Project Activities
The research team iteratively developed and refined a fraction intervention to enhance usability for teachers, feasibility for use in authentic middle school settings, and promise for efficacy. A randomized pilot study was conducted to test the promise of the intervention when carried out by teachers for improving proximal outcomes (i.e., fraction concepts and fraction arithmetic) and distal outcomes (i.e., mathematics achievement) for sixth-grade students with math difficulties.
Structured Abstract
Setting
The research took place in two middle schools in Delaware. Both schools were in suburban neighborhoods that served an ethnically and racially diverse population of students (Black: School A-32%, School B-39%; Hispanic: School A-23%. School B-20%; White: School A-35%, School B-27%). Percentage of low-income families was 25% for School A and 27% for School B.
Sample
Participants included 239 sixth graders with or at risk for mathematics difficulties. In the first 2 years, there were 84 intervention and 48 control children participating in the project. In the next year, six teachers who were teaching math intervention in the participating schools consented to participate in a mentorship program. Their students became the experimental group (n=54). There was no control group during this phase. For the pilot study, four teachers taught the fraction sense intervention and three classrooms became the control group. Consent was received to use the data for a total of 53 students (intervention: n=29; control: n=24).
The 24-lesson fraction sense intervention (FSI) was implemented during the schools' regular mathematics intervention period, when all sixth grade students with math difficulties receive specialized help for approximately 40 minutes daily. The intervention targeted fundamental understanding of (1) the meaning of a fraction, (2) fraction relations, and (3) fraction operations. Key components were taught with relatively few fraction denominators and centered on a number line with fraction bars as an additional model. The intervention was anchored by a meaningful storyline and employed learning 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 the first year, eligible students were 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 was implemented by researcher instructors in small groups. Data were collected at pre-test, post-test, and a 6-week follow-up test. Audiotaped lessons were examined for fidelity of implementation and developing a fidelity checklist. The research team used data and expert feedback to refine the intervention and develop practice conditions for the next iteration. The following year, students were selected using the same procedures and randomly assigned to the control group or to receive one of two practice conditions. Students received the same core fraction sense instruction in both conditions, but the type of practice differed by the model presented to the students for solving problems. One group was to solve problems using a number line model. The other group was to solve the same problems using fraction bar models. Data from pre- and post-test and audiotaped lessons were collected. The intervention was further refined based on data and feedback from experts and school personnel regarding usability, feasibility, and fidelity. The following year, researcher instructors co-taught the intervention with school intervention teachers. Data from audiotaped lessons and co-teaching planning meetings as well as usability and feasibility surveys were collected and used to inform further revisions. In the final year, a randomized study was conducted. 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 were used to evaluate the promise of the intervention for improving student outcomes and prepare the final version of the intervention.
Control condition
In the randomized studies, teachers delivered their own supplemental mathematics intervention for business-as-usual control groups.
Key measures
To screen students for eligibility, a fraction screener that includes released items from past National Assessments of Educational Progress (NAEP) was used. Student outcome measures included an established fraction number line estimation task (fraction magnitude understanding), the fraction screener (student learning of fraction concepts), written computation items (fraction arithmetic), and a fraction magnitude comparison task (fraction comparison fluency). Math achievement was assessed by the iReady Diagnostic for Mathematics. Measures of moderator variables included student demographics, the SWAN Rating Scale (attention), the Toolbox Picture Vocabulary Test (TPVT) (verbal skills) and List Sorting Working Memory Test (working memory), a researcher-developed proportional reasoning task, and a multiplication fluency task. Usability of the intervention was measured through weekly teacher surveys and post-intervention interviews. Fidelity was assessed through audiotaped lessons and a researcher-developed checklist.
Data analytic strategy
Analyses of co-variance were conducted to analyze the impact of the intervention on student outcomes. Multiple regression analyses were conducted for each proximal and distal student outcome to examine the unique contributions of moderating variables. Repeated measures analyses of variance were conducted to analyze growth over time. Qualitative data, obtained through audio recordings of the lessons and instructor debriefing meetings, were analyzed by identifying themes of factors that facilitate and hinder implementation of the intervention in an authentic middle school setting.
Key outcomes
The main findings of this study, as reported by the principal investigator, are as follows:
- A number line centered approach to teaching fractions that also incorporates evidence-based learning strategies helps struggling learners make durable gains in conceptual understanding of fractions. Effects on fractions arithmetic problems, however, were smaller and less meaningful.
- The fraction sense intervention, which incorporates animated slides to make explicit mathematical connections and facilitate use of cognitive learning strategies, holds promise for developing fraction knowledge in larger groups of students with mathematics difficulties. The slide-based intervention was shown to be feasible in a typical middle school intervention setting with classes of 12 to 16 students.
- The fraction sense intervention was shown to be usable for classroom intervention teachers, who carried out the intervention with high fidelity and enthusiasm. The intervention can be implemented in multi-tiered support systems in school settings.
People and institutions involved
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Project contributors
Products and publications
Publications:
ERIC Citations: Find available citations in ERIC for this award here.
Dyson, N. I., Jordan, N. C., Rodrigues, J., Barbieri, C., & Rinne, L. (2020). A Fraction Sense Intervention for Sixth Graders with or at Risk for Mathematics Difficulties. Remedial and Special Education, 41(4), 244–254.
Barbieri, C. A., Rodrigues, J., Dyson, N., & Jordan, N. C. (2020). Improving Fraction Understanding in Sixth Graders with Mathematics Difficulties: Effects of a Number Line Approach Combined with Cognitive Learning Strategies. Journal of Educational Psychology, 112(3), 628–648.
Related projects
Supplemental information
Co-Principal Investigators: Nancy Dyson and Henry May
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