An Exploratory Study of Schema-Based Word-Problem–Solving Instruction for Middle School Students with Learning Disabilities: An Emphasis on Conceptual and Procedural Understanding

The importance of mathematics literacy and problem solving has been emphasized by researchers (e.g., De Corte, Greer, & Verschaffel, 1996; Goldman, Hasselbring, & the Cognition and Technology Group at Vanderbilt, 1997; Patton, Cronin, Bassett, & Koppel, 1997) and in national reports (e.g., National Council of Teachers of Mathematics [NCTM], 2000; National Education Goals Panel, 1997). Although instruction that emphasizes reflective thinking and reasoning is considered by many to be critical to mathematics reform efforts (Baroody & Hume, 1991; Bottge, 1999; Hofmeister, 1993; Montague, 1997a), procedures that encourage memorization and the completion of lengthy worksheets requiring rote practice are common in many classrooms (Parmar & Cawley, 1991). Mathematics instruction in special education, particularly, has been characterized to a large extent by its emphasis on rote memorization of facts and computational skills, rather than on developing important concepts and applying mathematics to real-world problem situations (Baroody & Hume, 1991; Bottge, 1999; Parmar, Cawley, & Miller, 1994; Woodward & Montague, 2000). Many researchers argue that highly procedural instruction (meaningless drill and practice of computation facts) may sustain the characterization of students with learning disabilities as passive learners and fail to fill the gaps in their conceptual understanding of the core concepts and principles underlying mathematical thinking (Baroody & Hume, 1991; Parmar et al., 1994; Torgesen, 1982; Woodward & Montague, 2000). It is not surprising, then, that many students with learning disabilities have difficulty with higher level mathematics skills, such as solving word problems (Xin & Jitendra, 1999). Parmar, Cawley, and Frazita (1996) compared the performance of students with and without disabilities on arithmetic word problems involving all four operations and problems that contained direct or indirect statements, extraneous information, and one-step or two-step problems. Results indicated that the students with disabilities performed at significantly lower levels than the students without disabilities on all problem types. The students with disabilities experienced considerable difficulty with problem representation or identifying relevant information, along with difficulties in reading, computation, and identifying operations. One plausible deficiency of traditional mathematics instruction is its failure to make explicit the key aspects of domain knowledge needed for problem solving. Emerging views An Exploratory Study of Schema-Based Word-Problem–Solving Instruction for Middle School Students with Learning Disabilities: An Emphasis on Conceptual and Procedural Understanding