Math Achievement Growth Research Articles

Sensitivity of Fit Indices to Misspecification in Growth Curve Models

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of approximation, standardized root mean square residual, comparative fit index, and Tucker-Lewis Index. The fit indices were found to have differential sensitivity to different types of misspecification in either the mean or covariance structures with severity of misspecification controlled. No fit index was always more (or less) sensitive to misspecification in the marginal mean structure relative to those in the covariance structure. Specifying the covariance structure to be saturated can substantially improve the sensitivity of fit indices to misspecification in the marginal mean structure; this result might help identify the sources of specification error in a growth curve model. An empirical example of children's growth in math achievement (Wu, West, & Hughes, 2008) was used to illustrate the results.

Measuring Academic Growth in Students With Disabilities in Charter Schools

In the current climate of high-stakes accountability created under the No Child Left Behind legislation, public schools, including charter schools, are under tremendous pressure to show consistent improvement in student achievement for all students. Students with disabilities present unique challenges to schools attempting to meet Adequate Yearly Progress. An accountability system that relies exclusively on students’ ability to meet a fixed proficiency level is now under great scrutiny. Indeed, efforts to pilot an assessment system that measures individual students’ growth are underway in a number of states.What can be learned from analyzing the achievement of students with disabilities using a growth model? This question became the focus of a study conducted in 4 urban charter schools where growth in reading and math achievement were examined for students with and without disabilities. The challenges with measuring growth in charter environments and implications for policies around accountability are examined.

Assessing the Contribution of Distributed Leadership to School Improvement and Growth in Math Achievement

Although there has been sizable growth in the number of empirical studies of shared forms of leadership over the past decade, the bulk of this research has been descriptive. Relatively few published studies have investigated the impact of shared leadership on school improvement. This longitudinal study examines the effects of distributed leadership on school improvement and growth in student math achievement in 195 elementary schools in one state over a 4-year period. Using multilevel latent change analysis, the research found significant direct effects of distributed leadership on change in the schools’ academic capacity and indirect effects on student growth rates in math. The study supports a perspective on distributed leadership that aims at building the academic capacity of schools as a means of improving student learning outcomes.

Classroom Effects on Children’s Achievement Trajectories in Elementary School

This nonexperimental, longitudinal field study examines the extent to which variation in observed classroom supports (quality of emotional and instructional interactions and amount of exposure to literacy and math activities) predicts trajectories of achievement in reading and math from 54 months to fifth grade. Growth mixture modeling detected two latent classes of readers: fast readers whose skills developed rapidly and leveled off, and a typical group for which reading growth was somewhat less rapid. Only one latent class was identified for math achievement. For reading, there were small positive associations between observed emotional quality of teacher-child interactions and growth. Growth in math achievement showed small positive relations with observed emotional interactions and exposure to math activities. There was a significant interaction between quality and quantity of instruction for reading such that at higher levels of emotional quality there was less of a negative association between amount of literacy exposure and reading growth.

Health and the Education of Children from Racial/Ethnic Minority and Immigrant Families

Building on a conceptual model of the transition to elementary school, this study explored the role of health in the early cognitive achievement of children from various racial/ethnic minority and immigrant families by applying multilevel modeling to data from a nationally representative sample of American kindergarteners. Whites tended to have the best physical health before transitioning to first grade. Children from immigrant Latino/a and Asian families had the worst physical health but the best mental health. Compared to white children from native families, these health differentials partially explained the lower math achievement and achievement growth of black children (whether from native or immigrant families) in first grade as well as the lower math achievement of children from Latino/a immigrant families and the lower achievement growth of children from Asian immigrant families during this period.

Student engagement and classroom variables in improving mathematics achievement

The study explored how much student engagement and classroom variables predicted student achievement in mathematics. Since students were nested within a classroom, hierarchical linear modeling (HLM) was employed for the analysis. The results indicated that student engagement had positive effects on student academic growth per month in math after taking into account student variables such as gender, SES, race, and interaction effects. The effects of student engagement are consistent regardless of minority and gender. Among classroom level variables such as teachers’ degree, experience, certification, authentic instruction, content coverage, and class size, there is no significant predictor of student math achievement growth. The findings suggest that student engagement should be emphasized in a school and educational policy for students’ success in a school.

The Influence of School Policy and Practice on Mathematics Achievement During Transitional Periods

In this study, the effects of school policies and practices on math achievement growth, as students transitioned from middle to high school, were examined while controlling for school contextual variables. A pattern of accelerated growth in mathematics achievement from grades 8 to 12 occurred, in which higher achieving students in mathematics at grade eight accelerated more than lower achieving students in mathematics growth during the transition from middle to high school. Controlling for school context, school policy promoting parent involvement and academic counseling had significant positive impacts on the acceleration in growth during this period. The implications of using multilevel growth models to study growth during transition periods are discussed.

An examination of student mathematics learning in elementary and middle schools: A longitudinal look from the us

School districts in the U.S. increasingly rely on standardized testing to documentstudent achievement in mathematics, reading, science, and English. Educators and policy-makers have engaged in heated debates as to the effects of such standardized testing practices on actual student achievement. In studying these issues, it is important to examine the growth and improvement patterns for individual learners over time. In most studies to date, however, there is a lack of empirical data at the individual level; the studies are rather cross-sectional designs. The current study documents longitudinal math achievement growth based on 716 students in a single U.S. school district. The data for this study are student math scores on SAT 9 achievement tests administered yearly between 1997 and 2000. Multidimensional Scaling profile modeling was used in this investigation to track individual and group patterns over four years. Analysis revealed unequal growth rates. The results are discussed in light of recent school reform effects and raise questions about the expectation of incremental growth curves mandated in the No Child Left Behind Act of 2001 provision that requires Adequate Yearly Progress (AYP). Even in a relatively stable school district, children's actual math learning growth patterns do not mirror the AYP expectation.

The effects of ability grouping on student achievement and resource allocation in secondary schools

A school policy of grouping students by ability has little effect on average math achievement growth. Unlike earlier research, this paper also finds little or no differential effects of grouping for high-achieving, average, or low-achieving students. One explanation is that the allocation of students and resources into classes is remarkably similar between schools that claim to group and those that claim not to group. The examination of three school inputs: class size, teacher education, and teacher experience, indicates that both types of schools tailor resources to the class ability level in similar ways, for instance by putting low-achieving students into smaller classes. [JEL I21]

An “Elective Replacement” Approach to Providing Extra Help in Math: The Talent Development Middle Schools' Computer-and Team-Assisted Mathematics Acceleration (CATAMA) Program

In Talent Development Middle Schools, students needing extra help in mathematics participate in the Computer- and Team-Assisted Mathematics Acceleration course (CATAMA). CATAMA is a combination of computer-assisted instruction and structured cooperative learning that students receive in addition to their regular math course for about ten weeks during the school year. This paper reports on two studies of CATAMA. The first compares growth in math achievement for 96 seventh-graders, 48 of whom participated in CATAMA for ten weeks and 48 of whom were students of similar prior achievement who attended a comparison school where CATAMA is not offered. The second study reports data from interviews with, and observations of CATAMA participants. Growth in mathematics procedures achievement was higher for CATAMA participants than for comparison students and participants liked CATAMA and displayed high levels of engagement and cooperation.