Setting
The study took place in three school districts (two urban and one urban-adjacent) across two U.S states (one in the west and one in the southeast). The report does not specify the number of schools or provide descriptive details about the schools (e.g., the grade spans represented, whether or not they include charter schools or magnet programs) and does not specify the number of mathematics classrooms represented. The report also does not discuss the location of the tutoring sessions. Intervention and comparison group students received core mathematics instruction from their classroom mathematics teachers. The core curricula used included My Math (District 1), California Math (District 2), and GO Math! (District 3). The intervention was developed using the TransMath curriculum.
Study sample
The study participants were fifth-grade students who had not mastered fourth-grade mathematics material but did not have identified disabilities and were not in need of one-on-one interventions in mathematics. None of the students in the analytic sample had an IEP in mathematics. The analytic sample comprised approximately 48 percent females and 52 percent males. Among the student participants, approximately 15 percent were identified as Black, five percent as Asian, 17 percent as Hispanic/Latino, 38 percent as White, and 23 percent as multiracial. Approximately 56 percent of the student participants qualified for free or reduced-priced lunch, and approximately eight percent had an IEP.
All ten of the tutors were women. Half of them had a master's degree, and half had previous experience tutoring in math. Thirty percent of the tutors had no experience teaching elementary math, 30 percent had between two and six years experience, 30 percent had between 10 and 15 years experience, and ten percent had 28 years experience. The average classroom experience among the ten tutors was 7.7 years (SD=8.92). Most of the tutors had not previously taught fifth-grade mathematics (70 percent). The others ranged from minimal experience teaching fifth-grade mathematics (one year) to substantial experience (ten or more years). The average experience teaching fifth-grade mathematics among the ten tutors was 2.4 years (SD=4.86). Ten percent of the tutors held a K-6 teaching credential, 30 percent held a K-8 teaching credential, 30 percent held a multiple subject K-12 teaching credential, and 40 percent had no teaching credential.
Intervention Group
Students in the intervention group participated in 35-minute, small-group tutoring sessions three or four times a week for a period of six or seven months (October 2016 to March/April 2017). The sessions were conducted by trained tutors and focused on fourth- and fifth-grade fractions content. A total of 52 lessons were designed for this study using the TransMath curriculum, which utilizes number lines, discussions, and word problems. Each lesson included review, demonstrations of concepts, student-led problem solving, and individual practice. Lessons were organized to include five minutes for review, ten minutes for strategic explicit instruction, ten minutes for guided practice, and ten minutes for student explanations. The focus of the lessons varied. To start, tutors focused on foundational understandings, like what a fraction is, the magnitude of fractions, equivalent fractions, comparing fractions, ordering fractions, and estimating the placement of fractions on a number line (Lessons 1-18). Then, the focus shifted to the addition and subtraction of fractions (Lessons 19-28) followed by the multiplication and division of fractions and critical concepts related to computational procedures (Lessons 29-42). Lastly, tutors focused on adding and subtracting mixed numbers (Lessons 43-52). Tutors and students used number lines, Cuisenaire Rods, and area models to support the teaching and learning process.
Comparison Group
The comparison condition is described as business as usual. While the intervention group students participated in the tutoring sessions, comparison group students either participated in classroom instruction in academic subjects (e.g., mathematics) or non-academic subjects (e.g., physical education). Depending on the organization of the schools, comparison group students may or may not have participated in some form of mathematics intervention or received some form of supplemental mathematics support. According to teacher report, 17.24% of students received intervention in math, 17.24% received intervention in reading, 31.03% received core math instruction, 72.41% received other instruction, and 17.24 participated in non-instructional activities.
Support for implementation
Tutors attended a two-day training, which included an explanation of the research, an overview of the topics covered in the 52 lessons, demonstrations, and practice using concrete and visual representations of fractions. The training also focused on strategies for facilitating students' verbal and written explanations, demonstrations of fractions procedures, and identifying and solving word problems that require addition, subtraction, multiplication, and division. Tutors were given digital recorders to record the tutoring sessions, and a member of the research team listened to the third or fourth session of each tutor and provided feedback. If a tutor needed to improve, a researcher would listen to additional recordings and provide more feedback. Subsequently, all of the tutors participated as a group in coaching calls every three weeks, and individual support was provided to tutors as needed.
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