The study took place in two urban school districts (Houston and Nashville). Students were from 13 schools in Nashville and 18 schools in Houston.
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 (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)
The intervention being tested (T1) is strategic counting instruction with deliberate practice. The intervention took place in the context 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 condition looked at embedding strategic number combination instruction within validated word problem intervention.
Tutoring sessions were divided up into four units. The first unit focused on foundational skills and included one lesson on strategic counting. During this lesson, they learned about the strategy of “counting up” if they did not instantly know the answer to a problem and learned how to use this strategy for addition and subtraction problems. The remaining three units focused on one of three word problem types (total, difference, and change). During these units, students were taught how to identify different problem types, identify relevant information for solving the problem, and plug the relevant information into appropriate equations for that problem type. During these units, tutors worked to broaden students’ schemas for each problem type by teaching them to identify irrelevant information, solve problems where the missing information is in different locations in the relevant equation for the problem type, work with problems with double-digit numbers, and identify relevant information when it was displayed in pictographs, charts or pictures. Tutoring sessions followed a regular sequence: starting with a flash-card warm up, followed by a word –problem warm-up (starting in session 7), conceptual and strategic instruction, sorting word problems, and a paper-and-pencil review (p. 7-9).
The deliberate practice involved several components. First, at the start of each lesson, tutors reviewed the content that was covered in the strategic counting lesson with students. Second, during the flash card warm up, students were presented with problems to solve. If they did not produce the correct answer, the tutor prompted them to count up to the correct answer. Third, when students made errors during the rest of the tutoring session (after the flash card warm up), the tutor prompted the student to count up to arrive at the correct answer. Finally, when the tutor corrected the paper-and-pencil review, for any incorrect answers, he or she demonstrated how to arrive at the correct answers by using the counting up strategy.
The comparison condition consisted of a 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.
Support for implementation
Tutors were provided with scripted lessons and were instructed to study the lessons ahead of time rather than read straight from them during tutoring.