Mathematical Attainment Research Articles

Working memory predictors of written mathematics in 7- to 8-year-old children.

There is extensive evidence for the involvement of working memory in mathematical attainment. This study aims to identify the relative contributions of verbal, spatial-simultaneous, and spatial-sequential working memory measures in written mathematics. Year 3 children (7-8 years of age, n = 214) in the United Kingdom were administered a battery of working memory tasks alongside a standardised test of mathematics. Confirmatory factor analyses and variance partitioning were then performed on the data to identify the unique variance accounted for by verbal, spatial-simultaneous, and spatial-sequential measures. Results revealed the largest individual contribution was that of verbal working memory, followed by spatial-simultaneous factors. This suggests the components of working memory underpinning mathematical performance at this age are those concerning verbal-numeric and spatial-simultaneous working memory. Implications for educators and further research are discussed.

Study Habits and Attainment in Undergraduate Mathematics: A Social Network Analysis

In this article, we argue that although mathematics educators are concerned about social issues, minimal attention has been paid to student–student interactions outside the classroom. We discuss social network analysis as a methodology for studying such interactions in the context of an undergraduate course. We present results on the questions: Who studies with whom? What are students’ study habits, and are these systematically related to the habits of those with whom they interact? Do individual and collaborative study habits predict attainment? We discuss the implications of these findings for research on undergraduate learning and on social issues in mathematics education, suggesting that social network analysis may provide a bridge between mathematics education researchers who focus on cognitive and on social issues.

Learning the concept of eigenvalues and eigenvectors: a comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds

International comparative studies of education have shown that the increase in mathematical attainment differs significantly among students in relation to the different school types in which their mathematical foundations were acquired. In tertiary education, the same differences are observed with respect to simple tasks that relate to the subject matter of secondary education. Therefore, we investigate the question of whether this observation holds equally for concept construction in the field of eigen theory, by applying Dubinsky’s action, process, object, schema (APOS) theory, and Tall’s worlds of mathematics. We focus on eigen theory because we regard it as particularly representative of linear algebra in terms of its expressibility in the embodied and symbolic worlds. In our empirical study, we investigated concept constructions as correlates of educational trajectories of 36 students who covered the entire course program of a first semester mathematics course for first-year engineering students. Although significant differences in procedural knowledge were observed, results indicate that the type of secondary school does not affect concept construction among students who complete the entire course program. In our final discussion, we present implications for teaching and learning of linear algebra in heterogeneous classes and the integration of deeper learning methods into the course design.

Understanding the progress in mathematics of Chinese adolescents: Significant impacts from the socioeconomic status and the academic expectations of primary caregivers

Past research has found socioeconomic status (SES) and the academic expectations of primary caregivers (PCGs) to be important predictors of students’ attainment in mathematics. However, their effects might not be universal across cultures. Further, there exists conflicting evidence on how SES and academic expectations impact maths attainment together and over time. This study aimed to provide new empirical evidence on both issues by examining the maths attainment of a cohort of Chinese adolescents (n = 1407) over a 5-year period (2010–2014) and how maths attainment was related to SES and PCG academic expectations. Multilevel Structural Equation Modeling revealed that both SES and PCG academic expectations exerted positive effects on maths progress. Over time, the effect of SES became increasingly internalized within past maths attainment. Further, higher academic expectations from PCGs lessened the difference in maths attainment between students from lower and higher SES families when the studied cohort was at their youngest.

An Empirical study on Attainment in Mathematics at High School Leaving Certificate Examination

An Empirical study on Attainment in Mathematics at High School Leaving Certificate Examination

Towards a pedagogical model of teaching with ICTs for mathematics attainment in primary school: A review of studies 2008–2018

This article reviews literature in the field of ICTs in teaching/learning mathematics at an elementary school level. The findings to date in the field of teaching with technology in mathematics classrooms are very conflictual, with some studies indicating that ICTs impact positively on achievement through altering pedagogy, while other studies indicate that the effect on achievement and pedagogy is in fact negative. The current paper seeks to address the conflictual data by analysing a variety of meta-analyses and studies in order to answer the following questions: Does pedagogy alter with the use of ICTs in grade 6 mathematics classrooms and if so, in what ways does it vary? Secondly, does student achievement in mathematics change with the use of ICTs as teaching tools and if so, in what ways does it do so? Findings from the review indicate that student achievement in mathematics can be positively impacted using technology, depending on the pedagogical practices used by teachers. Technology on its own appears to have no significant impact on student's attainment. There is a dearth of findings regarding pedagogical variation with ICTs outside of a single meta-analysis that indicates that a ‘constructivist’ approach to teaching/learning with technology is the most effective approach to developing students' conceptually. Due to this gap in the literature, the paper outlines a theoretical framework for providing a nuanced study of pedagogical variation with ICTs drawing on Cultural Historical Activity Theory and TPACK that can track pedagogical change along various dimensions.

Multiplicative reasoning: An intervention’s impact on Foundation Phase learners’ understanding

Background: Given the context of low attainment in primary mathematics in South Africa, improving learners’ understanding of multiplicative reasoning is important as it underpins much of later math ...

算数達成度に関する継続的調査研究(III) : 第1児童集団の中学年段階における達成度

算数達成度に関する継続的調査研究(III) : 第1児童集団の中学年段階における達成度

Research protocol: Evaluating the impact of Eedi formative assessment online platform (formerly Diagnostic Questions or DQ) on attainment in mathematics at GCSE and teacher workload

This paper describes a cluster randomised controlled trial designed to test the efficacy of Eedi, a formative question setting and diagnostic digital platform, on attainment in mathematics at GCSE as well as its impact on teacher workload. The study is a pragmatic two arm trial that aims to randomise 180 English secondary schools to intervention and control (business as usual) conditions. The intervention is targeted at Year 10 pupils (aged 14–15 years) and their teachers commencing study of GCSE mathematics from September 2018 and will run for two years. The study is due to report at the end of 2021.

Mathematics education in the spotlight: Its purpose and some implications

This article proposes a reframing of the purposes of mathematics education for the twenty-first century that combines apparently divergent philosophical approaches, arguing that the consequent empowerment should as a matter of individual equity be available to all young people (as well as of benefit to wider society). It suggests that the global mathematics attainment 'spotlight', and the English policy context in particular, offer both opportunities and constraints for the development of such a high-quality mathematics education. The article also discusses the challenging implications for the curriculum, and for the nature of teacher expertise, particularly subject-specific expertise, that is needed.

The Impact of Writing Practices on Students’ Mathematical Attainment

The purpose of this meta-analysis was to examine the effects of writing intervention on students’ mathematical attainment based on their achievement (mathematics standardized test scores) and their attitudes toward mathematics (mathematical motivation and interest). Twelve studies with 19 effect sizes were selected for inclusion in the present meta-analysis. Results indicated that the overall effect size equalled 0.42. The small sample size (12 studies) in the present meta-analysis limits the generalizations that might be made regarding the overall impact of writing intervention on students’ mathematical attainment. However, the implication from the present study is that integrating writing into mathematics classrooms can be a useful instructional strategy to increase students’ mathematics success.

PISA and policy-borrowing: A philosophical perspective on their interplay in mathematics education

Mathematics achievement in different education systems around the world is assessed periodically in the Programme for International Student Assessment (PISA). PISA is deemed to yield robust international comparisons of mathematical attainment that enable individual countries and regions to monitor the performance of their education systems relative to standards being achieved internationally, with a view to informing their mathematics education policy decisions. Initially, the role of PISA in instigating mathematics education policy borrowing is outlined using England as a case study, and some existing technical critiques of PISA are then reviewed. Following this, aspects of Ludwig Wittgenstein’s later philosophy of mind are used to reason that an over-reliance on the use of PISA to inform policy decisions in mathematics education may be problematic. It is suggested that, when PISA is viewed through a later Wittgensteinian lens, a potential deficiency in the underpinning psychometric model, pertaining to the inherent indeterminism in unmeasured mathematical abilities, may weaken PISA’s utility in guiding mathematics education policy decisions. It is concluded that, whilst PISA mathematics scores may give some indication of the mathematical proficiency of a nation’s students, caution is required before mathematics education policies are borrowed from other jurisdictions on the basis of PISA performance. Implications for the other PISA domains are also outlined.

Preschool Attendance and Executive Function Mediate Early Academic Achievement Gaps in East Asia and the Pacific

ABSTRACTResearch Findings: This study investigated the relationship between family socioeconomic status (SES) and children’s early attainment, and the roles of preschool attendance and executive function (EF) in this association. Participants were 3,331 children (1,584 girls) ranging in age from 36 to 71 months from Cambodia, Mongolia, and Vanuatu. Children’s language, literacy, and mathematics attainment and EF were assessed using the East Asia-Pacific Early Child Development Scales. Mothers reported on family demographics and children’s preschool experience. Results indicated significant associations between SES and academic attainment in all three countries. Further analysis showed that preschool attendance and EF were significant mediators of SES- related disparities in attainment, but differed by country. Both served as parallel and sequential mediators in the associations between SES and performance in language, literacy, and mathematics in Mongolia. However, only preschool attendance mediated the association of SES with literacy attainment in Cambodia, and only EF mediated that with children’s mathematics and language performance in Vanuatu. Although SES is substantially related with early achievement in these developing countries, our findings indicate that preschool attendance and EF may attenuate this relationship. Practice or Policy: Implications for the provision of early childhood education programs and public policy are discussed.

Hitting the Target: Mathematical Attainment in Children Is Related to Interceptive-Timing Ability

Interceptive timing is a fundamental ability underpinning numerous actions (e.g., ball catching), but its development and relationship with other cognitive functions remain poorly understood. Piaget suggested that children need to learn the physical rules that govern their environment before they can represent abstract concepts such as number and time. Thus, learning how objects move in space and time may underpin the development of related abstract representations (i.e., mathematics). To test this hypothesis, we captured objective measures of interceptive timing in 309 primary school children (5–11 years old), alongside scores for general motor skill and national standardized academic attainment. Bayesian estimation showed that interceptive timing (but not general motor capability) uniquely predicted mathematical ability even after we controlled for age, reading, and writing attainment. This finding demonstrates that interceptive timing is distinct from other motor skills with specificity in predicting childhood mathematical ability independently of other forms of attainment and motor capability.

Attainment-aspiration gap in students with a migration background: The role of self-efficacy

Academic aspirations are important for academic success. Students with migration backgrounds tend to report high academic aspirations despite low success in school, a phenomenon known as the attainment-aspiration gap. This paper investigates whether the self-perception of ability (here, academic self-efficacy) can explain aspirations better than actual attainment in students with migration backgrounds. Data from 380 seventh-grade students enrolled in German schools showed background-specific patterns in multigroup structural equation analyses: In students without migration backgrounds, attainment and self-efficacy both predicted academic aspirations. In students with migration backgrounds, attainment in reading and mathematics did not predict aspirations, whereas academic self-efficacy did. Furthermore, a differential pattern of results for family background variables emerged across students depending on their familial countries of origin. As aspirations can influence behavior and facilitate academic and employment-related success, understanding factors that lead to their formation in students from diverse backgrounds is important for research and practice.

Measuring mathematical affect in an international context: influences on pre-university attainment and degree choice

In many contexts, mathematical self-efficacy is known to be an important and distinct predictor of mathematical attainment and the nature of further participation in the study of mathematics and mathematically based disciplines. This study reports on the results of cross-sectional questionnaire-based study of over 500 former International Baccalaureate (IB) students across 64 countries who had studied higher level pre-university mathematics. Two different sub-scales were employed in the online questionnaire measuring (i) mathematical self-efficacy on completion of the IB course (i.e. retrospectively) and (ii) mathematical self-concept at the time of completion of the survey (i.e. mainly during degree study) . These scales were found to be essentially unidimensional and to measure distinct but related constructs. In terms of predicting type of degree participation, important differences in patterns of influence were found relating to mathematical self-efficacy and attainment, although degree choice was not well-predicted in the modelling. Differences by gender and country are also reported, and the relationship between self-efficacy and self-concept is explored.

Parental Involvement in Primary School Education: its Relationship with Children’s Academic Performance and Psychosocial Competence through Engaging Children with School

The benefits of parental involvement in children’s education have been well established but increasing evidence suggests that overparenting may have adverse effects on children. The question of whether excessive parental involvement hinders children’s academic and psychosocial development warrants further investigations. This study examined the associations of parental educational involvement at home and in school with academic performance and psychological health of 507 Chinese Grade 3 schoolchildren in Hong Kong. Parents reported on their level of involvement in children’s schooling and their children’s psychosocial issues. Children were surveyed to determine their school engagement, and their Chinese language and mathematics attainment was assessed. We also explored the underlying mechanism by testing children’s engagement with school as a mediator of the relationships. Our results showed that home-based parental educational involvement was positively associated with children’s language competence and psychosocial wellbeing, and the associations were linked through engaging children with school. However, the benefits reached a plateau at higher level of parental involvement in children’s learning at home. School-based parental involvement had an indirect effect on children’s prosocial behavior through school engagement. These findings highlight the significance of optimal level of parental involvement in children’s education at home for children’s development.

First-Year Mathematics and Its Application to Science: Evidence of Transfer of Learning to Physics and Engineering

Transfer of mathematical learning to science is seen as critical to the development of education and industrial societies, yet it is rarely interrogated in applied research. We present here research looking for evidence of transfer from university mathematics learning in semester one to second semester sciences/engineering courses (n = 1125). A transfer index measure was derived from extant university assessments, calculated on content-matched questions requiring mathematical concepts and skills in students’ completed mathematics and science/engineering exams. We found that transfer could be measured in this way, and present path models of how transfer is associated with educational attainment and other factors. However, transfer was observed only in physics (n = 258) and engineering (n = 426); biology and molecular bioscience assessments did not provide opportunities for students to demonstrate their mathematical learning. In physics and engineering courses, mathematical attainment had a strong, direct, positive effect, with transfer of learning providing an additional direct and mediating effect upon students’ performance in these subjects. In physics and engineering, transfer was also associated with higher levels of educational attainment in general. This new, applied approach to examining transfer trialed here may provide opportunities for analysing, evaluating, and improving cross-disciplinary transfer of learning within universities.

An Estimation of Variances and Factors in Mathematics Attainment in Upper-Primary Schools

This study aimed at identifying variances related to school and pupil levels, and the performance indicators measuring the learning progress in mathematics. A longitudinal design was carried out and the stratified random sampling was used to obtain a sample of 5118 pupils from 60 primary schools. In each school three upper grades were selected, including their 180 class teachers and 60 headteachers. The data collection was carried out through questionnaires and school archives. Using multilevel analysis, the results showed that the proportion of total variance in pupil attainment for mathematics at the school level ranged from 20 to 29 per cent. When intake characteristics were taken into account as the baseline, the variance proportions were less than the prior attainments. Occupation and education of parents, besides reading facilities at home were significant explanatory variables for children progress in mathematics achievement. The outcomes have important consequences for school effectiveness research in determining the baseline and performance indicators.

The impact of participation in music on learning mathematics

Music psychologists have established that some forms of musical activity improve intellectual performance, spatial–temporal reasoning and other skills advantageous for learning. In this research, the potential of active music-making for improving pupils' achievement in spatial– temporal reasoning was investigated. As spatial–temporal skills are considered to be high-level mathematical abilities, this study also aimed to explore if learning music might have an effect on pupils' achievement in mathematics, and whether spatial–temporal reasoning plays a role in this process. The study had a quasi-experimental design in which groups of children aged 4 to 7 participated in a music programme containing a variety of musical, predominantly rhythmical, activities. Parallel classes made up control groups. Throughout the intervention, pupils' attainment in mathematics, reading, writing and spatial–temporal reasoning was recorded and compared between the music and control groups. The findings of the project supported the hypothesis that music instruction has an impact on the development of spatial–temporal skills. A statistically significantly greater progression was observed in most of the intervention groups, as compared in all periods of measurement to the control groups. The attainment in general mathematics did not always differ between the intervention and control groups but the analyses provided evidence of a consistent and statistically significant enhancement in learning mathematics between the youngest participants of the programme. This knowledge could inform pedagogical practice, while further research in this area could offer more insight into the association between music and mathematics.