Mathematical Attainment Research Articles

Émilie Du Châtelet’s Newton

Abstract This paper discusses the first French translator of Isaac Newton’s Principia Mathematica, Émilie Du Châtelet (1706-1749). It shows how her reputation suffered because as a woman her intellectual capabilities and her attainment in mathematics were not taken seriously and she was overshadowed by Voltaire, although he was no match for her expertise in mathematics. However, her extensive correspondence shows that in her lifetime she had an active intellectual life and was well-connected with the leading savants of her day. The letters shed light on the development of her interest in Newton – and indeed on the reception of Newton in eighteenth-century France. The paper concludes with an account of her Newton translation and the circumstances of its posthumous publication in 1759.

Expected and unexpected long-term effects of values affirmation in school.

An earlier study in a school in England found that a series of brief values affirmation writing exercises, performed over the course of a school year by students aged 11-14, increased the mathematics attainment of students of low socioeconomic status (SES). This pre-registered follow-up of the original study aims to investigate the long-term effects of values affirmation on low-SES students' attainment. The sample consisted of all students in the analytical sample of the original study who remained at the school and for whom the necessary data were available, N = 409 (95 low-SES). The students' results in high-stakes national standardized assessments at age 16, taken two to four years after the affirmation, were analysed. The evidence did not support the pre-registered hypotheses that values affirmation would raise the attainment of low-SES students in mathematics and English. However, exploratory analyses suggested that for low-SES students in two of the three-year groups, the intervention increased Attainment 8, a broad policy-relevant measure of academic attainment, and increased the attainment of boys in English (in particular English Literature) but reduced the corresponding attainment of girls. The results suggest that the benefits of values affirmation can differ by student cohort and by school subject and that they might be time-limited in some circumstances. This suggests a set of hypotheses that future research could test in order to advance understanding of when values affirmation is, and is not, successful for school students over a sustained period.

Young children with intellectual disabilities and their mathematical attainments: Do parents' attitudes toward mathematics, home numeracy, and literacy practices matter?

This study explored potential factors of numeracy acquisition in young children with intellectual disabilities (IDs). Those factors are determined to assess parents' academic expectations and home practices that they use with their children daily. The sample consisted of 187 Greek-speaking couples, comprising a total number of 374 parents. All of them had a child with mild IDs aged between 4 and 7 years old. Since Greece is placed among European countries with the lowest median disposable income it is significant to assess the potential effects of each family's socioeconomic status. We employed structural equation modeling to identify potential factors affecting a child's with IDs numeracy outcomes. Analysis of moments structures (AMOS) revealed that there is a good fit for the suggested second-order structural equation model. Results are discussed regarding their practical implications.

The mathematics pipeline in England: inclusion and the excellence stream

Abstract In England, there is currently heightened political interest in increasing mathematics attainment and maximizing post-16 participation. The latter is not merely an issue for upper secondary but requires a long-view of students’ mathematical progress. This paper reports such a system-level overview of the mathematics education pipeline in England based on analysis of linked data from the National Pupil Database (NPD) and Higher Education Statistics Agency (HESA). A sequence of mixed-effect logistic regression models at each phase of the education pipeline are developed to predict attainment in General Certificate of Secondary Education (GCSE), A level and undergraduate mathematics and participation in post-16 and university mathematics. In particular, we focus on the impact of prior attainment and student demographics: gender, ethnicity and socio-economic status. The analysis identifies four important findings. Firstly, female participation and attainment in A level Mathematics and Further Mathematics is lower than that of male students, which impacts their representation in undergraduate mathematics, despite them marginally outperforming male students at both GCSE and degree level. Secondly, the attainment and participation of students of Asian ethnicity in GCSE and A level Mathematics is striking in its positive divergence from the trends of other ethnic groups, whereas White students have higher attainment than other ethnic groups at university. Thirdly, many students from poorer backgrounds fall behind their peers during years 7 to 11, and their participation and attainment in A level Mathematics is also reduced compared to their more affluent peers. Lastly, students who study A level Further Mathematics are more likely to study undergraduate mathematics, but they are no more likely to achieve a first-class degree, compared to those who haven’t studied Further Mathematics. The findings should be informative to policymakers and other stakeholders who can put in place enhancements and interventions to improve the outcomes for underrepresented groups.

Educational Performance over Time: Changes in Mathematical Attainment between 1976 and 2009 in England

Abstract Over the past fifty years, there have been substantial attempts to improve students’ mathematical performance around the world. Many commentators have criticised the efficacy of these initiatives, arguing that performance in western developed countries has either stagnated or fallen. Yet, there is limited robust comparative evidence available. This paper reports a replication of a study of student performance from the 1970s. In 2008 and 2009, in England, Grades 6–8 students (N ≈ 7000), in a nationally representative sample based on a stratified random sample of schools, were tested on their understandings of algebra, decimals, ratio and fractions. The survey used tests administered in 1976 and 1977 to an equivalent nationally representative sample of students. The findings indicate that, at Grade 8, overall understandings have generally fallen, although there are different patterns of change across the topics. The challenges of replicating studies where the full statistical findings are not available are considered. The impact sheet to this article can be accessed at 10.6084/m9.figshare.25507276.

Black adolescents’ motivation to resist the false dichotomy between mathematics achievement and racial identity

This study investigates the racial-mathematical identity profiles of Black American adolescents. Survey data were collected in five schools across one U.S. urban school district at two time points (spring 2018 [n = 197] and spring 2019 [n = 210]). Based on extant research regarding psychological response patterns to racialized school stress, we investigated the existence of an identity negotiation pattern in which students were motivated to resist negative stereotypes about Black people by achieving well in mathematics. We conducted a latent profile analysis combining students’ self-beliefs across five indicators: racial centrality, racial public regard, mathematics attainment value, mathematics mastery experiences, and resistance motivation. Three distinct racial-mathematical identity profiles emerged: (1) Mathematics Devalued/Ambivalent, (2) Moderately Math Attained, and (3) Resistors. We found associations between profile membership and students’ gender, negative math emotions, and their receipt of cultural and critical mathematics instruction. We also found an association between the identity profiles and school type (academically selective “magnet” schools vs. open-enrollment neighborhood schools), but not in the direction that might be assumed. Moreover, we found that certain school environment factors (i.e., racial stereotyping and cultural and critical mathematics instruction) were significantly different in racially diverse magnet schools than in the neighborhood schools. Overall, our data reveal the existence of a highly motivated Resistor profile among Black students, that is predicted by cultural and critical mathematics instruction but underrepresented within this district’s selective magnet schools.

Relationships of Abstraction and Application Complexity in the Attainment between Mathematics and Electrical Engineering Modules in Diploma Courses of South Africa

In South Africa, universities are under pressure to meet increasing targets for student enrolment in engineering disciplines and fields. This has resulted in many students being enrolled in engineering programs without possessing the minimum required mathematical skills and understanding to tackle the challenging engineering disciplines. Hence, the engineering disciplines have a high student attrition and failure rate. This study aimed to evaluate the complex relationship of abstraction and application between mathematics attainment and principles of electrical engineering attainment by the students enrolled in diploma courses in technical universities of South Africa. A blend of quantitative and qualitative data was used. Legitimation code theory (LCT) was used to determine the complexity of higher learning levels. The relationships between six core courses in the Electrical Engineering curriculum were investigated to analyze the knowledge building from mathematics modules to principles of electrical engineering modules. The problem-solving, analytics, and abstract mathematical skills developed in these modules impact the overall progression into principles of electrical engineering courses at different levels for diverse students. The research examines the theoretical foundation, student performance, and practical application of mathematical ideas in electrical engineering using curriculum documents, student academic records, and interviews with electrical engineering lecturers. The study found a weak correlation between the two modules and examined how resources, cultural attitudes, and pedagogy affect student achievement. The results indicate an unexpected negative and fragile correlation between the lower mathematics and engineering modules at high levels. The LCT analysis showed the disconnect between the mathematics courses and the principles of electrical engineering in both the level of abstraction used in the studies and the extent of application principles taught.

Associations between children's school wellbeing, mindset and academic attainment in standardised tests of achievement

Childhood wellbeing is essential for positive outcomes in adulthood, as is academic attainment. Schools play a pivotal role in laying the foundations for children to live well. However, research investigating the relationship between wellbeing and attainment has relied on conceptualisations of wellbeing that are too broad (i.e. overall and domain-general wellbeing) or samples spanning large age ranges (thereby overlooking developmental differences). Additionally, the role of mindset, a potentially co-occurring psychological state of both wellbeing and attainment, has been neglected. This study therefore investigated the wellbeing-attainment relationship in 942 children aged 9–11 (447 male, Mage = 10.5; 495 female, Mage = 10.6) across 17 schools in England (UK). Structural equation models distinguished between overall wellbeing, life satisfaction, and eudaimonia, examining associations of each with children's attainment on standardised tests, accounting for mindsets, achievement goals, and sociodemographic factors. Results indicated lower life satisfaction was significantly associated with higher attainment on average, and in English and Mathematics, while eudaimonia was not significantly related to attainment. Overall wellbeing was negatively associated with Mathematics attainment only. A growth mindset was positively associated, while a fixed mindset was negatively associated, with wellbeing. In turn, a growth mindset was significantly positively associated, while a fixed mindset was negatively associated, with attainment. Implications for policy and practice are discussed.

Broken Homes and Intact Homes Students’ Academic Attainment in Mathematics in the Kasena-Nankana Municipality, Ghana

Students’ academic attainment in mathematics can be influenced by several factors including the structure of student’s home. This study was therefore conducted to compare the academic achievement of students from intact homes and their colleagues from broken homes in mathematics in the Kasena-Nankana Municipality, Ghana. The study embraced a survey design using 26 students from broken homes who were purposely and conveniently selected and 26 students from intact homes selected using simple random sampling technique. The study relied on secondary data (mathematics scores from students report cards) and the data was analysed using independent sample t-test. The test results revealed a significant difference in mean scores between the two groups of students and this difference was in favour of the students from intact homes suggesting that students from broken homes performed poorly compared to those from intact homes. The finding implied that, family structure (broken or intact) is a factor that should not be undermined when looking at students’ performances in mathematics. The study concluded that broken home has a negative impact on basic school students’ academic achievement in mathematics.

Shame, entitlement, and the systemic racism of mathematics “ability” grouping in Aotearoa New Zealand

AbstractDecades of research has documented the consequences of allocating school students into a hierarchy of classes with narrow ranges of mathematics attainment, a process known as streaming, tracking, setting, or “ability” grouping. The purported benefits of streaming are inconsistent and disputed, but the harms are clear, in particular, (1) the limiting curriculum often available in low streams and (2) the loss of self-confidence that results from being positioned in a low stream. Building on this foundation, we discuss streaming in mathematics as tied to systemic racism in Aotearoa New Zealand, where the harmful effects of streaming fall most heavily on Māori and Pasifika students. Previous analyses of race and streaming have focused primarily on the racial composition of streamed classes, bias in stream allocation, and racialised teacher expectations in streamed settings. In contrast, we focus on the emotional consequences of streaming, arguing that streaming produces racialised emotions of shame and entitlement as unintended but predictable consequences. We illustrate the racialised production of entitlement and shame through collaborative storying, interweaving our own biographies with a re-analysis of student interviews from two prior studies.

Longitudinal associations between parental mathematics anxiety and attitudes and young children’s mathematics attainment

The associations between parental mathematics anxiety and attitudes and children’s mathematics attainment in early primary school were explored. Initially, parents of preschool children (Mage = 3;11 [years;months]) completed a questionnaire indexing parental mathematics anxiety and attitudes and the frequency of preschool home number experiences. The children completed mathematics assessments in their first year (n = 231, Mage = 5;2) and second year (n = 119, Mage = 6;3) of schooling and a mathematics anxiety questionnaire in their third year of schooling (n = 119, Mage = 6;7). A questionnaire indexing the frequency of primary school home number experiences was completed by 119 of the parents in their children’s second year of schooling (Mage = 6;0). All indices of parental mathematics anxiety and attitudes predicted children’s mathematics attainment in their first school year. These associations were independent of parental mathematics attainment and were not mediated by the frequency of preschool home number experiences. Furthermore, the positive association between preschool home number experiences and children’s mathematics attainment was not weaker in the context of high parental mathematics anxiety or negative parental mathematics attitudes. One index of parental mathematics attitudes predicted children’s mathematics attainment in their second school year, but this association was not significant when prior attainment was controlled. There was a stronger association between maternal mathematics anxiety and girls’ attainment versus boys’ attainment. Parental mathematics anxiety did not predict children’s mathematics anxiety. The findings suggest that children whose parents have high mathematics anxiety or negative mathematics attitudes are more likely to have lower mathematics attainment in their first year of school. However, the mechanism underpinning this association is not yet established.

Early home learning support and home mathematics environment as predictors of children's mathematical skills between age 4 and 6: A longitudinal analysis using video observations and survey data.

This large-scale and longitudinal study examines early home support for learning, formal/informal home mathematics activities, and their associations with children's mathematical development between age two and six. Data were collected in Germany between 2012 and 2018, N = 1184 (49% girls, 51% boys), and 15% of children had parents with a migration history. Linguistically and mathematically stimulating, attentive, and responsive parent-child engagement at age two predicted children's mathematical skills at age four and six (small-to-medium effect size). Both formal and informal home mathematical activities at age five predicted children's mathematical skills at age six (small effect size), and were associated with children's prior mathematics attainment. This study also provides indicators where individual differences and social circumstances are relevant to understanding different early mathematics outcomes.

Beyond Life Satisfaction: Wellbeing Correlates of Adolescents’ Academic Attainment

Academic attainment is a core education policy priority. Wellbeing is recognized as critical for adolescent development, and is linked to academic attainment. Yet research with adolescents primarily focuses on life satisfaction or overall wellbeing, despite differentiating conceptually between two wellbeing components feeling good (life satisfaction) and functioning well (eudaimonia). This study examined whether operationalizing wellbeing as overall, life satisfaction, or eudaimonia, derived different associations with academic attainment. Potentially cooccurring motivational states were also accounted for. Participants were 607 adolescents (354 male, Mage = 15.03; 253 female, Mage = 15.10) from seven English schools (UK). Adolescents’ wellbeing questionnaire responses were matched to prior and current academic attainment in English and Mathematics. Structural equation models demonstrated adolescents reporting higher eudaimonia and overall wellbeing had significantly higher academic attainment in school-based examinations (General Certificate in Secondary Education, England). Life satisfaction was not significantly related to academic attainment. Findings suggest eudaimonia has developmental significance during adolescence, requiring greater attention. Impact Statement This study found adolescents’ overall wellbeing at school was positively associated with their academic attainment in English and Mathematics. Further analyses demonstrated eudaimonia (feeling competent, successful and good about themselves) was the most important wellbeing experience for adolescents’ academic attainment. At the policy-level, implications include ensuring whole-school wellbeing approaches and curricula avoid solely focusing on happiness while overlooking eudaimonia. At the practice-level, findings suggest schools should pay attention to adolescents’ eudaimonia, creating space for adolescents to actively cultivate their personhoods. For example, supporting adolescents to identify their unique talents, set personal goals and contemplate their lives temporary. Overall, our findings suggest teachers can support positive adolescent development by helping pupils make meaningful connections between their personal strengths and academic work, tailored to their life goals and interests.

ILearn? Investigating dialogical interaction with tablets in mathematics lessons

ABSTRACT There is a significant body of research that indicates that the use of tablets to learn mathematics in elementary school motivates students to learn. Low mathematical attainment in international benchmarking tests of mathematics in South Africa led the authors to investigate the potential that the mobility of the tablet provided for children to learn how to reason using what Mercer called ‘exploratory’ talk, a form of dialogical interaction indicative of reasoning. In this article the authors investigate two grade 6 classrooms in two schools where students are learning mathematics using tablets. In this multiple case study, the authors videotaped children during mathematics lessons where they used tablets to solve mathematical problems, and the data were transcribed. Findings indicate that the tablets across both contexts facilitate what Mercer calls exploratory talk, which is indicative of reasoning and, therefore, learning.

Mathematics Anxiety and its Relationship with Mathematics Achievement Among Secondary School Students

: Mathematics attainment has taken on a global focus for the furtherance of economic advancement, thus, magnetizing for the appraisal of mathematical edification among school students. However, evidence suggests that mathematics anxiety is a salient contributing factor that obstructs success in mathematics. Drawing upon the evidence, this investigation explores the relationship between mathematics anxiety, performance and strategies that students perceived that could attenuate mathematics anxiety. Data from this study was collected using the mixed method approach of a survey and interview from forty-two Form One students with different levels of academic achievements from one school in Alor Setar, Kedah, Malaysia. All participants demonstrated a moderate level of mathematics anxiety. However, students from the low performance level displayed inverse and strong relationship between mathematics anxiety and mathematics performance. This indicates that mathematics performance declines with augmented mathematics anxiety. The linear regression revealed that all the three factors of emotion, assessment, and environment are not statistically significant predictors of mathematics achievement. Regardless, emotion has been discerned as a significant predictor of mathematics anxiety for high performance group of students. The interview revealed that students perceive games, cooperative groups, teaching aids, demonstration, rewards, and teachers with positive classroom attitude have contributed to overcoming mathematics anxiety. Results from this study suggest a strong relationship between anxiety and mathematics performance among low performing students which further indicated the importance for mathematics teachers to vary their teaching and learning activities in assisting students to cope with mathematics anxiety.

The effect of siblings’ sex ratio on physical capital, human capital, and gendered time use among adolescents in Ethiopia

We examine the role of siblings’ sex ratio on adolescents’ physical and human capital development, as well as gendered time allocation using data from the Young Lives project in Ethiopia. We use BMI-for-age and Weight-for-age to measure physical capital and grade attainment and scores in Mathematics and English tests as human capital indicators. Gendered time use is proxied by the hours per day the adolescent spends doing traditionally female-specific chores. Our identification strategy relies on the absence of sex-selective reproduction in our study area which implies that for a given number of siblings, their sex ratio should be exogenous. Our results show that having relatively more brothers than sisters increases both physical and human capital for adolescents, typically with a stronger effect for boys. Yet it also increases girls’ time spent on traditionally female-specific tasks, especially in the rural areas. This points to a complex relationship between siblings’ sex composition and long-term life outcomes for women.

Cognitive factors and educational placement affecting mathematical attainment in middle school students with mild intellectual disability

The study investigated the relationship between mathematics achievement, cognitive and motor skills, and general intellectual ability among seventy 10–12 years old students with mild intellectual disability (MID) attending regular school (n = 30) and special school (n = 40). The purpose of the study was to identify the critical deficits teachers need to consider when teaching mathematics at the secondary school level. The students attending regular schools had significantly higher fluid intelligence scores (p = 0.036), but we found no difference in the total score of the math achievement test. Special school students were more eager to use assistance and aids when solving math problems (p = 0.040). The study indicated significant associations between basic mathematical skills, verbal and visuospatial processing, and motor skills. Thus, it is essential to compensate for the delay of students' cognitive development to improve their basic mathematical skills and, in general, mathematical performance. The educational placement affects the willingness or ability to seek academic help when solving mathematical problems.

Factors Influencing Ghanaian Public Junior High School Students’ Performance in English Language, Mathematics and Science and its Implications on the National Policy on Progression

The study examined the factors that influence the performance of students in selected public junior high schools in Ghana using English Language, Mathematics and Science as cases and also to determine whether these observed performances support the continued implementation of the national policy on progression. In all, 98 teachers and 982 Junior High School (JHS) 2 students were randomly selected from three districts in the Central Region of Ghana. Data were analyzed using descriptive statistics (percentages and means) and standard deviation. It was found that the majority of the research participants’ levels of attainment in English Language, Mathematics and Science did not permit automatic progression. Also, it was found that several teacher factors such as the inability to complete the planned curriculum due to numerous co-curricular activities and their challenges in teaching some of the topics may have contributed to the low performance of the students. Recommendations for the need to collect data on students’ performance regularly at the various grade levels through assessment/tests to identify students’ learning difficulties early and offer appropriate interventions to support such learners have been made to further strengthen the progression policy.

Stereotype threat, gender and mathematics attainment: A conceptual replication of Stricker & Ward.

Stereotype threat has been proposed as one cause of gender differences in post-compulsory mathematics participation. Danaher and Crandall argued, based on a study conducted by Stricker and Ward, that enquiring about a student’s gender after they had finished a test, rather than before, would reduce stereotype threat and therefore increase the attainment of women students. Making such a change, they argued, could lead to nearly 5000 more women receiving AP Calculus AB credit per year. We conducted a preregistered conceptual replication of Stricker and Ward’s study in the context of the UK Mathematics Trust’s Junior Mathematical Challenge, finding no evidence of this stereotype threat effect. We conclude that the ‘silver bullet’ intervention of relocating demographic questions on test answer sheets is unlikely to provide an effective solution to systemic gender inequalities in mathematics education.

Clash of cultures? Exploring students’ perceptions of differences between secondary and tertiary mathematics education

Research has identified several aspects that influence students’ transition to mathematics studies at university, but these aspects have often been studied separately. Our study contributes to the field's understanding of the transition between upper secondary and university mathematics by taking a multifaceted perspective not previously explored. We analyse experiences and attainment in mathematics of 154 engineering students with respect to known aspects of this transition, and our results show that it is important to consider several aspects together in order to understand the full complexity of the transition. It is revealed that students with previous experiences of university studies, when compared with new first year undergraduates, perceive a larger difference between studying mathematics at the upper secondary level and university. Our results also show that the engineering students enrolled in distance programmes experience larger differences between secondary and tertiary levels than engineering students enrolled in campus programmes. Furthermore, our analyses show that students’ success in mathematics is related to their perceptions of the rift experienced in the transition. In all, our results highlight the importance of taking a student perspective in the development of explanatory and useful models of students’ transition between upper secondary and university mathematics.