The study took place in 25 schools in a metropolitan school district across four cohorts (one per year for 4 years). Whole-class instruction was delivered November to March and tutoring was delivered December to March during the school year.
Demographic characteristics of the students in the Calculation RtI condition are as follows: 47% male; 53.1% African American, 10.4% White, 5.2% other, and 31.3% Hispanic; 93.8% qualified for free or reduced priced lunch; 8.3% were identified as having a disability; 18.8% were English Language Learners; and 7.3% had been retained.
Demographic characteristics of the students in the Control condition are as follows: 39.7% male; 52.6% African American, 20.5% White, 9% other, and 17.9% Hispanic; 88.5% qualified for free or reduced priced lunch; 14.1% were identified as having a disability; 17.9% were English Language Learners; and 11.5% had been retained.
The two-tiered Calculation intervention is a combination of Tier 1 whole-class lessons and Tier 2 small-group tutoring lessons. Tier 1 consisted of 34 whole-class lessons with two lessons per week over a 17-week period. Each lesson lasted approximately 40 to 45 minutes and was delivered by research assistants in the students’ classrooms. Tier 2 consisted of 39 small-group tutoring lessons delivered by research assistants to groups of 2 to 3 students. Tutoring started at the beginning of weeks 4 or 5 of the Tier 1 intervention and lasted for 13 weeks with 3 lessons a week. Each lesson lasted 25 to 30 minutes and took place outside of the student’s classroom (i.e., library, conference room, hallway). The Calculation whole-class intervention and small-group tutoring focused on 1) interconnected knowledge about number (e.g., cardinality, inverse relation between addition and subtraction, commutative property) and 2) practice. Both are important in developing conceptual and procedural competence with one- and two-digit addition and subtraction calculations (e.g., Fuchs et al., 2013; Fuson & Kwon, 1992; Geary et al., 2008; Groen & Resnick, 1977; LeFevre & Morris, 1999; Siegler & Shrager, 1984).
Students in the comparison classrooms received their math instruction from the district curriculum, Houghton Mifflin Math.
Support for implementation
Research assistants participated in two 6-hour training sessions where they learned to implement the Tier 1 and Tier 2 interventions. Before entering schools, research assistants had to demonstrate proficiency on a practice lesson (95% fidelity against the lesson’s fidelity checklist). Weekly meetings were held with the first author, project coordinators, and research assistants to discuss upcoming lessons and problems encountered.