Participants were drawn from 58 fourth-grade classrooms in 12 schools in a large United States city.
The intervention group (Fractions Magnitude intervention) was 45% male. The racial and ethnic breakdown of the comparison group was 44% African American, 16% white non-Hispanic, and 26% Hispanic. The race/ethnicity for the other 14% of students in this group was not specified. 16% of students in the comparison group were receiving special education services, and of these, 50% had a learning disability. 19% of students in the comparison group were classified as English learner students. 89% of the students in the comparison group qualified for free or reduced price lunch.
The comparison group (business as usual control group) was 46% male. The racial and ethnic breakdown of the comparison group was 46% African American, 18% white non-Hispanic, and 26% Hispanic. The race/ethnicity for the other 10% of students in this group was not specified. 13% of students in the comparison group were receiving special education services, and of these, 60% had a learning disability. 20% of students in the comparison group were classified as English learner students. 87% of the students in the comparison group qualified for free or reduced price lunch.
For this review, the intervention condition is the Fraction Magnitude intervention group. Lessons, which lasted 35-minutes, were taught to student dyads, three times per week for 12 weeks (36 lessons). Each lesson had the same structure: warm-up, training (tutors model new ideas), relay (guided practice, with students providing reasoning for their problem solving thinking), sprint (fluency building skills), and individual contest (students complete problems independently and are given feedback). The lessons used the Fraction Face-Off! program, which includes a self-regulation component. The lessons focus on fraction magnitude understanding, particularly by comparing fractions to benchmark fractions like 1/2. Tutors teach students about comparing and ordering fractions, finding equivalent fractions, and placing fractions on 0-1 and 0-2 number lines. Sessions use manipulatives (fraction tiles and fraction circles) and number lines.
During the warm-up of each lessons beginning in lesson 7, students received instruction on fraction applications, which involved working with fraction change-increase and change-decrease word problems. Students learned how to categorize word problems and then apply strategies that are specific to that problem type.
In this contrast, the comparison condition was business-as-usual math instruction. The district’s fourth-grade math program was envisionMATH, which addresses fractions in two units: Understanding Fractions and Adding/Subtracting Fractions. The authors administered a questionnaire to district teachers, and results indicated that five of the 39 math teachers reported using only the Common Core Math Standards, one reported using only enVisionMATH, and 33 reported using a combination of the Common Core Math Standards, enVisionMATH, and the state standards. Researchers found that students in the comparison group focused more on part-whole understanding with respect to fractions and relied more on procedural methods when comparing fractions. Intervention group students, on the other hand, focused more on conceptual and magnitude understanding and emphasized more strongly the assessment of fraction and decimal magnitude with number lines. Additionally, intervention group activities restricted fraction denominators to 12, whereas comparison group activities included denominators to 100. Also, almost a third of teachers did not integrate decimal and fraction concepts, and when they did, they did not tend to include manipulatives and real-life applications or emphasis comparing, ordering, and number line placement strategies (as did the intervention tutors). Lastly, comparison group instruction utilized picture-drawing and the identification of key words, whereas the intervention instruction focused on identifying word problem types. Students across conditions (both intervention conditions and the comparison condition) received similar amounts of math instruction.
Support for implementation
Tutors were trained in two phases. The first phase, which was 20 hours in duration, focused on the manualized intervention. After practice delivering lessons with peers and achieving 95% implementation accuracy, tutors could begin working with the student participants. The second phase of training involved weekly meetings for additional support on upcoming teaching content. The researchers conducted frequent live observations during intervention sessions and audio-recorded all sessions to monitor implementation fidelity and provide feedback. To determine fidelity, they randomly selected 1322 (46%) of 2880 recordings across 80 groups and 36 sessions. Research assistants listened to the recordings and used a checklist to assess implementation fidelity.