Setting
The study took place across 52 classrooms in 14 schools in one school district. The state or general region where the school district is located was not provided, and a description of the setting (e.g., urban/rural/suburban) was not provided. Tutors typically delivered the intervention to pairs of students during math instructional time, but the location for the tutoring sessions was not discussed.
Study sample
Percentages were provided for the explanation component and control groups separately. Respectively, the explanation component and control were 58% and 48% female; 15% and 19% English learners; 93% and 87% received subsidized lunch; 7% and 13% received special education, 49% and 43% Black, 19% and 21% White, 27% and 30% Hispanic, and 4% and 6% other. The author reported that chi-square tests indicated groups were demographically comparable.
Intervention Group
Pairs of students participated in 35-minute tutoring sessions three times per week for a total of 105 minutes of tutoring per week. Students participated in the tutoring sessions for 12 weeks. Tutors were employees of the research grant, and most were not licensed teachers, though some were. Each tutor worked with 2 – 4 groups of students in both intervention conditions. The intervention tutoring sessions typically occurred during classroom mathematics instructional time. When the sessions took place at other times, there was no pattern to the types of instruction that intervention participants missed.
Twenty-eight of the 35 minutes of each session were identical across the two intervention groups. Both intervention conditions included a multicomponent element that focused on the measurement interpretation of fractions and incorporated substantial instruction on comparing fraction magnitudes. The interventions did not emphasize the part-whole interpretation, which the authors report is often the focus in American schools. The remaining seven minutes of each session differed in that one intervention condition included a self-explaining component (EXP) and the other did not. Instead of the self-explaining component, and to control for intervention duration, the second intervention condition (WP) included a previously validated component focused on fraction word problems requiring multiplicative reasoning. The intervention condition with the explanation component focused on supported explaining (rather than invented self-explaining). Researchers modeled high-quality explanations, children practiced analyzing and applying the explanations, and children were encouraged to elaborate on and discuss important features of the explanations. In the WP condition, tutors focused on schema theory, teaching the students to categorize any given word problem as one of the word problem types and then to apply a strategy specific to that type to solve the problem.
Comparison Group
Comparison group students received an average of 419.71 minutes (SD=81.67) of mathematics instruction per week and 27.43 minutes (SD=50.43) of supplemental mathematics instruction per week for an average total of 447 minutes of mathematics instruction each week. The supplemental instruction was typically delivered in small groups. The district employed the enVisionMATH mathematics program, which focuses on understanding fractions (70 percent of lessons) and adding and subtracting fractions. The authors summarize the differences between the comparison group and the two intervention groups as follows: the comparison group focused on part-whole understanding while the intervention groups focused on measurement interpretation; the intervention groups restricted the range of denominators and the comparison group did not; the comparison group did not emphasize explaining work and when work was explained the focus was on words more than pictures, whereas the intervention groups did emphasize explaining work and the focus was on pictures more than words; and for word problems the comparison group focused more on drawing pictures, making tables, and identifying key words, whereas the intervention group with the word-problem component focused on explaining thinking in words, classifying problems into problem types, and representing the structure of problems.
Support for implementation
The authors refer to Fuchs, Schumacher, Malone, and Fuchs (2013) for more information on tutor training, materials, and the structure of the manual. Materials were color-coded to avoid contamination across experimental conditions. Researchers periodically conducted live observations of the tutoring sessions, regularly monitored audio recordings of tutoring sessions, and during biweekly meetings, provided guidance and sought solutions to any problems that arose.
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