The study took place in an urban southeastern school district. The classrooms were Tier 1 general education third-grade classrooms.
The study focused on students with mathematics and reading difficulties. The analytic sample of 25 students was 44 percent male and 56 percent female. The majority (89 percent) received subsidized lunch, and 9 percent had a learning disability. The racial breakdown was 56 percent black, 24 percent white, 14 percent Hispanic, and 6 percent other.
The intervention condition received preventative tutoring using an explicit schema-broadening tutoring protocol that focused on word problem solving skills. The tutoring instruction covered three problem types: total problems, in which two quantities combine into a total; difference problems, in which bigger and smaller quantities are compared to find the difference; and change problems, in which starting quantities are increased or decreased to find a new quantity. The tutoring began with two weeks of introductory sessions, with tutors focusing on foundational skills for solving addition and subtraction problems, such as using a number line, solving two digit problems, solving algebraic equations, and using strategies such as making sure answers make sense, lining up numbers before adding/subtracting, and labeling work. Following the introduction, there were 3 one-week units about the three problem types. The tutoring instruction taught students to understand the structure of the three problem types, recognize problems as belonging to those problem types, solve the problem type, and transfer their problem-solving approaches to new problems. Tutors explicitly taught students how to solve problems with missing information in the first, second or third position of a problem, and how to transfer relevant and irrelevant information into graphs, charts, and pictures. In the last week of the intervention, tutors implemented a review unit that addressed all three problem types. Each session involved three activities: (1) basic fact flash cards in which the tutor provided corrective feedback; (2) 12-17 minute schema-broadening instruction in which tutors taught a three step process for problem solving: run through the problem (read it), underlining the question, naming the problem type (RUN strategy); (3) daily review in which students had 2 minutes to answer 14 problems. Throughout all lessons, the tutors used reinforcement strategies (such as earning tokens for correct responses that could be redeemed for prizes). Students were tutored one-on-one outside of their regular classroom for 20-30 minute sessions over the course of 12 weeks, with 3 sessions per week. The tutoring was provided by 4 graduate students at a local university.
The comparison condition in the study was the continuation of regular classroom Tier 1 mathematics instruction. Teachers used Math Advantage (Burton & Maletsky, 1999) and delivered explicit instruction of the same problem types as the intervention condition; however, students were not taught how to sort problems into problem types or broaden their schema. The comparison condition used teacher-guided worked examples, group practice, independent work, and homework.
Support for implementation
Lesson scripts for the intervention condition were used, though they were not delivered verbatim to allow for different teaching styles.