 1.19), and 1.2h (recognize seven dots on a 10 frame; M  = 2.92, SD  = 0.28). Easier items were 1.4b (create a set of 7; M  = 3.77, SD  = 0.83), 1.7k (count backwards from 5; M  = 3.67, SD  = 0.89), 2.1d (identify repeating and non-repeating patterns; M  = 3.54, SD  = 1.13), 1.2a (identify 3 on a die, M  = 3.54, SD  = 0.52), and 1.2b (identify 4 on a die, M  = 3.54, SD  = 0.52).

Given that four out of 10 apps involved drawing numbers, an increase in this skill was anticipated from the pre- to the post-test. However, of the two items assessing drawing numbers, only one item (i.e., 1.7b drawing the number 6) revealed a significant increase from M  = 2.86 and SD  = 1.46 to M  = 3.29 and SD  = 1.25, following the intervention.

When comparing mean scores, the experimental and control group differed by 0.01 on the pre-test (see Table  2 ). After the intervention, the experimental group increased slightly (+ 0.02) and the control group decreased slightly (− 0.04). On the post-test, the two groups differed by 0.05 with the experimental group having the higher mean score (see Table  2 ). These differences are too small to suggest the intervention had any effect on students’ mathematics ability.

Observational findings

All children were keen to use the iPads over the 10 days of mathematics lessons as they asked the teacher each day when the research team was arriving so that they could use the iPads. During the introduction to a new app phase at the beginning of each guided mathematics lesson, where the children were shown how to use an app (if they needed help), children did not use a headset so that they could hear the instructions (volume was turned down on the ipads). During this guided instruction, children were more apt to collaborate with each other to share what was on their screens and provide help to get to another level or step. When the children wore a headset, there was a greater tendency for children to focus on their own screen as they were not distracted by sounds coming from other iPads or giggles and exclamations coming from their peers.

The four stronger children in the class (as identified by the teacher and confirmed by the pre-test) appeared to have a better understanding of how to maneuver through different levels in an app whereas the weaker children frequently needed guidance on how to proceed to the next level. Another observation related to levels in an app was the difficulty of the level. When an the app level became too challenging, children would either look to abandon the app or randomly select answers until they eliminated all incorrect responses and identified the correct response. An example of this type of question was the equation 2 + 3 = ? which was supplemented by corresponding dots along with responses of 4, 5, and 6. When we debriefed the teacher about this trial and error process of selecting the correct response, she believed that children were learning more than we were giving them credit for which was encouraging; however, we were still concerned that children may be learning by memorizing rather than having a conceptual understanding of the concept. Another finding related to children’s ability was that stronger children exhibited more independence in using apps. These children were able to use a new app by listening to the audio instructions provided in the app or were confident enough to skip over the audio instructions and starting using the app immediately. In comparison, weaker children frequently needed the research assistant to provide oral instruction as well as provide a demonstration (i.e., model using the app) for new apps.

When drawing numbers, three children would opt to use their index finger to trace the number. Given that children were still developing their fine motor skills, we believed that it was important to encourage children to use a stylus; hence, we encouraged children to use a stylus at all times but particularly when they were drawing numbers.

After every 3 days, children were asked, what was their favorite app? The last app that they played was the most common response, likely because it was the most current in their mind. When prompted further to think about the other apps, the most favored apps were not the most pedagogically structured apps but rather apps that had a lot of bling. For example, children were drawn to apps that had exploding stars when they completed a set of tasks or would see a funny character dance across the screen (e.g., Endless 123). In the same vein, children were quick to move from one app to another. For example, all children quickly grew tired of number drawing and when left to their own choices they would not select apps with this skill development. When debriefing this finding with the teacher she noted that an app tended to have a life expectancy of a few days and then children would become tired with the simplicity of the app unless the app captured their attention with bling. Table  3 displays the app and frequency of children’s preference for the app, which was based on the frequency they choose the app during their structured playtime. This is a holistic measure taking into consideration that there were parts of an app children played frequently, while other parts of the app were ignored. The frequency is also influenced by mathematics ability in that more challenging apps were used less frequently by weaker children.

In terms of the teacher’s experience with the iPads, pre-experiment meetings revealed that she was completely new to using iPads and did not own an iPad of her own. She received instruction on how to (a) access the internet, (b) link the iPads so that apps could be downloaded automatically to more than one device, (c) download apps, (d) organize apps into a folder, and (e) delete apps that were no longer being used or accidentally downloaded. Throughout the study, the teacher would periodically sought assistance for these tasks. Following the study, we met twice to solve problems related to purchasing new apps and simultaneously downloading them to all four devices.

This discussion is framed by the two research questions posed in this study. In addition, other insights garnered in the study are discussed.

To what extent does the use of mathematical apps using iPads enhance children’s learning of numeracy in kindergarten?

Considering the small gains in achievement by the experimental group in comparison to a slight decrease in achievement in the control group, there was no significant difference in children’s understanding of numeracy as measured on the pre- and post-tests between the two groups. Although a difference was anticipated based on prior research, these findings were the same as Mattoon et al. ( 2015 ) who also reported small gains but no significant difference between their two groups in a 6-week long study. Despite the absence of significant gains between the two groups, this study provides evidence that using technology in this context did not deter or lessen children’s development of numeracy skills. This study adds to the work of Bebell et al. ( 2012 ) who reported that iPads do not hinder early learning of literacy. We can now conclude that iPads do not hinder early learning of numeracy as well as literacy. This is an important finding that will broaden the utility of iPads in the early years classroom. In summary, the use of mathematical apps on iPads slightly enhanced children’s learning of mathematics as shown by gains from the pre- to the post-test; however, the gains were not significant between groups.

What factors influence children’s use of interactive technology in a play-based learning environment?

Factors that influenced children’s use of interactive technology focused on (a) collaboration, (b) ability, (c) use of a stylus, (d) maturity, and (e) teachers’ skill level. A factor known to influence children’s use of interactive technology was their affinity for collaboration. Given that prior research documented how technology fostered a collaborative learning environment (Shifflet et al. 2012 ), it was not surprising that children naturally collaborated without any guidance to do so from the researcher. During the introduction phase of a new app, children naturally gravitated towards each other to share what was on their iPad as well as to help each other progress to the next level or game. This affinity for collaboration is an asset to learning mathematics that needs to be supported so that when children leave the play-based learning environment they are still drawn to helping each other with tasks in general but specifically, in the learning of mathematics.

Another observation focused on the impact of children’s prior mathematics ability and experience with apps. No research was found that examined the relationship between children’s mathematics ability and interaction with apps. However, Hung et al. ( 2015 ) reported that when children were challenged, they reported higher levels of engagement and satisfaction. Extending Hung et al.’s ( 2015 ) finding, it appears that children with stronger skills in mathematics were more apt to persevere and be engaged with the app. In contrast, weaker children were more apt to abandon the app or use a trial and error process to progress to the next level, in which case, the quality of their learning was questioned, as learning may be memorized rather than conceptual. Children’s ability level can be connected to attention span since apps that required greater concentration would be met with a shorter attention span. This short attention span appeared to be age appropriate considering the attention span for 4- to 5-year-olds is a maximum 6 to 7 min (i.e., chronological age + 1); although attention span for children playing or being socially engaged can exceed, these maximum times are typically reserved for formal instruction (Wesson 2011 ). Hence, challenging and less creative apps (e.g., Montessori Math) might be perceived more like a formal lesson whereas entertaining and creative apps with bling (e.g., Count-up-to-ten) may be perceived as play.

Further endorsing the need for more research in this area was the absence of research focusing on the use of a stylus versus the index finger to interact with iPads. Although children naturally gravitated towards using their index finger, we encouraged children to use the stylus to reinforce printing skills learned with a pencil. More research is needed to corroborate this practice.

The fact that children in this study gravitated towards apps that stimulated laughter through humorous animated characters or bursts of stars or sparkles confirmed our thoughts about their level of maturity and corresponding desire for play. Once children had been exposed to the new app each day, they were able to choose any app to play with for the remaining time. The outcome of children’s decision-making resulted in the selection of apps that were creative and fun in contrast to other apps that were more pedagogically accurate containing appropriate levels of difficulty and sequencing of questions. This finding needs further research to explore the extent to which this affinity for creative and fun apps continues through the elementary and primary grades.

The last factor that influenced children’s use of interactive technology was the teachers’ skill level and interest in implementing apps as curricular learning resources. As noted above, the teacher participating in this study could be described as a beginner in using interactive technology and her skill set was similar to what was previous documented as limited to downloading images for presentations (Public Broadcasting Service and Grunwald Associates 2009 , 2011 ). However, her interest, rather than ability, was the catalyst for implementing technology in her classroom and through opportunities for professional development as called for by other researchers (i.e., Simon et al. 2013 ); this teacher can now be described as experienced and innovative in her use of interactive technology in the classroom. Key to this transformation was providing professional development in a one-to-one session and in an as-needed basis.

With the advancement of interactive technology and more user-friendly touchable interfaces, the use of these devices in early years classrooms is not only suitable but also appropriate in preparing early years children for the technological world they will live in (Gordon and Williams Browne 2016 ). This study revealed that children using interactive technology in the form of mathematics apps as part of a play-based learning environment for mathematics had small gains in achievement as measured using a pre- and post-test. Although the gains in achievement were not significant between the control and intervention groups, learning using interactive technology did not lessen children’s opportunity to learn about numeracy concepts as children were observed collaborating and were highly engaged, particularly with apps that were creative. A longer experiment with a larger sample is needed to validate this finding.

Another important finding related to using interactive technology in a play-based learning environment was the need for guided direction in selecting quality apps that supported learning. When children were left to their own accord, they almost always selected apps or segments of apps that were high in entertainment value and low in educational value. Given the premise of play-based learning environments where play is situated in intentional and specific learning contexts that nurtures learning while providing children with independence to choose activities, it is important to select mathematical apps that are not only aligned with the curriculum but are also creative and fun and provide opportunities to learn. In these learning environments, pleasurable, entertaining play is encouraged in balance with other play-based activities that foster learning in specific domains such as numeracy. This finding was connected to children’s attention span which appeared to be dependent on the creativity of the app as well as the difficulty level of the app such that more creative apps held children’s attention spans longer but also the difficulty level influenced student engagement with apps. This finding corroborates the work of Couse and Chen ( 2010 ) who reported that engagement increased with age and by extension mathematics ability.

In sum, interactive technology in the form of iPads with mathematical apps promoted student collaboration and engagement. However there is still much to learn about the quality of apps and their impact on children’s learning, particularly when children are encouraged to make choices in a play-based learning environment.

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Strengthening the Numeracy Skills of Grade 7 Students through an Intervention Program Title: Strengthening the Numeracy Skills of Grade 7 Students through an Intervention Program

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This guidance intends to provide guidance to class students of elementary school 1 Lamokato in using the Jarimatika method. This guidance is carried out because it is motivated by the low numeracy literacy of students at elementary school 1 Lamokato. This has an impact on the low ability of students to count. Therefore, guidance is needed for students using a different method from the method used by teachers at elementary school 1 Lamokato. This training was carried out from June to August 2022 at elementary school 1 Lamokato. The methods used in this training are demonstration methods, question and answer, and practice using the Jarimatika method. The students were very enthusiastic during the training. Students are interested in using the Jarimatika method. Students actively ask and answer about the Jarimatika method. Each student practices the method of Jarimatika in front of the class. The result of this training activity is that there is an increase in students&#39; numeracy li...

To Be or Not to Be a Great Educator

A growing body of evidence including international level studies (e.g. PISA, TIMSS) demonstrate that numeracy skills (also known internationally by other terms such as mathematical literacy) is crucial for a person’s educational achievements and for informed and participatory citizenship. Early and successful interventions to improve students’ numeracy skills lie in developing and using valid and reliable diagnostic tests for numeracy skill assessment. This study explored how developing a numeracy test based on three-dimensional framework could be used for numeracy diagnostic purposes in grade 7. To achieve this, initially a three-dimensional numeracy framework based on 1) content knowledge of mathematics, 2) information literacy skills, 3) complexity levels of SOLO taxonomy, was prepared. Then the framework was used to construct a 32-item numeracy test assessing the ability to use relationships, functions and numerical information in different contexts including science. Next, the ...

Journal of Physics: Conference Series

Estimation and mental computation abilities can be viewed as a key to transforming the teaching and learning of Mathematics in Malaysia and towards a more dynamic Mathematics education especially because both abilities are needed in order to develop good numeracy thinking. The purpose of this paper is to determine students’ level of numeracy and the problematic questions faced by students in the Numeracy Test. The sample consisted of 414 students in Form 1, Form 2 and Form 4 from six secondary schools located in a district in Malaysia. This is a descriptive correlation study using stratified random sampling. The findings show that the students were weak in numeracy. Is this normal? The finding of students’ common weaknesses and strengths may serve a good reference for the curriculum refinement and may relate to 21st century skills in learning Mathematics. Keywords: estimation; mental computation; numeracy; thinking.

Government programs in fostering a culture of reading and making students literate individuals are welcomed by the implementers of the education program. The purpose of this study was o analyse the implementation of the numeracy literacy in mathematics le rn , to analyse the supporting and inhibiting factors of numeracy literacy rogram in grade IV mathematics learning in elementary schools. This research use descriptive qualitative approach. Data collection uses observation, in-depth interviews, and documentation studies. This study also uses research instruments to guide data collection. This research was conducted in several Muhammadiyah elementary schools, they are SD Muhammadiyah 1 and SD Muhammadiyah 5 Kota Malang. The subjects in this study were the principal as policy makers, class IV teachers, students and parents. The results showed that in learning numeracy literacy was good enough in contextual and problem-based concept planting, but rarely used projection based learning....

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