Setting
Participants were drawn from 58 fourth-grade classrooms in 12 schools in a large United States city.
Study sample
For this contrast, the intervention group (Fraction Magnitude + Decimal Magnitude) was 42% male. The racial and ethnic breakdown of the intervention group was 38% African American, 15% white non-Hispanic, and 24% Hispanic. The race/ethnicity for the other 23% of students in this group was not specified. 12% of students in the intervention group were receiving special education services, and of these, 67% had a learning disability. 22% of students in the intervention group were classified as English learner students. 89% of the students in the intervention group qualified for free or reduced price lunch.
The comparison group in this contrast (Fraction Magnitude) 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.
Intervention Group
For this review, the intervention condition is the Fraction Magnitude + Decimal Magnitude 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.
In the warm-up portion of the session beginning in lesson 7, the fraction magnitude + decimal magnitude group received the decimal magnitude portion of the intervention. In these sessions, instruction integrated fraction magnitude and decimal magnitude. Lessons 7-12 focused on writing decimal-fraction equivalencies with tenths, and Lessons 13-15 compared decimal tenths and fraction tenths. Lessons 16-18 focused on placing decimal tenths on a number line, Lessons 19-21 focused on decimal-fraction equivalencies with hundredths, Lessons 22-30 mixed tenths and hundredths, Lessons 31-33 involved ordering decimals (tenths and hundredths), and Lessons 34-36 were review.
Comparison Group
For this review, the comparison condition is the fraction magnitude intervention. The structure of the sessions was the same as the intervention condition, and students similarly received the Fractions Face-Off intervention. The only difference between the comparison and intervention conditions was during warm-up. Beginning in lesson 7, students in the comparison group 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.
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.
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