Setting
The sample includes 213 at-risk 4th grade students from 45 general education classrooms in 14 schools.
Study sample
The sample consisted of at-risk students. The authors defined risk as performance below the 35th percentile at the start of fourth grade on a broad-based calculations test (Wide Range Achievement Test–4 [WRAT]; Wilkinson & Robertson, 2006). They sampled half the at-risk students from the 15th percentile and the other half between the 15th and 34th percentiles. Two subtests of the Wechsler Abbreviated Scales of Intelligence (WASI; Wechsler, 1999) were administered to students who met the risk criterion and 18 students with T-scores below the 9th percentile on both subtests were excluded. The sample of 213 students includes 56.3% females, 16.6% English learners, 88.4% free/reduced lunch, 14.7% receiving special education, 58% African American, 36.4% White, 20.7% Hispanic, and 5.7% Other.
Intervention Group
The Multiplicative Word Problem (M-WP) condition included 36 lessons from the Fraction Face-Off! intervention program (Fuchs, Schumacher, Malone, & Fuchs, 2015). Each lesson was 35 minutes long and was delivered to students in groups of 2 by tutors hired by the research team. A focus of the lessons was the measurement interpretation of fractions, which involved comparing, ordering, placing fractions on a number line, equivalencies, and the use of manipulatives. Two multiplicative word problems were taught: "splitting" and "grouping." The M-WP condition limited the denominators to 2, 3, 4, 5, 6, 8, 10, and 12 and the pool of equivalent fractions and reducing activities to 1/2, 1/3, 1/4, 1/5, and 1/1. It focused on using words to explain thinking, identifying problems as belonging to word problem types, and representing the structure of word problems using arrays.
The Additive Word Problem (A-WP) condition included 36 lessons from the Fraction Face-Off! intervention program (Fuchs, Schumacher, Malone, & Fuchs, 2015). Each lesson was 35 minutes long and was delivered to students in groups of 2 by tutors hired by the research team. A focus of the lessons was the measurement interpretation of fractions, which involved comparing, ordering, placing fractions on a number line, equivalencies, and the use of manipulatives. Two additive word problems were taught: "increase" and "decrease." The A-WP condition limited the denominators to 2, 3, 4, 5, 6, 8, 10, and 12 and the pool of equivalent fractions and reducing activities to 1/2, 1/3, 1/4, 1/5, and 1/1. It focused on using words to explain thinking, identifying problems as belonging to word problem types, and representing the structure of word problems using a number sentence.
Comparison Group
The comparison group used the enVisionMATH program (Scott Foresman--Addision Wesley,
2011) for an average of 60 minutes per day and focused mainly on part-whole understanding,
rather than the measurement interpretation of fractions. Also, it covered advanced skills like
estimation and did not restrict the range of fractions used. The comparison group utilized drawing
pictures, making tables, and focusing on key words. Comparison teachers reported at-risk
comparison students received an average of 57.43 minutes per week of supplemental
mathematics (beyond the classroom mathematics program).
Support for implementation
The authors conducted follow-up trainings for tutors biweekly for 1 hour to provide opportunities for (a) dynamic feedback as the fraction lessons progressed in difficulty and (b) solving problems related to students’ challenging behavior and skill-level differences in dyads.
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