The study took place in 36 middle schools in 5 school districts in one western and one southeastern state. The majority of schools were located in suburban (31) areas and also included a few urban (2) and rural schools (3).
A total of 1,411 students in grade 7 mathematics classes were included in the study. The 1,411 students in middle schools were taught by 59 teachers in 36 schools. Approximately 56 percent of the students were White, 8 percent were Black, 5 percent were Asian, and 31 percent did not report race. Approximately 26 percent of students were Hispanic and 24 percent were receiving free/reduced price lunch. About 50 percent of the students were male, 49 percent were female, and 1 percent did not report gender. In addition, there were 9 percent of students who were English learners and 9 percent of students had an unspecified disability.
Students in the intervention group received schema-based instruction (SBI), a mathematical program designed to assist students in their problem-solving reasoning that involves proportional relationships. The program consists of 21 lessons that were completed in approximately 30 days. The first 10 lessons focused on the meaning of ratios, equivalent ratios, and rates and solving these in the context of scale drawings in word problems. The second set of 10 lessons focused on percent (including fractions and decimals as alternative representations) and solving word problems involving part–whole comparisons, percent of change, including problems involving sales taxes, discounts, tips, and simple interest, as well multistep adjustment percent of change problems. The last lesson reviewed all of the lessons.
SBI was provided during regularly scheduled grade 7 mathematics classes. Instruction was administered daily to the whole class for 6 weeks, averaging 45 minutes per session.
Students in the comparison group received business-as-usual grade 7 mathematics instruction. Topics discussed included the same content taught in the intervention classes but using practice standards (for example, look for and make use of structure, model with mathematics) identified by the school district.
Similar to the intervention group, instruction was administered daily for 6 weeks, averaging 45 minutes per session. However, teachers assigned to the comparison condition did not have access to SBI materials that were available to teachers in the intervention condition.
Support for implementation
An expert in problem solving outside of the research team provided a 2-day SBI training to teachers assigned to the intervention condition. The training familiarized teachers with the lessons and scope of the program, taught the critical SBI practices, and provided teaching material.