Early Mathematics Achievement Research Articles

Pathways of mathematics achievement in preschool: Examining executive function and task orientation

Despite research demonstrating the importance of mathematics achievement to children's educational success and trajectories, many children enter kindergarten without the foundational mathematics skills needed to succeed (Garcia & Weiss, 2015). Children's executive function (EF) skills and their learning-related behaviors (Anthony & Ogg, 2020) may play a key role in supporting their early mathematics achievement (Morgan et al., 2019). Additionally, there is some evidence that children's learning behaviors are a mechanism through which EF is related to math achievement (e.g., Nesbitt et al., 2015), however this pathway hasn't been fully explored. There is also little to no research that has explored whether the pathways through which EF is related to math achievement function similarly for boys versus girls, although some literature suggests that differences in the nature or strength of the associations could contribute to differences in mathematics achievement among boys and girls in elementary school (e.g., Fryer Jr and Levitt, 2010; Robinson-Cimpian et al., 2013; Robinson & Lubienski, 2011). In this study, we used longitudinal data from a racially/ethnically and linguistically diverse sample of 467 preschoolers to examine (1) if children's EF at the beginning of pre-kindergarten predicts growth in their mathematics achievement across the pre-kindergarten year, (2) whether growth in learning behaviors, specifically task orientation, mediate the associations between EF and mathematics achievement, and (3) if there are sex differences in these associations. We found that growth in children's task orientation partially mediates the association between EF and mathematics achievement for the preschoolers in our study. Although girls had significantly higher task orientation, we did not find a statistically significant difference in the direct associations between EF, task orientation, and mathematics or in the mediating effect of task orientation for boys and girls. The discussion reviews implications and directions for future research.

Investigation of Working Memory Performances of Children with Low Early Mathematics Achievement

This study examined the working memory performance of children with low early mathematics achievement in comparison with their peers and analyzed the relationships between these skill areas. The distribution of children with low, average and high early mathematics achievement according to their working memory levels was also examined. The participants consisted of 100 kindergarten children with typical development and average and above-average intelligence. The Colored Progressive Matrices Test (CPM) was used to determine nonverbal intelligence levels, the Test of Early Mathematics Ability, Third Edition (TEMA-3) to evaluate early math skills and the Working Memory Scale (WMS) to determine working memory performances of the children. Children were divided into three groups of low, average and high achievement according to their early mathematics achievement assessed by the TEMA-3. It was found that the working memory performances of children with low, average and high achievement in early mathematics differed significantly. The working memory performance of children with low early mathematics achievement was significantly lower than their peers with average and high achievement. The results of the relationships between early math skills and working memory showed that early math skills and working memory components, except for visual short-term memory, were correlated to a small and medium degree. The distributions of working memory levels of the groups were examined and the results showed that children with low early mathematics achievement had low and average working memory performance, while children with high early mathematics achievement mostly had average and high working memory performance. However, none of the children with low early mathematics achievement showed high working memory performance. The results are discussed within the framework of the literature.

Variation in early number skills and mathematics achievement: Implications from cognitive profiles of children with or without Turner syndrome.

Individuals with Mathematics Learning Disabilities have persistent mathematics underperformance but vary with respect to their cognitive profiles. The present study examined mathematics ability and achievement, and associated mathematics-specific numerical skills and domain-general cognitive abilities, in young children with Turner syndrome compared to their matched peers. We utilized two independent peer groups so that group comparisons would account for verbal skills, a hypothesized strength of girls with Turner syndrome, and nonsymbolic magnitude comparison skills, a hypothesized difference of girls with Turner syndrome. This individual matching approach afforded characterization of mathematics profiles of girls with Turner syndrome and girls without Turner syndrome that share potential key features of the Turner syndrome phenotype. Results indicated differences in mathematics ability and nonsymbolic magnitude comparison tasks between girls with Turner syndrome and peers with similar levels of verbal skill. Mathematics ability and mathematics achievement scores of girls with Turner syndrome did not differ significantly from their peers with similar levels of accuracy on a nonsymbolic magnitude comparison task. Cognitive correlates of mathematics outcomes showed disparate patterns across groups. These quantitative and qualitative differences across profiles enhance our understanding of variation in mathematics ability in early childhood and inform how mathematics skills develop in young children with or without Turner syndrome.

Predicting the growth patterns in early mathematics achievement from cognitive and environmental factors among Chinese kindergarten children

One hundred and seventy-three Chinese kindergarten children (85 girls, Mage = 67.25 months) were assessed on measures of domain-general cognitive skills (nonverbal IQ, inhibition, and working memory), approximate number system acuity (nonsymbolic estimation and symbolic estimation), and early mathematics achievement at the beginning of the academic year. Their parents completed a questionnaire on family's factors (family's socioeconomic status, parents' numeracy expectations, and the home numeracy environment). In addition, children were reassessed on early mathematics achievement at the halfway and end of the academic year. Analysis with latent growth modelling showed that nonverbal IQ, working memory, nonsymbolic estimation, symbolic estimation, family's socioeconomic status, and parents' numeracy expectations uniquely predicted the intercept in early mathematics achievement, while the home numeracy environment uniquely predicted the growth rate. In addition, path analysis showed that the home numeracy environment also indirectly predicted the intercept in early mathematics achievement through nonsymbolic estimation and symbolic estimation, while parents' numeracy expectations indirectly predicted the slope of early mathematics achievement through the home numeracy environment and indirectly predicted the intercept of early mathematics achievement through serial pathways.

RME Approach and Mind Map Methode to Enhance Mathematical Cognition of Elementary School Students

Early mathematics achievement has been found to be important for later mathematical development. Intelligence and other cognitive factors typically explain no more than half of the variability in mathematical variation. This study aimed to investigate the effect of applying a Realistic Mathematics Education approach and mind map method to enhance mathematic cognitive at elementary school students. The participants were recruited from elementary schools in Bukittinggi, West Sumatra, Indonesia. The constant comparative and grounded theory techniques were used for data analysis. The theoretical contribution of this study is a very detailed diagnosis of increasing at mathematical cognition resulting in a profile rather than in a single score. Practically, this profile enabled efficient intervention that resulted in students’ high mathematical cognition and achievement in students’ learning achievement.

Early mathematics learning in reading and writing numerals: Learning through “What are the numbers?” A picture book made up of Flora and Fauna in Borneo

Learning through picture books is a method which is widely used in preschools to teach mathematics. However, the research findings on the benefits of using picture books in learning mathematics remain inconclusive. This study aimed to i) investigate the effects of a picture book entitled “What are the numbers?” (a picture book made up flora and fauna in Borneo) on early mathematics achievement (reading and writing numerals up to 20) and ii) to get feedback on how appropriate the use of “what are the numbers” from teachers and parents. The book consists elements of critical thinking, communication, collaboration and creative thinking. The effects were measured by comparing the change in early mathematical ability of children in reading and writing numerals up to 20 by using the Rasch measurement model. The mean of the pre-test achievement was -1.99 logits and the mean of the post-test achievement was 1.75 logits which shows a difference of 3.74 logits. The effect size of the difference between the post-test and pre-test achievement was 1.4, which is considered large. Teachers and parents gave positive feedback on the use of the picture book. They commented that the picture book is able to attract children’s attention, enhance their thinking skills and nurture creativity among children. In conclusion, the picture book based on the 4C approach enhanced early mathematics achievement of children.

The interaction of procedural skill, conceptual understanding and working memory in early mathematics achievement

Large individual differences in children’s mathematics achievement are observed from the start of schooling. Previous research has identified three cognitive skills that are independent predictors of mathematics achievement: procedural skill, conceptual understanding and working memory. However, most studies have only tested independent effects of these factors and failed to consider moderating effects. We explored the procedural skill, conceptual understanding and working memory capacity of 75 children aged 5 to 6 years as well as their overall mathematical achievement. We found that, not only were all three skills independently associated with mathematics achievement, but there was also a significant interaction between them. We found that levels of conceptual understanding and working memory moderated the relationship between procedural skill and mathematics achievement such that there was a greater benefit of good procedural skill when associated with good conceptual understanding and working memory. Cluster analysis also revealed that children with equivalent levels of overall mathematical achievement had differing strengths and weaknesses across these skills. This highlights the importance of considering children’s skill profile, rather than simply their overall achievement.

Predictive Relation between Early Numerical Competencies and Mathematics Achievement in First Grade Portuguese Children.

Early numerical competencies (ENC) (counting, number relations, and basic arithmetic operations) have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children (n = 123). The children’s ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC) were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties.

Gender Differences in Early Literacy and Mathematics Achievement and Self-regulatory Behaviours in the First Year of School: An Australian Study

THIS PAPER PRESENTS ANALYSES of gender differences in classroom behaviours (e.g. attentiveness and task persistence) and early academic outcomes. Data is drawn from Growing Up in Australia: The Longitudinal Study of Australian children (LSAC). In these analyses, data from Wave 1 data collection (2004) and Wave 2 data collection (2006) for the Kindergarten Cohort are used. A sample of 2315 children who were in Year 1 of school at Wave 2 data collection are the focus for the analyses reported. The analyses draw on teacher ratings of children's literacy and language competence and mathematical thinking in Year 1 of school; as well as ratings of children's self-regulatory behaviour in the classroom and level of problem behaviours. Girls were rated by their teachers as having better literacy and language outcomes that were predicted by more positive classroom behaviours. Results are discussed with respect to the influence of children's classroom behaviours on academic learning at the beginning of formal schooling.

Effortful Control and Academic Achievement in Rural China

ABSTRACTResearch Findings: This study investigated the relationships between effortful control and early literacy and mathematics achievement. A total of 181 children (85 girls and 96 boys) from rural China were assessed when they were in Grades 1 and 2. Path analyses controlling for maternal education indicated that effortful control at the beginning of Grade 1 predicted incremental achievement in literacy and mathematics at the end of Grade 1 and mathematics achievement at the end of Grade 2. Growth in effortful control during Grade 1 also contributed significantly to the prediction of both literacy and mathematics achievement at the end of Grade 2. Although girls performed significantly better than boys in literacy achievement, gender did not moderate the relationships between effortful control and literacy and mathematics achievement. Practice or Policy: Children’s effortful control appears to be an important predictor of early literacy and mathematics achievement. Findings suggest that children’s effortful control should be fostered during the preschool and early years of formal schooling, and this can be done in both home and school contexts.

Early mathematics achievement of boys and girls: Do differences in early self-regulation pathways explain later achievement?

The degree to which a true gender gap exists in mathematics achievement is still debated, and empirically-supported explanations for any gap rarely address very early childhood self-regulatory pathways. This study examines whether mathematics achievement at 8–9years differs by gender, how achievement is associated with self-regulatory pathways beginning at 2–3years of age, and whether these pathways differ by gender. Participants were 5107 children involved in the nationally-representative Longitudinal Study of Australian Children (LSAC). Boys outperformed girls in mathematics achievement and girls generally had better early attentional and emotional regulation. Path analysis revealed that attentional regulation was directly associated with mathematics achievement from 4 to 5years, and emotional regulation was indirectly associated. These self-regulatory pathways to mathematics achievement were not moderated by gender. We discuss the implications for further research and new approaches to early years mathematics education that embed self-regulatory support and development for all children.

How socioeconomic status, executive functioning and verbal interactions contribute to early academic achievement in Chinese children

The present study investigated the relative importance of executive functioning, parent–child verbal interactions, phonological awareness and visual skills on reading and mathematics for Chinese children from low-versus middle-socio economic status (SES) backgrounds. A total of 199 kindergarten children were assessed on executive functioning, verbal interactions, phonological awareness, visual skills, mathematics and word reading in Chinese and English. Results revealed that low-SES children exhibited lower levels of cognitive-linguistic skills, verbal interactions, reading and mathematics achievement than their middle-SES counterparts. Path analyses also indicated that executive functioning and verbal interactions made significant and direct contributions to mathematics, and indirect contributions to reading through phonological awareness. These results suggest that executive functioning and verbal interactions provide the foundation for phonological awareness and visual skills, which in turn affect reading and mathematics achievement. Overall, findings underscore the potential importance of SES inequalities, cognitive-linguistic skills and parental verbal input to their children for early reading and mathematics achievement.

Construct Confounding Among Predictors of Mathematics Achievement

Identifying which early mathematics skills have the largest effects on later mathematics achievement has important implications. However, regression-based estimates often rely on untested assumptions: (a) Scores on different mathematics skills reflect unique constructs, and (b) other factors affecting early and later mathematics achievement are fully controlled. We illustrate a process to test these assumptions with a sample of third and fourth graders who completed measures of mathematics skills, working memory and motivation, and standardized mathematics and English language arts tests. Factor analyses indicated that mathematics skills largely reflect the same underlying construct. The skills that loaded highest on the general factor most predicted both later mathematics and English language arts, even after adjusting for working memory and motivation. Findings suggest that relations between earlier mathematics and later achievement largely reflected more general factors that contribute to children’s learning. We discuss the importance of establishing construct validity in correlational studies.

Of Huge Mice and Tiny Elephants: Exploring the Relationship Between Inhibitory Processes and Preschool Math Skills.

The cognitive mechanisms underpinning the well-established relationship between inhibitory control and early maths skills remain unclear. We hypothesized that a specific aspect of inhibitory control drives its association with distinct math skills in very young children: the ability to ignore stimulus dimensions that are in conflict with task-relevant representations. We used an Animal Size Stroop task in which 3- to 6-year-olds were required to ignore the physical size of animal pictures to compare their real-life dimensions. In Experiment 1 (N = 58), performance on this task correlated with standardized early mathematics achievement. In Experiment 2 (N = 48), performance on the Animal Size Stroop task related to the accuracy of magnitude comparison, specifically for trials on which the physical size of dot arrays was incongruent with their numerosity. This highlights a process-oriented relationship between interference control and resolving conflict between discrete and continuous quantity, and in turn calls for further detailed empirical investigations of whether, how and why inhibitory processes matter to emerging numerical cognition.

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations.

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n = 1,362), this study tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first-grade and adolescent mathematics achievement was present (β = .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division serving as significant mediators.

State and Trait Effects on Individual Differences in Children’s Mathematical Development

Substantial longitudinal relations between children’s early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children’s mathematics achievement across time. We hypothesized that individual differences in children’s later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children’s mathematics achievement over time. Latent trait effects on children’s mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed.

Contributions of executive function and spatial skills to preschool mathematics achievement

Early mathematics achievement is highly predictive of later mathematics performance. Here we investigated the influence of executive function (EF) and spatial skills, two generalizable skills often overlooked in mathematics curricula, on mathematics performance in preschoolers. Children (N=44) of varying socioeconomic status (SES) levels were assessed at 3years of age on a new assessment of spatial skill (Test of Spatial Assembly, TOSA) and a vocabulary measure (Peabody Picture Vocabulary Test, PPVT). The same children were tested at 4 years of age on the Beery Test of Visual–Motor Integration (VMI) as well as on measures of EF and mathematics. The TOSA was created specifically as an assessment for 3-year-olds, allowing the investigation of links among spatial, EF, and mathematical skills earlier than previously possible. Results of a hierarchical regression indicate that EF and spatial skills predict 70% of the variance in mathematics performance without an explicit math test, EF is an important predictor of math performance as prior research suggested, and spatial skills uniquely predict 27% of the variance in mathematics skills. Additional research is needed to understand whether EF is truly malleable and whether EF and spatial skills may be leveraged to support early mathematics skills, especially for lower SES children who are already falling behind in these skill areas by 3 and 4years of age. These findings indicate that both skills are part of an important foundation for mathematics performance and may represent pathways for improving school readiness for mathematics.

Early Disparities in Mathematics Gains among Poor and Non-Poor Children

Multilevel modeling was used to investigate the relationship between poverty status, mathematics achievement gains, and behavioral engagement in learning over kindergarten. Data included information on 11,680 poor, low-income, and non-poor kindergartners from the Early Childhood Longitudinal Study—Kindergarten Cohort of 1998–1999 (ECLS-K). Results show that accounting for teachers' reports of non-poor students' higher behavioral engagement (e.g., attentiveness, task persistence) explains the disparity in mathematics gains between poor and non-poor students over kindergarten. Furthermore, results suggest that exposing poor and low-income students to higher classroom behavioral engagement could play a substantial role in equalizing mathematics gains. Given these findings, strategies designed at narrowing economic disparities in early mathematics achievement should take into consideration the impact of behavioral engagement at the intrapersonal and contextual levels.

Preschool Children's Early Mathematics Achievement Based on Gender and Ethnicity

Achievements in Mathematics are said to be influenced by several factors including gender and ethnicity. The purpose of this study was to determine the overall early mathematics achievements of preschool children and whether there were significant differences in those achievements based on gender and ethnicity. The instrument used in this research was the Early Mathematics Achievement Test(EMAT) which was adapted from two preschool mathematics modules and the National Standard Preschool Curriculum Malaysia. The research sample consisted of 138 preschool children from six Ministry of Education preschools in Malaysia stratified according to gender and ethnicity. The data was analyzed descriptively and inferentially. The t-test and ANOVA were used to test gender and ethnic differences in the mathematics achievements. The findings showed that the level of preschool children's early mathematics achievements was above average. There were no significant differences in their mathematics achievement based on gender. However, there were significant differences in their early mathematics achievement based on ethnicity. We therefore argue that ethnicity is a factor that can probably affect preschool children's early mathematics achievement. The role of gender in mathematics achievement needs to be further examined in future studies to clarify the inconclusive findings of past research.

Early mathematics achievement trajectories: English-language learner and native English-speaker estimates, using the Early Childhood Longitudinal Survey.

This study used data from the Early Childhood Longitudinal Survey, Kindergarten Class of 1998-1999, to (a) estimate mathematics achievement trends through 5th grade in the population of students who are English-language proficient by the end of kindergarten, (b) compare trends across primary language groups within this English-language proficient group, (c) evaluate the effect of low socioeconomic status (SES) for English-language proficient students and within different primary language groups, and (d) estimate language-group trends in specific mathematics skill areas. The group of English-language proficient English-language learners (ELLs) was disaggregated into native Spanish speakers and native speakers of Asian languages, the 2 most prevalent groups of ELLs in the United States. Results of multilevel latent variable growth modeling suggest that primary language may be less salient than SES in explaining the mathematics achievement of English-language proficient ELLs. The study also found that mathematics-related school readiness is a key factor in explaining subsequent achievement differences and that the readiness gap is prevalent across the range of mathematics-related skills.