The study took place in four urban school districts in the south central and southwestern United States. The districts all had at least 14 elementary schools in which there were at least three first-grade classrooms. The districts also used a district-wide mathematics curriculum and did not use any small group mathematics interventions.
The study used a cluster-level randomized controlled trial (RCT) design in which students were randomized to condition by schools in matched pairs (i.e. one school within each pair was randomly assigned to the intervention and the other to the comparison group). After random assignment of schools, one comparison school dropped out of the study leading the authors to also drop its matched pair in the intervention group. As such, the final cluster-level analytic sample consisted of 76 schools (38 in each group assignment). After randomization, these schools distributed consent forms to eligible students: 2,526 intervention and 2,318 comparison students. In total, 1,643 intervention and 1,076 comparison students consented to participate in the study. The consenting students were then administered a screening battery (six short math tests) to identify students at-risk (AR) for difficulties in mathematics. Students scoring below the 35th percentile of the composite screening score were identified as at-risk: 615 intervention students and 379 comparison students. Missing posttest scores were imputed using multivariate stochastic sequential regression-based multiple imputation for 60 intervention and 53 comparison students.
The study recruited 78 schools in 4 urban school districts in 4 states of the United States. Only 76 schools were included in the analytic sample: 38 in the intervention group and 38 in the control group. Within the 38 intervention schools, 615 students identified as at-risk math consented to participate. Within the 38 comparison schools, 379 students identified as AR math consented to participate. Posttest data were collected from 555 intervention and 326 comparison students. Missing posttest scores were imputed using multivariate stochastic sequential regression-based multiple imputation.
In the intervention group, 47 percent of students were female, 1 percent were American Indian/Asian/other, 44 percent were black, 8 percent were white, 47 percent were Hispanic, 36 percent qualified for free or reduced price lunch, and 8 percent were on an Individualized Education Programs (IEP).
In the comparison group, 51 percent of students were female, 1 percent were American Indian/Asian/other, 44 percent were black, 11 percent were white, 44 percent were Hispanic, 32 percent qualified for free or reduced price lunch, and 8 percent were on an Individualized Education Programs (IEP).
The intervention, Number Rockets, was administered to students as a supplement to regular classroom math instruction. Number Rockets is a scripted mathematics program that focuses on the number line, addition and subtraction problems, magnitude comparison, and basic arithmetic using whole numbers. The instruction is teacher-led and given in small groups of two to three. Students are given opportunities to practice new concepts or strategies modeled by their teachers and receive immediate feedback. Each lesson lasted 40 minutes which included 30 minutes of instructional time and 10 minutes of fact practice. The intervention lasted about 17 weeks, with the aim of completing 45 lessons; 86 tutors delivered the intervention in the small groups.
The comparison condition was business as usual. Students received regular core instruction and any additional support the teacher might typically give. Most comparison schools provided interventions for students struggling in reading, but they were not eligible for the study if they provided supplemental mathematics interventions.
Support for implementation
The 86 tutors were recruited from local pools of retired and substitute teachers. Tutors received a one-day training prior to implementation and two two-hour follow-up trainings.