Direct Instruction in Math Word Problems: Students With Learning Disabilities
Everyday acts such as deciding whether one can afford to purchase an item require the application of problem-solving skills. Because students with mild disabilities will live independent and productive lives, problem-solving skills are as essential for them as for students without disabilities. However, students with disabilities are less likely to adopt a strategic approach to problem solving (Torgesen & Kail, 1980); thus, they are likely to experience difficulty in mastering the skill. It is crucial that the mathematics program for these students include problem solving as a part of the curriculum.
An examination of elementary school mathematics curricula has shown that the design of commonly used basal arithmetic programs may largely be responsible for the difficulty students have in solving word problems (Silbert, Carnine, & Stein, 1981). Major concerns about basal programs include a lack of adequate provision for practice and review, inadequate sequencing of problems, and an absence of strategy teaching and step-by-step procedures for teaching word problem solving.
Mathematics curricula of students with mental disabilities also lack adequate, strategic, and sequenced instruction (Cawley, Fitzmaurice, Shaw, Kahan, & Bates, 1978, 1979a, 1979b; Cawley & Goodman, 1968, 1969; Englemann 1977). In fact, Englemann argued that it is inadequate instruction rather than deficits in cognitive processes that accounts for the greatest proportion of failure of students to learn basic academic skills. Furthermore, for students with mild disabilities, the curricula too often emphasize rote development of computational skills (Cawley et al., 1978, 1979a, 1979b; Cawley & Goodman, 1968, 1969).
A review of the literature specific to math and students with learning disabilities revealed that only "scant attention" is directed toward the word-problem-solving skills of these students (Cawley, Miller, & School, 1987, p. 87). The little research that exists suggests that consideration must be given to sequencing, providing adequate practice, cognitive strategies, direct instruction, and techniques to promote generalization (Darch, Carnine, & Gersten, 1984; Fleischner & O'Loughlin, 1985; Jones, Krouse, Feorene, & Saferstein, 1985; Montague & Bos, 1986).
Two studies (Darch et al., 1984; Jones et al., 1985) evaluated the effectiveness of direct instruction. Darch et al. compared the effectiveness of a direct-instruction approach to that of a basal-math approach for teaching fourth graders without disabilities to solve word problems. The results indicated that students who were taught using direct instruction performed significantly higher on the posttest than did students who were taught by more traditional methods.
This study focused on the effects of sequencing problem types and using a direct-instruction strategy for problem solving. This study sought to build on a study by Jones et al. (1985), who compared two variations of a direct-instruction strategy for teaching students without disabilities to solve addition and subtraction word problems. In both variations, the "big number" concept (Silbert, Carnine, & Stein, 1981) was taught. With it, students determined whether a problem gives the big number of a fact family. If it does, the problem requires subtraction; if not, the problem requires addition. This approach calls for direct teaching of articulated strategies for translation of word problems into equations. In the sequential variation, students practiced solving word problems sequenced according to type; in the concurrent variation, students practiced a balanced combination of problem types. Jones et al. found that students in the sequential condition made significantly greater gains over the 9-day instructional period than did the concurrent group. …