Co-Principal Investigator: Dyson, Nancy; May, Henry

Purpose: The purpose of this project is to examine the efficacy of the fraction sense intervention (FSI), developed with funding from an IES grant, on student mathematics performance to understand mediators and moderators of the effects on student outcomes. Competence with fractions is crucial for success in math as well as for many careers and vocations. Students who leave 6th grade without fundamental understandings of fractions may experience cascading difficulties that lead to lifelong avoidance of math. At the same time, there is a great need for validated interventions in this age group to help circumvent a cycle of failure. This project seeks to address this need.

Project Activities: The research team will use a multiple-cohort randomized control trial to test the efficacy of FSI. Each year in years 1 to 3, researchers will recruit 16 classrooms using response to intervention (RTI) and randomly assign them to the FSI or business as usual (BAU) condition for a total of 48 RTI classrooms (24 FSI and 24 BAU). Data will be collected from students to understand their numerical and fraction knowledge in addition to other potential mediators and moderators including student demographics, attentive behavior, verbal ability, working memory, and proportional reasoning. Data will also be collected to assess fidelity of implementation and quality of instruction to understand mediation of the effect of FSI on student outcomes.

Products: Dissemination products include information about the efficacy of the FSI intervention presented to school district leaders and other stakeholders, The project will also result in a released final data set, peer-reviewed publications and presentations as well as additional dissemination products that reach education stakeholders such as practitioners and policymakers.

Structured Abstract

Setting: The research will take place in five large school districts in the state of Delaware which serve a socioeconomically and ethnically diverse population of students.

Sample: The sample will include 720 sixth graders and 48 teachers from 12 public schools.

Intervention: The fraction sense intervention (FSI) is designed specifically for students who have not responded to conventional instruction in fractions. It is intended for supplemental use in classrooms using response to intervention (RTI) to build foundational fraction knowledge that will empower math learners to profit from instruction in general education. The goal of the FSI is to improve students' understanding of fractions as numbers with magnitudes, fraction equivalence and ordering, and fraction arithmetic. The FSI centers on the number line and employs learning strategies informed by cognitive science research.

Research Design and Methods: A multiple-cohort randomized controlled trial is used to test the efficacy of the intervention with low-performing 6th graders in authentic RTI settings. The 48 classrooms will be nested within schools (approximately 12 schools). Teachers will be randomly assigned to condition (FSI or business-as-usual RTI) and students will be randomly assigned to the RTI classroom/teacher at the beginning of the school year when class rosters are developed as approved by school administrators. Researchers will collect data to understand the level of fidelity of implementation and whether changes in instruction mediate the effect of FSI on student outcomes. Researchers will also determine whether any student level characteristics moderate student outcomes.

Control Condition: The control condition is the schools' a business-as-usual RTI mathematics intervention.

Key Measures: The student measures used to assess numerical and fraction knowledge include researcher developed proximal measures of fraction number line estimation, fraction comparison and fraction arithmetic. In addition, released fraction items from the National Assessment of Educational Progress (NAEP) will be used as a more general student outcome measure. Moderator variables include student demographics, attentive behavior (SWAN Rating scale), receptive vocabulary and working memory (using validated measures from the NIH toolbox), and proportional reasoning (iPad adaptation of a non-symbolic scaling task). Teacher measures include researcher developed assessments of fidelity of implementation and quality of instruction.

Data Analytic Strategy: The researchers will use multilevel modeling with students nested within classes/teachers and fixed effects for schools to assess the efficacy of the FSI. They will include pre-intervention student performance as a student-level and class-level covariate. Researchers will use multilevel structural equation modeling to explore whether the effects of FSI are mediated by changes in instruction. They will also perform a cost analysis following the ingredients approach and will utilize the CostOut Tool Kit from the Center for Benefit-Cost Studies of Education. Researchers will examine cost-effectiveness using a ratio that estimates the cost per one-quarter standard deviation improvement in student outcomes.

Related IES Projects: National Research and Development Center on Improving Mathematics Instruction for Students with Mathematics Difficulties (R324C100004); Developing a Fraction Sense Intervention for Students with or at Risk for Mathematics Difficulties (R324A160127)