Math Achievement Growth Research Articles

GAMM과 PGM을 적용한 성장모형의 탐색

Exploring a growth model in a longitudinal study is as important as verifying the effectiveness of variables related to growth. In this study, in identifying the growth model, the analysis was conducted using the generalized additive mixed model (GAMM) and the piecewise growth model (PGM) in longitudinal study. For empirical data, GAMM and PGM were used for identifying changes in students' academic achievement in mathematics through the Korean Education Longitudinal Study (KELS-2013) data. As a result, the exponent of the growth model function optimized in GAMM was calculated as 2.98, confirming that the growth model was most suitable for a cubic function. In addition, as a result of verifying the random effect by applying GAMM, a growth of 198.73 points was confirmed in the first year, the starting point of the survey, and it was confirmed that female students showed 2.97 points higher growth than male students in terms of growth in students' math achievement. On the other hand, as a result of applying PGM, the turning point appeared at 2.54, and it was confirmed that the greatest change was shown at the time of school grade change from elementary school to middle school. Such results as in this study show different approaches through GAMM and PGM to explore data-based growth models, and these results can be greatly expanded to analyze growth models such as data-based machine learning methods.

The timing of executive function development is associated with growth in math achievement from preschool through second grade

We examined whether the timing of executive function (EF) development was associated with growth in children's math achievement across eight measurement occasions from preschool through second grade. Using a prospective longitudinal sample of 351 children, we found that children who developed EF later, entered preschool with the lowest levels of math performance and did not catch-up to their intermediate or early EF developing counterparts despite exhibiting a similar math growth rate through second grade. This trend was also observed after controlling for children's biological sex, early language skills, and socioeconomic background. These findings suggest that developing EF late might place children at a unique risk for math difficulties independent of important child and family level characteristics and can provide insights for instructional strategies that take into account differences in children's EF development.

Inattention, hyperactivity/impulsivity, and mathematics: Exploring gender differences in a nonclinical sample

In this study, we considered two subscales of attention problem (AP) behaviour, inattentiveness and hyperactivity/impulsivity, as latent traits, extreme values of which indicate attention deficit hyperactivity disorder (ADHD). We examined gender differences in these traits in a community sample of Russian schoolchildren and estimated the extent to which the association of AP behaviour and math achievement varied for boys and girls. The data from a three-wave longitudinal study of math achievement of 958 children (49 % girls) were used, and growth in math achievement was estimated. The levels of inattentiveness and hyperactivity/impulsivity of each child were measured based on teachers’ responses using the Behaviour Rating Scale (BRS).The results demonstrated that inattentiveness had a negative association with math achievement, while hyperactivity/impulsivity was positively associated with math achievement when inattentiveness was controlled for. Inattentiveness was negatively associated with math achievement in both boys and girls. However, the size of this association decreased over time for boys, so the gap between boys with high inattentiveness and low inattentiveness decreased from grade 1 to grade 2. Meanwhile, for girls, the association between inattentiveness and math remained stable, so the gap between girls with high inattentiveness and girls with low inattentiveness did not change.

Grounding Novel Words Into Emotion: ERP Investigation

In this study, we considered two subscales of attention problem (AP) behaviour, inattentiveness and hyperactivity/impulsivity, as latent traits, extreme values of which indicate attention deficit hyperactivity disorder (ADHD). We examined gender differences in these traits in a community sample of Russian schoolchildren and estimated the extent to which the association of AP behaviour and math achievement varied for boys and girls. The data from a three-wave longitudinal study of math achievement of 958 children (49 % girls) were used, and growth in math achievement was estimated. The levels of inattentiveness and hyperactivity/impulsivity of each child were measured based on teachers’ responses using the Behaviour Rating Scale (BRS).The results demonstrated that inattentiveness had a negative association with math achievement, while hyperactivity/impulsivity was positively associated with math achievement when inattentiveness was controlled for. Inattentiveness was negatively associated with math achievement in both boys and girls. However, the size of this association decreased over time for boys, so the gap between boys with high inattentiveness and low inattentiveness decreased from grade 1 to grade 2. Meanwhile, for girls, the association between inattentiveness and math remained stable, so the gap between girls with high inattentiveness and girls with low inattentiveness did not change.

Children’s Flexible Attention to Numerical and Spatial Magnitudes in Early Childhood

ABSTRACT Young children are sensitive to both numerical and spatial magnitude cues early in development, but many questions remain about how children’s attention to magnitudes relates to their early math achievement. In two studies, we tested three hypotheses related to the flexible attention to magnitudes (FAM) account, which suggests that young children’s flexible attention to both numerical and spatial magnitudes is an important predictor of early math success. In Study 1, we recruited 318 preschool-age children (51.5% female; Mage = 54.7 months, SDage = 4.24 months) and assessed them at two time points on a battery of math, executive function, and language measures, including a novel assessment of FAM ability developed for this study. Consistent with our hypotheses, we found that young children had specific difficulty flexibly shifting between numerical and spatial magnitudes, that their FAM ability was related to both their executive function and math skills controlling for covariates, and finally that their FAM ability at the first time point was predictive of their math achievement growth over time controlling for executive function skills and covariates. In Study 2, we recruited 157 preschool-age children (47.4% female; Mage = 53.36 months, SDage = 7.17 months). We replicated the findings of Study 1 and extended them to account for children’s non-symbolic numerical magnitude discrimination skills. Implications of the results of these studies for early math activities development are discussed.

Fuzzy Regression in Predicting Math Achievement, Based on Philosophic-Mindedness, Creativity, Mathematics Self-efficacy, and Mathematics Self-concept

ABSTRACT The present study proposes a flexible/soft model for investigating the role of philosophic-mindedness, creativity, mathematics self-efficacy, and mathematics self-concept in predicting math achievement. To do this end, a fuzzy regression model is developed. Two common criteria are used to evaluate the obtained model. Moreover, the predictability of the model is explained. The case study involves 28 male students from Marand, Iran (year 2015–2016) who took part in a test of mathematics achievement. The participants were junior high-school students in science field of study who were asked to answer four questionnaires pertaining to philosophic-mindedness, creativity, mathematics self-efficacy, and mathematics self-concept. The analysis of the results through fuzzy regression revealed that philosophical-mindedness is not linked to participants' math achievement, while the variables of creativity, mathematics self-efficacy, and mathematics self-concept are positively correlated. The results of this study provide suggestions to any educational system in planning for students' math achievement growth. The proposed methodology is general, so that it can be employed in other educational levels and fields of study.

Selective Enrollment Public Schools and District-Level Achievement Outcomes from 3rd to 8th Grade

Fierce local debates throughout the United States surround the equity of admitting students to public schools using academic criteria. Although research has evaluated the central assumption of these debates—that Selective Enrollment Public (SEP) schools enhance the welfare of students who attend them—none has addressed the district-level outcomes associated with these schools. This is important because the selectivity and scope of SEP schools produce tiered school systems (SEP districts). This district-level process, in turn, calls for an analysis of district-level achievement outcomes. To address this gap, I compile an original list of SEP schools using an innovative web scraping procedure. I combine these data with newly available district-level measures of third to eighth grade achievement from the Stanford Education Data Archive. Analyses follow a difference-in-differences design, using grade level as the longitudinal dimension. This approach facilitates a falsification test, using future treated districts, to reject spurious causation. I find evidence of overall slower growth in mean math achievement in SEP districts and for white, black, and Latinx racial/ethnic groups separately. SEP districts also see an increase in the white–Latinx math achievement gap. This work highlights the importance of considering SEP schools as part of a differentiated school system.

School Readiness Profiles and Growth in Academic Achievement

The purpose of this research was to identify the presence of different school readiness profiles and to determine whether profiles could differentially predict academic growth. The Early Childhood Longitudinal Study: 2010-11 (ECLS-K: 2011) public data set was used, and participants were 14,954 first-time kindergarteners. The age of entering kindergarten ranged from 44.81–87.98 months with a mean of 76.13 months. In Study 1, a six-dimensional construct of school readiness was used: health, self-regulation, social and emotional development, language development, cognitive development, and approaches to learning. Results revealed 41 profiles with the top six school readiness profiles covering 85% of the sample: (1) Positive Development (28%); (2) Comprehensive At-Risk (24%); (3) Personal and Social Strengths (20%); (4) Cognitive and Language Strengths (5%), (5) Health Strength (5%); and (6) Cognitive, Personal and Social Strengths (3%). Study 2 examined whether school readiness profiles could predict children’s reading and math achievement growth using growth curve models. Results showed that different school readiness profile membership had unique academic growth patterns and could predict academic growth above and beyond child and family background variables. Moreover, children with the Positive Development profile had higher academic achievement over time. Children with the Personal and Social Strengths profile had the largest growth rates. In sum, findings support the inclusion of self-regulation as another dimension of school readiness and the important role of personal and social skills in the development of reading and math achievement.

The Role of School Adaptation and Self-Concept in Influencing Chinese High School Students' Growth in Math Achievement.

A longitudinal designed research study was conducted to provide empirical evidence regarding the influences of three dimensions of students’ school adaptation on their math achievement growth over the first year of high school. These dimensions included learning adaptation, stress management, and personal communication. Student math achievement growth was measured using the student growth percentile (SGP) score. Structural equation modeling (SEM) was used to test for the possible mediating role of self-concept behind those three relationships. Based on the model comparison, it was discovered that school adaptation significantly and positively influences student math achievement growth via mediating effects of student academic self-concept, as opposed to showing a direct impact on students. The findings of this study have important implications for educators and parents to aid students in their pursuit of academic success.

How School Socioeconomic Status Affects Achievement Growth across School Transitions in Early Educational Careers

Our study investigates how changing socioeconomic status (SES) composition, measured as percentage free and reduced priced lunch (FRL), affects students’ math achievement growth after the transition to middle school. Using the life course framework of cumulative advantage, we investigate how timing, individual FRL status, and legacy effects of a student’s elementary school SES composition each affect a student’s math achievement growth. We advance research on school transitions by considering how changing contexts affect achievement growth across school transitions. Furthermore, we improve on school context research by measuring the ways that SES compositions across school transitions may be interconnected. Using state administrative panel data for third through eighth graders from 2009 to 2015, we use fixed effects to estimate math achievement growth by the end of eighth grade. Findings suggest that a student’s elementary SES composition has a legacy effect on middle school achievement growth net of his or her own achievement growth and middle school SES composition. In addition, SES composition effects differ depending on the timing of exposure and a student’s individual FRL status. Our study has important implications for both educational transition research and school effects research, which are discussed.

School District Reform in Newark: Within- and Between-School Changes in Achievement Growth

In the 2011–12 school year, the Newark Public School district (NPS) launched a set of educational reforms supported by a gift from Facebook CEO Mark Zuckerberg and Priscilla Chan. Using data from 2008–09 through 2015–16, the authors evaluate the change in Newark students’ achievement growth relative to similar students and schools elsewhere in New Jersey. They measure achievement growth using a “value-added” model, controlling for prior achievement, demographics, and peer characteristics. By the fifth year of reform, Newark saw statistically significant gains in English language arts (ELA) achievement growth and no significant change in math achievement growth. Perhaps because of the disruptive nature of the reforms, growth declined initially before rebounding in later years. Much of the improvement was attributed to shifting enrollment from lower- to higher-growth district and charter schools.

Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study.

Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics. In the current study I ask whether students may be motivated to forget mathematics because of academic experiences threaten the self-perceptions they are committed to maintaining. Using a large dataset of 1st and 2nd grade children (N = 812), I hypothesize that math anxiety creates negative experiences in the classroom that threaten children’s positive math self-perceptions, which in turn spurs a motivation to forget mathematics. I argue that this motivation to forget is activated during the winter break, which in turn reduces the extent to which children grow in achievement across the school year. Children were assessed for math self-perceptions, math anxiety and math achievement in the fall before going into winter break. During the spring, children’s math achievement was measured once again. A math achievement growth score was devised from a regression model of fall math achievement predicting spring achievement. Results show that children with higher math self-perceptions showed reduced growth in math achievement across the school year as a function of math anxiety. Children with lower math interest self-perceptions did not show this relationship. Results serve as a proof-of-concept for a scientific account of motivated forgetting within the context of education.

The role of PS ability and RC skill in predicting growth trajectories of mathematics achievement

There are relatively few studies in Australia and South-East Asian region that combine investigating models of math growth trajectories with predictors such as reasoning ability and reading comprehension skills. Math achievement is one of the major components of overall academic achievement and it is important to determine what factors (especially domain-general factors) predict levels of achievement over time. This study presents large-scale data (N = 5,886) from Australia to examine the trajectories of growth in math achievement and how problem solving (PS) ability and reading comprehension (RC) skills predict this growth among government school students (grades 3–8) in Victoria. Latent growth modelling showed that PS ability predicts growth in math achievement and this relationship is partially mediated by RC skill. Both PS ability and RC skill predict initial status in math achievement, but only PS ability predicts growth. The data also fit a model in which an improvement in general reasoning ability of students allows those with lower initial levels in math achievement to catch up. This can be interpreted as evidence that improving growth rates in PS ability may lift growth rates in math achievement.

The long-term differential achievement effects of school socioeconomic composition in primary education: A propensity score matching approach.

The effects of school socio-economic composition on student achievement growth trajectories have been a hot topic of discussion among politicians around the world for many years. However, the bulk of research investigating school socio-economic composition effects has been limited in important ways. In an attempt to overcome the flaws in earlier research on school socio-economic composition effects, this study used data from a large sample, followed students throughout primary education, addressed selection bias problems, identified the grade(s) in which school socio-economic composition mattered the most, and studied the differential effects of school socio-economic composition by individual socio-economic status (SES). In a longitudinal design with seven occasions of data collection, the authors drew on a sample of N=3,619 students (age at T1 about 5years, age at T7 about 12years) from 151 primary schools in Flanders (the northern part of Belgium). Students in low-, medium-, high-, and mixed-SES schools were matched using propensity scores. To compare students' achievement growth trajectories in the different school compositions, multilevel regression modelling with repeated measurements was applied. The results showed that students had more positive achievement growth in high-SES as compared to low-SES and mixed-SES schools. In two of the three comparisons, students in mixed-SES schools showed the lowest math development. The negative effects of mixed-SES schools on math achievement growth were the strongest for high-SES students. Our findings contribute to the ongoing discussion on the effects of school socio-economic composition on student achievement growth.

Teacher–child relationship quality and academic achievement in elementary school: Does gender matter?

Using data from the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development (N = 1,364) and 2-level hierarchical linear models with site fixed effects, we examined between- and within-child associations between teacher–child relationship closeness and conflict and standardized measures of children’s math and reading achievement from 1st through 5th grades. In addition, we tested whether longitudinal effects varied by gender. Results revealed a between-child effect of conflict and a within-child effect of closeness on reading achievement for the full sample. In addition, there were moderated between- and within-child effects of conflict on math achievement: Girls with more conflictual relationships showed lower overall levels of math achievement and less growth in math achievement than did boys with similar levels of conflict. Implications are discussed.

Bayesian longitudinal item response modeling with restricted covariance pattern structures

Educational studies are often focused on growth in student performance and background variables that can explain developmental differences across examinees. To study educational progress, a flexible latent variable model is required to model individual differences in growth given longitudinal item response data, while accounting for time-heterogenous dependencies between measurements of student performance. Therefore, an item response theory model, to measure time-specific latent traits, is extended to model growth using the latent variable technology. Following Muthen (Learn Individ Differ 10:73---101, 1998) and Azevedo et al. (Comput Stat Data Anal 56:4399---4412, 2012b), among others, the mean structure of the model represents developmental change in student achievement. Restricted covariance pattern models are proposed to model the variance---covariance structure of the student achievements. The main advantage of the extension is its ability to describe and explain the type of time-heterogenous dependency between student achievements. An efficient MCMC algorithm is given that can handle identification rules and restricted parametric covariance structures. A reparameterization technique is used, where unrestricted model parameters are sampled and transformed to obtain MCMC samples under the implied restrictions. The study is motivated by a large-scale longitudinal research program of the Brazilian Federal government to improve the teaching quality and general structure of schools for primary education. It is shown that the growth in math achievement can be accurately measured when accounting for complex dependencies over grades using time-heterogenous covariances structures.

Behavioral Engagement in Learning and Math Achievement over Kindergarten: A Contextual Analysis

Using nationally representative data on 12,462 kindergarten children, this report examines the link between behavioral engagement and math achievement growth during kindergarten. Multilevel models show that students with higher individual engagement tend to experience larger math achievement growth over kindergarten, that classroom engagement makes a difference in how much achievement growth students experience over kindergarten, and that students with higher individual engagement benefit more from being in highly-engaged classrooms than children with lower individual engagement. Students with higher math test scores at kindergarten entry also benefit more from highly-engaged classrooms than children with lower prior math scores. Results from this study provide new evidence that behavioral engagement affects students’ achievement growth on multiple levels, with the individual, the classroom environment, and the interaction of the individual and classroom environment all relating to math outcomes. Evidence...

Motivation + Skill = Success

Education![Figure][1] CREDIT: THINKSTOCK Both motivational and cognitive variables play a role in academic achievement. The relationship between these variables and academic success at a specific time point has been described, yet there has been little research on whether these variables can predict long-term academic gains. Controlling for intelligence, Murayama et al. examined how motivation and strategies used by students to learn the material related to growth in academic achievement in mathematics over time. German students in grades 5 to 10 were assessed longitudinally for both math skills and self-reported motivation and learning strategies, and latent growth curve modeling was used to evaluate growth in mathematics achievement. Results showed that although the initial level of achievement was strongly related to intelligence, motivation and learning strategies predicted growth in math achievement over time. Although correlational, these findings suggest that motivation and learning strategies should be further examined, as one of the ultimate goals in education is to enable sustainable learning. Child Dev. 10.1111/cdev.12036 (2012). [1]: pending:yes

Classroom order and student learning in late elementary school: A multilevel transactional model of achievement trajectories

This study examines the association between classroom order in 4th and 5th grades and student achievement growth over a school year. A three level transactional model tested the effects of classroom order on students' rates of growth in math and reading during the school year controlling for starting achievement levels, student risk factors, and classroom poverty. Classroom order influenced students' rates of math and reading growth and accounted for a significant portion of variance in student achievement trajectories above and beyond student-level risk factors. Cross-level analyses identified the moderating effects of classroom order on achievement growth for at-risk students with higher levels of classroom order predicting greater rates of math achievement growth among disadvantaged minority students.

The Impact of Peer Ability and Heterogeneity on Student Achievement: Evidence from a Natural Experiment

This paper estimates the impact of peer achievement and variance on math achievement growth. It exploits exogenous variation in peer characteristics generated at the transition to upper-secondary school in a sample of Berlin fifth graders. Parents and schools are barely able to condition their decisions on peer characteristics since classes are newly built up from a large pool of elementary school pupils. I find positive peer effects on achievement growth and no effects for peer variance. Lower-achieving pupils benefit more from abler peers. Results from simulations suggest that pupils are slightly better off in comprehensive than in ability-tracked school systems.