Description:

Co-Principal Investigator: Kerry Hofer

Purpose: This project is designed to explore the learning trajectories in mathematics of children at risk for academic difficulties. Through a longitudinal study, this project is intended to capture both the concurrent and longitudinal predictors of middle school children’s mathematics achievement as measured via state standardized assessments and detailed individually-administered standardized mathematics achievement tests in the middle school grades. Using information from a previously funded IES project, Scaling Up TRIAD: Teaching Early Mathematics for Understanding with Trajectories and Technologies, the research team will utilize data that is already available on these children’s prior early mathematics and behavioral skills. This data will be used to track the relation between children’s earlier mathematics and behavioral skills and later mathematics achievement. The research team will also assess the contribution of children’s early mathematics skills to later mathematics achievement while accounting for variability in important cognitive skills. This research will help identify malleable factors among children from low-income families that are particularly important for success in school mathematics and that might lend themselves to the development of interventions targeting math acuity.

Project Activities: The research team is using a longitudinal research design to track students’ mathematics, cognitive, and behavior skills from pre-kindergarten through 8th grade. Participants in the study will include a subset of those who participated in the prior IES-funded study when they were in pre-kindergarten through first grade. Most of these participants will be entering 6th grade during Year 1 of the project, and the research team plans to follow those who consent through their middle school years to track their mathematics achievement and cognitive skills. In Year 1, the research team will contact past participants and obtain their consent for this study. In the spring of Years 1-3 of the project, the team will conduct direct assessments of participants and collect brief survey information from teachers. In the fall of Years 2-4 of the project, the team will collect information on state achievement test scores from the state database. Students will be surveyed about their planned high school courses at the end of Year 3. Data analyses will be ongoing across all years of the project.

Products: The products of this project will be the identification of malleable factors that are important for success in mathematics as well as peer-reviewed publications.

Project Video:

Structured Abstract

Setting: The majority of the participants will be recruited from urban districts in Tennessee, though some participants may be from suburban and rural districts in Tennessee.

Sample: The study participants will include approximately 500 of the 757 children who participated in the prior IES-funded study, Scaling Up TRIAD: Teaching Early Mathematics for Understanding with Trajectories and Technologies. The project team will follow these participants into their 6th, 7th, and 8th grade school years. The participants will have the same general characteristics as children from the prior study. In the prior study, 56% of the participants were female; 78% of the participants were African American; 10% of the participants were English Language Learners; and over 80% of the participants participated in the Free and Reduced Price Lunch program in prekindergarten.

Intervention: This project will seek to identify malleable factors among children from low-income families that are particularly important for success in school mathematics as well as to understand the relationships between mathematics achievement and cognitive skills such as executive function skills, approximate quantity estimation, and visuospatial reasoning. These findings will inform the development of interventions targeting math acuity.

Research Design and Methods: The research team is employing a longitudinal research design and will be linking data from the prior IES-funded study to data collected during this project in order to track mathematics, cognitive, and behavior skills from preschool through 8th grade. In Year 1, the research team will contact past participants and obtain their consent for this study. In the spring of Years 1-3 of the project, the team will conduct direct assessments of participants and collect brief survey information from teachers. In the fall of Years 2-4 of the project, the team will collect information on state achievement test scores from the state database, which lags one year behind the school year in which the tests are administered. Students will be surveyed about their planned high school courses at the end of Year 3.

Control Condition: Due to the nature of this research design, there is no control condition.

Key Measures: The study will focus on middle school math achievement, domain general cognitive skills, domain-specific (math) cognitive skills, and early math and behavior skills. Middle school math achievement will be measured with the four subscales from the Key Math 3 Diagnostic Assessment (numeration, algebra, geometry, and mental computation and estimation), the Woodcock-Johnson Achievement Battery III: Quantitative Concepts Subtest, and the Partnership for Assessment of Readiness for College and Careers (PARCC) end of grade test. Domain-general cognitive skills will be measured with the Directional Stroop Task for Children and the Corsi Blocks Task. Domain-specific cognitive skills will be measured with a symbolic number comparison task, a groupitizing task, and a non-symbolic enumeration fluency task. Early math and behavior skills were measured in a prior study with the Woodcock-Johnson III Achievement Battery, the Early Math Assessment (EMA), and the Work-Related Skills scale from the Cooper-Farran Behavioral Rating Scales (CFBRS).

Data Analytic Strategy: Clusters of math and executive function skills will be developed and used in regressions to predict achievement. To examine the within-year and longitudinal associations between general math performance and performance on cognitive tasks, the research team will use multilevel structural equation modeling (MSEM) and multilevel regressions. To examine associations between middle school math competence and growth and early mathematics and behavioral skills, the research team will use MSEM with latent growth curves for math and behavior skills. To examine the contribution of a comprehensive set of domain-general and domain-specific cognitive tasks to understanding the connections between middle grades math competency and earlier math learning trajectories, the research team will further the MSEM analyses by adding the set of middle school cognitive measures to the models as additional predictors of middle-school math achievement trajectories. To identify a subgroup of at-risk middle school students whose early math skills and cognitive components suggest dyscalculia, the research team will use latent class analysis to identify profiles of children who struggle with specific cognitive skills and/or math concepts.

Products and Publications

Journal article, monograph, or newsletter

Mowrey, S. and Farran, D. (2017). Performance and Preparation: Alignment between Student Achievement, Teacher Ratings, and Parent Perceptions in Urban Middle-Grades Mathematics Classrooms. Journal of Urban Learning Teaching and Reading, 12: 61–74.

Price, G.R. and Wilkey, E.D. (2017). Cognitive mechanisms underlying the relation between nonsymbolic and symbolic magnitude processing and their relation to math. Cognitive Development, 44: 139–149.

Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G. and Farran, D. C. (2016). Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11. Child Development.