Grade Math Research Articles

Education pathways to the labour market for 16-year-olds who struggle to achieve maths and English in General Certificate of Secondary Education

We examine the post age-16 educational pathways taken by the 44% of young people who do not gain “good” grades in English and Maths at age 16 years. We then assess the causal effects of attending General Further Education (GFE) colleges on education and labour market outcomes for this group.
 We use the Longitudinal Education Outcomes dataset, which comprises linked administrative education, employment and income records for the population of English school pupils aged 16 in 2011. To summarise complex post-16 education trajectories, we present Sankey charts stratified by indicators of disadvantage. We study the effects of attending GFE at age 17 on whether a pupil gains a Level 3 qualification by age 19, and their earnings and employment status at age 24. To estimate a causal impact, we use distance from home to the closest GFE college as an instrumental variable, controlling for a rich set of background characteristics.
 Our graphical results highlight the complexity of post-16 educational pathways and transitions, which are differentiated by disadvantage. Over 50% have GFE as their first post-16 destination. Results from instrumental variable analyses show a positive association between attending GFE and gaining a Level 3 qualification by age 19, among pupils who do not gain a “good” pass in the General Certificate of Secondary Education (GCSE) in either English and/or Maths. Restricting analyses to the bottom of the distribution – those who gain an E, F or G grade in both English and Maths - we do not detect an impact of GFE on qualifications at age 19. Among both subgroups, we do not detect any impact of attending GFE on earnings and employment at age 24 years.
 While the post-16 pathways taken by disadvantaged, lower-attaining pupils do increase qualification attainment for some, the value these have in the labour market appears limited. These results may indicate the importance of “soft-skills” and early employment experiences for this subgroup of lower-attainers.

A Survey and Research on High School Students' Motivation for Mathematics Learning

In our real life, any activity of people is motivated and directed towards a certain purpose, so learning activities are also the same. At the same time, high school grades are to some extent determined by learning motivation. This survey of high school students' learning motivation is not only conducive to discovering the current situation, but also to developing students' mathematical literacy. The following conclusions are drawn in this article: (1) The overall level of mathematical motivation among high school students is relatively high, but in both dimensions, external learning motivation is weaker. (2) There are differences in learning motivation among different grades, and the second year of high school is a low period. (3) There is no significant difference between mathematical motivation and gender. (4) There is not much difference between math motivation and math grades, so poor math grades do not necessarily mean poor math learning motivation. (5) The factors of teachers, parents, and classmates cannot be ignored.

Predicting students’ math self-concepts to explain gender differences through teachers’ judgments and students’ perceived teachers’ judgments

The present study examined to what extent teachers’ judgments of students’ aptitude and students’ perceived teachers’ judgments explain gender differences in the early development of students’ math self-concepts. A sample of N = 519 elementary school students was investigated at four measurement occasions from the end of third until the end of fourth grade. We assessed students’ self-concepts and their perceived teachers’ judgments of their aptitude in math. Teachers (N = 27) judged students’ aptitude in math and provided students’ math grades. First, we found significant gender differences in students’ math self-concepts, teachers’ judgments, and students’ perceived teachers’ judgments, but not in students’ math grades. Second, structural equation models showed that teachers’ judgments of students’ aptitude as well as students’ perceived teachers’ judgments of students’ aptitude longitudinally predicted students’ self-concepts. Mediation analyzes demonstrated that teachers’ judgments and students’ perceived teachers’ judgments contributed to gender differences in students’ math self-concepts. Implications for future research and practice are discussed.

Improving Community College Students’ Success in Math: Findings From Two Utility-Value Studies

Although designed to prepare students for future coursework or to fulfill basic degree requirements, introductory math courses often serve as barriers to student success. In two double-blind randomized field experiments, we tested the efficacy of a utility-value intervention on improving community college students’ perceived math relevance and achievement in introductory math courses. Building upon prior research, we examined whether the intervention particularly benefited first-generation and racially marginalized students. Study 1 (N = 696) was conducted before the COVID-19 pandemic and within in-person classrooms, whereas Study 2 (N = 1,318) was conducted during the pandemic and within virtual learning environments. Across Studies 1 and 2, students in the utility-value condition benefited more in terms of their perceived relevance compared to their peers in the control condition. Additionally, in both studies, math relevance mediated the effects of the intervention on math grades. In Study 2, with a larger sample, the positive effect of the intervention on math relevance was more pronounced for first-generation students. Our findings imply that community colleges could significantly improve students’ academic experiences by investing in motivation-enhancing activities such as utility-value interventions in introductory math courses. This strategy could especially help first-generation students’ academic achievement and retention rates.

Elementary Teachers’ Perceptions and Reported Enactment of Autonomy From Prescribed Pacing Guides

Pacing guides are commonplace yet controversial in American public schools. For teachers who question their usefulness, one means to circumvent them is to exercise autonomy in pedagogical decision-making, though doing so comes with challenges. Through interviews, we examined how 87 gifted and general education 4th and 5th grade math and reading/language arts teachers in one large, diverse public school district expressed their autonomy and reported enacting it in their classrooms. Findings indicated teachers’ perceptions of autonomy differed, and their reported pacing guide deviations also differed accordingly. We discuss implications for those in environments where use of pacing guides is mandated.

Self-Determination in Maths Education: How to Strengthen Students’ Positive Attitude to Mathematics and Develop Their Emotional/Social Competences

The aim of this study was to verify the effectiveness of the self-determination theory (SDT) in mathematics teaching methodology. In the experimental group, 62 fifth-graders had 10 months of maths lessons according to an original programme that prioritises three needs: autonomy, competence and relatedness.
 The following research questions were formulated:
 
 How did students’ attitudes towards mathematics change under the influence of methodological interventions aimed at satisfying the three SDT needs?
 Did the methodological solutions contribute to better emotional/social competences in the students?
 Did the intervention result in higher maths achievement, measured by a maths knowledge and skills test and grades in the subject?
 
 The findings included statistically significant differences in 1) positive attitude towards mathematics (measured by the semantic differential technique), 2) emotional/social competences (measured by the KA scale from the tool called TROS-KA) and 3) mathematical achievements (measured by a maths test and grades in school) in comparison to the control group (N = 59), where less positive attitudes towards mathematics, lower maths grades and no significant increase in emotional/social competences were observed.

Noticing for Equity in Written Work: Exploring One Teacher’s Student Work Analysis Practices

ABSTRACT Attending to students’ thinking and using it to inform instruction has been shown to be an effective and equitable teaching practice. Research on teachers’ noticing of thinking conceptualizes noticing as a cognitive process, while work on noticing for equity treats noticing as culturally situated but primarily focuses on participation. Drawing on theories of noticing thinking and noticing for equity, I extend noticing for equity to students’ written work. This article describes a case study of what and how one sixth grade math teacher noticed when analyzing her students’ written work, as well as what connections existed between her pedagogical commitments and her noticing. Close examination of this teacher’s student work analysis revealed that she (1) attended to the details of students’ strategies with an inquiry stance, (2) contextualized their understandings through a dual lens on student and teacher, (3) interpreted understandings through a strengths-based lens, and (4) planned to respond by identifying a range of work to share with the class. Additionally, this teacher’s pedagogical commitments and equity stance were embedded in much of her noticing. Findings suggest important theoretical intersections between noticing of thinking and noticing for equity.

Math-Failure Associations, Attentional Biases, and Avoidance Bias: The Relationship with Math Anxiety and Behaviour in Adolescents

BackgroundMath anxiety in adolescence negatively affects learning math and careers. The current study investigated whether three cognitive biases, i.e. math-failure associations, attentional biases (engagement and disengagement), and avoidance bias for math, were related to math anxiety and math behaviour (math grade and math avoidance behaviour).MethodsIn total, 500 secondary school students performed three cognitive bias tasks, questionnaires and a math performance task, and reported their grades.ResultsMath-failure associations showed the most consistent associations with the outcome measures. They were associated with higher math anxiety above and beyond sex and education level. Those math-failure associations were also associated with lower grades and more avoidance behaviour, however, not above and beyond math anxiety. Engagement bias and avoidance tendency bias were associated with math avoidance behaviour, though the avoidance bias finding should be interpreted with care given the low reliability of the measure. Disengagement biases were not associated with any math anxiety nor behaviour outcome measure.ConclusionsWhereas a more reliable instrument for avoidance bias is necessary for conclusions on the relations with math performance and behaviour, the current results do suggest that math-failure associations, and not attentional bias, may play a role in the maintenance of math anxiety.

Profiles of afterschool motivations: A situated expectancy-value approach

Despite the benefits of afterschool programs, we know very little about what motivates adolescents to attend and what costs they might associate with doing so. Situated expectancy-value theory (SEVT) proposes that expectancy for success, value, and cost perceptions are motivational beliefs that are important precursors to students’ engagement in such programs, and thus may shape the extent to which students can benefit from them. Accordingly, we examined profiles of expectancy, value, and cost beliefs associated with afterschool program participation in a sample of middle school students (N = 197) in an urban context. We then examined profiles for their relations to student demographics (gender, grade, race/ethnicity), achievement (English and Math grades), and program attendance. Latent profile analyses yielded three profiles: a moderate-low mixed motivation profile, a high cost and mixed motivation profile, and a positively motivated with moderate effort cost profile, thus uniquely contributing to the literature by describing the nature and incidence of how multiple motivational beliefs co-occur among groups of students in afterschool spaces. Subsequent analyses revealed that the positively motivated with moderate effort cost profile was associated with higher program attendance rates than the other two profiles. These results extend the theoretical knowledge base by exploring students’ expectancies, values, and costs in an informal educational context and have important implications for afterschool educators and policymakers.

Assessment of Students’ Mathematical Skills in Relation to Their Strengths and Weaknesses, at Different Levels of the European Qualifications Framework

Many scientific studies focus on finding the relationship between students’ mathematical skills and socio-economic, demographic, and ontogenetic factors. In this publication, we answer the question of how students’ mathematical skills are achieved in relation to their strengths and weaknesses, also with regard to the use of mathematics in everyday life. In this article, we examine the relationship between the results of the mock final math exam for eighth grade primary school students/final year high school students and additional math classes, the application of math in everyday life and the greatest difficulties with specific areas of taught material. The study was conducted in Poland on almost ten thousand eighth graders and high school leavers who took part in mock exams online, respectively: eighth-grader exam, and school-leaving maturity exam. The participants of these online exams were asked to respond to a survey that pertained to their math grades, attending additional math classes, their perceived most useful mathematical topics in everyday life and future professional work, and identification of their strengths and weaknesses. In the following paper, the relationships between the answers to the survey questions and the results of the mock online exam are analyzed. The results indicate that there are differences in the area of results of the mock exam and answers about strengths and weakness in mathematical literacy. The analysis of answers about use the mathematical knowledge are different for eight-graders and high-school students. Eight-graders indicate the importance of arithmetic operations while high -school students point out more abstract topics like probability, statistics and geometry. The results of the study are compared to the existing results.

A novel machine-learning tool to identify community risk for firearm violence: The Firearm Violence Vulnerability Index.

Firearm violence in the United States is a public health crisis, but accessing accurate firearm assault data to inform prevention strategies is a challenge. Vulnerability indices have been used in other fields to better characterize and identify at-risk populations during crises, but no tool currently exists to predict where rates of firearm violence are highest. We sought to develop and validate a novel machine-learning algorithm, the Firearm Violence Vulnerability Index (FVVI), to forecast community risk for shooting incidents, fill data gaps, and enhance prevention efforts. Open-access 2015 to 2022 fatal and nonfatal shooting incident data from Baltimore, Boston, Chicago, Cincinnati, Los Angeles, New York City, Philadelphia, and Rochester were merged on census tract with 30 population characteristics derived from the 2020 American Community Survey. The data set was split into training (80%) and validation (20%) sets; Chicago data were withheld for an unseen test set. XGBoost, a decision tree-based machine-learning algorithm, was used to construct the FVVI model, which predicts shooting incident rates within urban census tracts. A total of 64,909 shooting incidents in 3,962 census tracts were used to build the model; 14,898 shooting incidents in 766 census tracts were in the test set. Historical third grade math scores and having a parent jailed during childhood were population characteristics exhibiting the greatest impact on FVVI's decision making. The model had strong predictive power in the test set, with a goodness of fit ( D2 ) of 0.77. The Firearm Violence Vulnerability Index accurately predicts firearm violence in urban communities at a granular geographic level based solely on population characteristics. The Firearm Violence Vulnerability Index can fill gaps in currently available firearm violence data while helping to geographically target and identify social or environmental areas of focus for prevention programs. Dissemination of this standardized risk tool could also enhance firearm violence research and resource allocation. Prognostic and Epidemiological; Level IV.

Paternal mind-mindedness and children's academic achievement: Investigating developmental processes.

This study tested a 5-year sequential mediation model linking paternal mind-mindedness in toddlerhood to child early academic achievement through a developmental process unfolding in the preschool years. A sample of 128 mostly White middle-class families (68 girls) living in Montreal, Canada was assessed for paternal mind-mindedness when children were 18 months old, child language at age 2, theory of mind and effortful control at age 4, cognitive school readiness in kindergarten, and finally, achievement in math and reading in first grade. Controlling for maternal mind-mindedness assessed at age 12 months, the results showed prospective associations from paternal mind-mindedness to both math and reading achievement, mediated by theory of mind, effortful control, and school readiness in sequence. Results suggest that paternal mind-mindedness may support child academic outcomes by promoting the acquisition of intermediate skills during preschool years. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Universal Early Childhood Education and Care for Toddlers and Achievement Outcomes in Middle Childhood

We estimated the effects of Norway’s universal ECEC program—expanding access to 1- and 2-year-olds starting in the early 2000s—on standardized math and achievement tests in 5th grade (age 10) using a population-based survey sample (Norwegian Mother, Father, and Child Cohort Study, MoBa, n = 102,352), linked with national administrative records of child achievement test scores. We used two methods to test the effects of attending ECEC: fixed-effects and instrumental variable regressions. Although both approaches found small and mostly insignificant main effects, the effect of ECEC is consistently stronger for children from families with low parental education. The fixed-effects analyses showed that ECEC reduced inequalities in achievement across levels of parental education by about 10% while the instrumental variable analyses, using variation in ECEC induced by the expansion, showed reduction of about 50%. These results suggest that expanding access to ECEC for toddlers has the potential to reduce achievement inequality.

Expert Teams in Instructional Leadership Practices Based on Collaboration and Their Transference to Local Teaching Improvement Networks

This article shows the research results of implementing a professional learning model based on instructional leadership practices and structured teacher collaboration. The primary purpose was to promote a collaboration model focused on developing communities of practice, formed by school leaders and teachers, focusing on instructional improvement in 8th grade Math and English. The model consists of a cycle with 4 iterative practices: planning, classroom observation, feedback, and refinement and three guiding principles: deprivatisation, collaboration, focus on learning. The methodological approach was a design-based research model, with school teams (within-school level) and collaboration networks (between schools-level) that included principals and teachers. 22 schools in two districts in Chile, 44 school leaders, 74 teachers, 49 non-participating teachers as a control group, and at least 1,000 students in 40 classes were part of the study sample that participated in the research between 2019 and 2020. Mixed methods were used for data analysis. The research team conducted a five-scale questionnaire and semi-structured interviews with participants and non-participants teachers as the control group. The main progress was the deprivatisation of pedagogical practice and joint decision-making for teaching improvement. The practical implications of the model, adjusted for local characteristics, are that it facilitates professional development at three levels: individual, within school teams, and allows professional exchange between schools. It enabled the enactment of peer collaboration practices, and the role of instructional leadership shared between teachers and the school leadership team members were bolstered.

Is There Evidence for Intelligence-by-Conscientiousness Interaction in the Prediction of Change in School Grades from Age 11 to 15 Years?

Fluid intelligence and conscientiousness are the most important predictors of school grades. In addition to this main effect, researchers have suggested that the two traits might also interact with each other in the prediction of school success. A synergistic and a compensatory form of interaction have been suggested, but past evidence has been mixed so far. Most previous studies on this subject have been cross-sectional and many of them focused on older adolescents or adults in upper secondary school or university. We thus investigated the main and interaction effects of fluid intelligence and conscientiousness on school grades in math and German in a longitudinal sample of 1043 German students from age 11 to 15 years. Results from latent growth curve models with latent interaction terms showed a small compensatory interaction effect for baseline levels of math grades but not for their development. No interaction effect was found for German grades. These findings are discussed against the background that (synergistic) interaction effects between intelligence and conscientiousness might be more relevant in older students from higher secondary school or university context.

Race, academic achievement and the issue of inequitable motivational payoff.

As racial inequities continue to pervade school systems around the world, further research is necessary to understand the factors undergirding this pressing issue. Here across three studies conducted in the United States (N = 8,293), we provide evidence that race-based differences in student achievement do not stem from a lack of motivation among Black, Latinx and Indigenous (BLI) students, but a lack of equitable motivational payoff. Even when BLI and non-BLI students have the same levels of motivation, BLI students still receive maths grades that are an average of 9% lower than those of their non-BLI peers (95% confidence interval 7 to 11%). This pattern was not explained by differences in students' aptitude, effort or prior achievement but was instead linked to teachers' diminished expectations for their BLI students' academic futures. We conclude by discussing statistical power limitations and the implications of the current findings for how researchers consider the sources of, and solutions for, educational inequity.

Charter Schools and the Segregation of Students by Income

The share of students attending charter schools has been rising. There is evidence that charter school growth has increased socioeconomic segregation of students between schools. In this paper, we assess whether charter school growth affects how students are organized within nearby traditional public schools (TPS). We use administrative data from North Carolina to estimate the impact of charter school openings on segregation by income within nearby TPS. Our models exploit variation in the presence and location of charter schools over time between 2007 and 2014 for students in Grades 3 to 8. We find limited evidence that the segregation of students by income at the classroom level increases when charters open nearby. We find some evidence of increasing segregation in third grade and fourth grade math and third grade ELA classrooms at TPS within 2 miles of new charters in large urban districts schools. Our results vary somewhat depending on how we control for underlying trends and measure segregation. We find no effect of charter school growth on income segregation in higher grades.

Student achievement trajectories in Ontario: Creating and validating a province-wide, multi-cohort and longitudinal database.

Longitudinal data that tracks student achievement over many years are crucial for understanding children's learning and for guiding effective policies and interventions. Despite being Canada's most populous province, Ontario lacks such large-scale and longitudinal data on student learning. Linking datasets across cohorts requires rigorous linkage protocols, flexible handling of complex cohort structures, methods to validate linked datasets, and viable organizational partnerships. We linked administrative data on early child development and educational achievement and merged two datasets on characteristics of students' neighborhoods and schools. We developed a linkage protocol and validated how the resulting database could be generalized to Ontario's student population. Two main individual-level data sources were linked: 1) the Early Development Instrument (EDI), a school readiness assessment of all Ontario public school kindergartners that is administered in three-year cycles, and 2) Ontario's Educational Quality and Assessment Office's (EQAO) math and reading assessments in grades 3, 6, 9, and 10. To compensate for their lack of a common personal identification number, a deterministic linkage process was developed using several administrative variables. A school-level and a neighborhood-level dataset were also later linked. We examined differences between unlinked and linked cases across several variables. We successfully linked 50% of the EDI's 374,239 cases, 86,778 of which contained all five datapoints, creating a database tracking achievement for multiple cohorts from kindergarten through grade 10, with covariates for their development, demographics, affect, neighborhoods, and schools. Analyses revealed only negligible differences between linked and unlinked cases across several demographic measures, while small differences were detected across a neighborhood socioeconomic index and some measures of child development. In conclusion, we recommend the filling of key voids in sustainable research capacity by creating representative data through linkage protocols and data verification.

Linear and nonlinear relationships between self-evaluation and self-evaluation bias with grades

There is an ongoing debate whether a bias in self-evaluated competence (SE bias) affects academic achievement, typically assessed as grades. Different rationales about possible relations (e.g., linear, nonlinear, or no relations) between SE bias and academic achievement have been proposed. We compared these rationales in a study with 504 secondary school students in highest academic track secondary schools in math, using response surface analysis (RSA). At t1, students' self-evaluated math competence, their competence in math (i.e., objective competence test scores), and their academic achievement in math (i.e., math grades) were assessed. At t2, students' math grades were assessed again. The model that fit the data best was the beneficial self-evaluation and competence model, positing only linear relationships of self-concept and competence with change in grades beyond control variables (i.e., gender, parental education, number of books at home) and no SE bias effects.

Understanding Basic Relational Concepts in Directions: A Study of Native Mexican and U.S. Children in Early Elementary Grades

The present study uses both quantitative and qualitative approaches to examine: (1) U.S. and Mexican children’s ability to understand basic relational concepts in directions; and (2) to analyze language arts and math textbooks to determine the levels of complexity in directions (i.e., number of qualifiers or concepts embedded in the directions). A total of 265 first grade (n = 128) and second-grade (n = 137) children in Mexico were assessed using the Boehm Test of Basic Concepts-Revised (BTBC-R) Applications Booklet. Their performance was compared to the U.S. standardized sample of the BTBC-R to make cross-cultural comparisons. Results from the quantitative study suggest that U.S. children at both grade levels outperformed Mexican children on direction following tasks. Furthermore, both cultural groups demonstrated developmental progression from first to second grade. Qualitative analysis of language arts and mathematics textbooks in both U.S. and Mexico revealed that the majority of instructions had “no complexity.” Mexico’s first grade language arts textbooks had significantly more “no complexity” directives than the U.S. textbooks; whereas first grade math textbooks in Mexico had significantly more “moderately complex” directives than in the U.S. The “very complex” directives were minimal in both cultures. Cross-cultural differences were discussed in terms of linguistic transparency, conceptual complexity, item biases, and the education system.