Setting
The study was conducted on students with mathematics difficulties in grade four through five from one school in Minnesota. The school’s total enrollment in grades kindergarten through five was 762 students, of which 69 percent were white and 34 percent were eligible for free or reduced-price lunch (p. 84).
Study sample
The study sample included students in grades four through five with mathematics difficulties from one elementary school (grades kindergarten through five). The study sample was 45.6 percent white (41 students), 27.8 percent Black (25 students), 4.4 percent Asian (4 students), 2.2 percent Native American (2 students), and 20 percent Hispanic (18 students). About half of the study sample was female (53.3 percent, 48 students), and one third were English learners (33.3 percent, 30 students). More than a quarter of the study sample were students with an individualized education plan (IEP; 26.7 percent, 24 students) (p. 84).
Intervention Group
The intervention was a supplemental model-led test explicit instruction approach using manipulative items in activities developed by Van de Walle and Loving (2006) outside of regular mathematics instruction time (pp. 85-86). Intervention group students were randomly assigned to work on 6s and 7s multiplication facts or 8s and 9s multiplication facts in the intervention (p. 85).
The intervention consisted of two 15-minute sessions (30 minutes total) of supplemental mathematics instruction covering four activities: (1) Base-10 manipulative blocks, (2) Fill the Chutes, (3) Build It In Parts, and (4) Broken Calculator (p. 85). During each activity, interventionists first presented and modeled each activity, then students attempted to complete a problem with assistance, and finally students independently completed a problem (p. 85).
In the Base-10 manipulative blocks activity, students use blocks to solve multiplication problems. They are presented with a problem (for example, 6 x 6 = ?) and instructed to solve using blocks (for example, using six squares with six blocks in each square). Students are encouraged to talk aloud as they complete each problem (p. 85).
In the Fill the Chutes activity, students use chutes (columns) and game pieces (such as Milton Bradley’s Connect Four game) to solve multiplication problems. They are presented with a multiplication problem (for example, 6 x 9 = ?) and instructed to solve by filling chutes with the game pieces (for example, by filling six chutes with nine game pieces per chute) (p. 85).
In the Build It In Parts activity, students use colored counters to explore multiplication facts. They are instructed use the counters to form groups and create as many different combinations as possible (p. 85) to get to a given total number (for example, for the total number of 12, they might use 6 green and 6 blue counters to represent 6 x 2 = 12 or 4 green and 4 blue and 4 yellow counters to represent 4 x 3 = 12).
In the Broken Calculator activity, students use calculators to explore multiplication facts. They are presented with a multiplication problem (for example, 7 x 8 = ?) and instructed to use a calculator to find the product without the use of the multiply key (for example, by pressing the addition key seven times and then the equal sign eight times) (p. 85).
Two school psychology graduate students in their first or second year of graduate training delivered the intervention to groups of 7 to 8 students at a time in a small classroom (pp. 85, 88).
Comparison Group
Students in the comparison condition received “business as usual” mathematics instruction from their first grade teachers; therefore, they received 15 minutes less mathematics instruction than the intervention group (pp. 85-86).
Support for implementation
Approximately 20 percent of the intervention sessions were observed by school psychology graduate students using an implementation fidelity checklist. The checklist comprised essential implementation steps such as “Are the students sitting at their individual computers for the majority of their computer lab time?” and “Are students moving through the problem sets depicted on the computer screen?” (p. 86). The interventionists achieved implementation fidelity of 100 percent, as rated on the checklists, across the observed sessions (p. 86).
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