Co-Principal Investigators: Nancy Dyson and Henry May

Purpose: This project aims to develop a fraction sense intervention for middle school students with or at risk for mathematics difficulties. Many middle-school students struggle to develop a basic understanding of fractions. Fractions are not only foundational for learning algebra, but facility with fractions also affects daily life functioning (e.g., managing personal finances). Unfortunately, many students fail to develop these foundational skills, which can lead to negative educational, vocational, and personal outcomes. The current project addresses this need by developing and testing the promise of an intervention to improve fraction learning for sixth-grade students with or at risk for mathematics difficulties.

Project Activities: In Years 1–3, the research team will iteratively develop and refine the fraction intervention to enhance usability for teachers, feasibility for use in authentic middle school settings, and promise for efficacy. In Year 4, a randomized controlled trial will be conducted to test the promise of the intervention for improving proximal outcomes (i.e., knowledge of fraction concepts and procedures, fraction fluency) and distal outcomes (i.e., mathematics achievement) for sixth-grade students with or at risk for math difficulties.

Products: The products of this project will include a fully developed intervention and evidence of promise of its efficacy, peer-reviewed publications, and presentations.

Structured Abstract

Setting: The research will take place in middle schools in Delaware.

Sample: Approximately 252 sixth graders with or at risk for math difficulties will participate in the project, as well as approximately 30 school intervention teachers, over the course of the project.

Intervention: The 24-lesson fraction sense intervention will be implemented during the schools' mathematics intervention period, when all sixth-grade students with math difficulties receive specialized help for approximately 40 minutes daily. The intervention will target fundamental understanding of (1) the meaning of a fraction, (2) fraction relations, and (3) fraction operations. Key components will be taught with relatively few fractions and centered on a number line. The intervention will be anchored by a meaningful storyline and will employ general principles from cognitive science to support fraction learning, including use of gestures to guide students' attention, instructional explicitness, and clear visual models to minimize cognitive load.

Research Design and Methods: In Year 1, eligible students will be randomly selected from two districts to participate and then randomly assigned to the fraction sense intervention or a business-as-usual control group. The intervention will be implemented by researcher instructors in small groups. Data from pre-test, post-test, and 6-week follow-up; standardized test scores (spring); and audiotaped lessons (for examining fidelity of implementation and developing a fidelity checklist) will be collected. The research team will use data and expert feedback to refine the intervention and develop practice conditions for the Year 2 iteration. In Year 2, students will be selected using the same procedures as Year 1 and randomly assigned to receive one of two practice conditions. Students will receive the same core fraction sense instruction in both conditions, but the type of practice will differ by speed at which students must recognize the larger fraction. Data from pre- and post-test and audiotaped lessons will be collected. The intervention will be further refined based on data and feedback from experts and school personnel regarding usability, feasibility, and fidelity. In Year 3, researcher instructors will co-teach the intervention with school intervention teachers. Data from audiotaped lessons and co-teaching planning meetings as well as usability and feasibility surveys will be collected and used to inform further revisions. In Year 4, a randomized controlled trial will be conducted, with 36 students assigned to the intervention group (delivered by school intervention teachers) and 36 to the control group. Data from pre-test, post-test, and 6-week follow-up; standardized test scores (spring); audiotaped lessons; fidelity checklists; and interviews with school intervention teachers will be used to evaluate the promise of the intervention for improving student outcomes and prepare the final version of the intervention.

Control Condition: For the business-as-usual control group, used in Years 1 and 4, school intervention teachers will deliver their own supplemental fraction materials.

Key Measures: To screen students for eligibility, a fraction screener that includes released items from past National Assessments of Educational Progress (NAEP) will be used. Proximal student outcome measures will include an established fraction number line estimation task (fraction magnitude understanding); a researcher-developed proportional reasoning task (ability to judge the proportional equivalence of two visually depicted proportions); the fraction screener (student learning of fraction concepts); written computation items (fraction procedures); and a timed fraction magnitude comparison task (fraction comparison fluency). The distal student outcome, math achievement, will be assessed by the Smarter Balanced Assessment Consortium, a statewide standardized assessment of students' attainment of the Common Core State Standards. Measures of moderator variables will include student demographics; the SWAN Rating Scale (attention); the Peabody Picture Vocabulary Test, 4th edition (verbal skills); the Matrix Reasoning subtest of the Wechsler Abbreviated Scale of Intelligence (nonverbal reasoning); the Counting Recall subtest of the Working Memory Test Battery for Children (working memory); and the multiplication fluency subtest of the Wechsler Individual Achievement Test (whole number fluency). Usability of the intervention will be measured through weekly teacher surveys and post-intervention interviews. Fidelity will be assessed through audiotaped lessons and a checklist developed by the research team.

Data Analytic Strategy: Analyses of co-variance will be conducted to analyze the impact of the intervention on student outcomes. Multiple regression analyses will be conducted for each proximal and distal student outcome to examine the unique contributions of moderating variables. Qualitative data, obtained through audio recordings of the lessons and instructor debriefing meetings, will be analyzed by identifying themes of factors that facilitate and hinder implementation of the intervention in an authentic middle school setting.

Related IES project: National Research and Development Center on Improving Mathematics Instruction for Students with Mathematics Difficulties (R324C100004)