Setting
The study took place in two urban school districts (Houston and Nashville). Students were from 13 schools in Nashville and 18 schools in Houston (p. 5).
Study sample
The strategic counting with deliberate practice group included 39% female students. 73% of students in this group were receiving subsidized lunches and 43% were receiving special education services. For 18%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 59% African American, 8% Caucasian, 31% Hispanic, and 2% other. 31% of the students in this group had been retained in grade. The strategic counting without deliberate practice group included 43% female students. 71% of students in this group were receiving subsidized lunches and 45% were receiving special education services. For 16%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 63% African American, 14% Caucasian, 20% Hispanic, and 2% other. 35% of the students in this group had been retained in grade. The control group included 48% female students. 82% of students in this group were receiving subsidized lunches and 18% were receiving special education services. For 24%, English was the student's second language. The racial and ethnic breakdown for this group was as follows: 46% African American, 10% Caucasian, 36% Hispanic, and 8% other. 32% of the students in this group had been retained in grade (p. 22).
All students in the study were experiencing math difficulty. This was determined based on the students' scores on two screening measures. All students scored below the 26th percentile on the Arithmetic subtest of the Wide Range Achievement Test-3 and below the 36th percentile on the Iowa Test of Basic Skills: Problem Solving and Data Interpretation (p. 5, 10). Students were also screened for reading difficulties using the reading subtest of the Wide Range Achievement Test-3. Students who scored below the 26th percentile on this assessment were classified as having reading difficulties. In the final analytic sample (including the control group), 27% of students met criteria for math difficulties alone and 73% met criteria for both math and reading difficulties (p. 6, 10).
Intervention Group
The study examined two variations of instruction in number combinations that was embedded in a word problem tutoring intervention, called Pirate Math: strategic counting instruction with deliberate practice and strategic counting instruction without deliberate practice. The study design also included a control group. The intervention consisted of one-on-one tutoring and was supplemental to the core mathematics. Tutoring lasted 16 weeks and included 48 sessions divided across 4 units. Each session was 20-30 minutes in duration. The tutoring conditions (T1 and T2) looked at embedding number combination instruction within validated word problem intervention.
T1 included schema-based instruction on word problems where students were taught to distinguish between problems types with additive and subtractive structures (combine, compare, change). The embedded strategic counting practice included explicit teaching of counting up to solve addition and subtraction basic facts. Flash cards to build fluency were included and students were asked to correct any incorrect answers provided by using the taught strategy.
T2 included schema-based instruction on word problems where students were taught to distinguish between problems types with additive and subtractive structures (combine, compare, change). Strategic counting practice was NOT included; however, students were taught at the start of tutoring on one occasion a strategy for counting up to solve addition and subtraction basic facts. To account for time spent in T1 on flash card practice, T2 also included flash cards to build fluency on number identification 0-9999.
Comparison Group
The comparison condition was business as usual instruction. This varied somewhat across the two sites (Houston and Nashville). However, in both sites, business as usual instruction involved very little instruction in number combinations. Students did receive instruction in word problems, including the three problem types taught in the intervention condition. Instruction also included more complex word problem types. The business as usual instruction did not include efforts to broaden students’ schemas about word problems. In Nashville, Houghton Mifflin Math was the curriculum that was used. Instruction in word problems focused on explicit steps that students should take to solve problems. In Houston, schools were provided with some latitude about which curriculum to use so long as it aligned with the district’s Horizontal Alignment Planning Guide, which emphasized “communication, justification, and reasoning; proper use of manipulatives; multiple models and representations; and problem-solving strategies” (p. 6-7).
Support for implementation
Tutors were provided a script for each tutoring session. Tutors studied the scripts prior to tutoring sessions so that they could conduct the tutoring sessions without having to read directly from the script (p. 7).
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