Setting
The study included 49 classrooms and 14 schools (in one urban school district, although the exact location is not specified).
Study sample
For this contrast, the fluency condition sample demographics were: 58% African American, 17% White, 24% Hispanic, 1% Other, 63% Female, 14% English learners, 93% receiving subsidized lunch, 8% receiving special education. The conceptual condition sample demographics were: 61% African American, 14% White, 22% Hispanic, 3% Other, 62% Female, 14% English learners, 95% receiving subsidized lunch, 10% receiving special education.
Intervention Group
For this contrast, the intervention condition was the fluency intervention group. The intervention occurred 3 times per week for 12 weeks. The sessions were 30 minutes long. Trained tutors delivered the interventions in small groups of students during either math time or the school's intervention time depending on the teacher preferences. Tutors used the Fraction Face-Off! program. Sessions focused on interpreting fractions, particularly comparing fraction magnitude and ordering and placing fractions on number lines. In the first two weeks, tutors introduced key vocabulary related to fractions (numerator, denominator, unit, equivalent, etc.) and had students practice reading and naming fractions, and comparing fractions with the same denominator or the same numerator. In weeks 3-5, tutors focused on fractions equivalent to 1/2 2/4, 3/6, 4/8, 5/10, and 6/12, and on using 1/2 has a benchmark when comparing fractions. Weeks 6-8 focused on improper fractions and mixed numbers, while week 9 focused on subtracting and adding fractions with like and unlike denominators, as well as mixed numbers. In week 10, tutors removed 1/2 from the number line so students did not have that benchmark when ordering fractions. Finally, weeks 11 and 12 were cumulative review. Each session had four components: training (8-12 minutes), group work (8-12 minutes), activity (5 minutes), and individual practice (5 minutes). In the fluency condition, the activity component focused on students performing strategic speed activities used flashcards. Students worked together to answer as many flashcards correctly each session, with tutors setting the goal of beating the previous session's score. When students made errors, they had to give the correct answer before they could proceed to the next flash card.
Comparison Group
For this contrast, the comparison condition is the conceptual intervention group. The conceptual intervention was identical to the fluency intervention except during the activity (5 minutes) component of each session. In the conceptual intervention this time involved students using manipulatives to represent different fractions and explained their reasoning to the group; students earned points for each correct representation and explanation (in comparison, the fluency condition had speeded flashcard practice during this time).
Support for implementation
The intervention was delivered by tutors who were full- or part-time graduate students and attended a week-long training and biweekly 1 hour follow-up trainings. Each was responsible for 1 to 2 groups in each condition.
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