...studies utilizing approach for teaching problem solving to students with LD were previously evaluated to determine its status as evidence-based practice. The results of this evaluation are described, and the self-regulation component embedded in the cognitive routine for each of the studies is presented. The article concludes with a discussion of several principles associated with research and practice in strategy instruction and some practical considerations for implementation in schools.

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This article provides a review of research in strategy instruction for improving mathematical problem solving for students with learning disabilities (LD) with a focus on one of the salient components of this instructional approach--self-regulation. Research has consistently shown that students with LD are poor self-regulators who benefit from strategy instruction that incorporates self-regulation training (Graham & Harris, 2003; Wong, Harris, Graham, & Butler, 2003).

Self-regulation, the ability to regulate one's cognitive activities, underlies the executive processes and functions associated with metacognition (Flavell, 1976). Metacognition has to do with knowledge and awareness of one's cognitive strengths and weaknesses as well as self-regulation, which guides an individual in the coordination of that awareness while engaged in cognitive activities (Wong, 1999). Self-regulation strategies, such as self-instruction, self-questioning, self-monitoring, self-evaluation, and self-reinforcement, help learners gain access to cognitive processes that facilitate learning, guide learners as they apply the processes within and across domains, and regulate their application and overall performance of a task.

Swanson's (Swanson, 1999; Swanson & Sachs-Lee, 2000) meta-analyses of 30 years of both group and single-subject intervention studies conducted with students with LD revealed that direct instruction and strategy instruction were the two most effective instructional approaches, particularly when combined, for teaching students with LD across academic domains (i.e., reading, writing, and mathematics).

Interventions were considered direct instruction if they contained the following components: (a) drills and probes, (b) repeated feedback, (c) rapidly paced instruction, (d) individualized instruction, (e) breaking the task down into a sequence of steps, (f) pictorial diagrams, (g) small-group instruction, and (h) direct questioning by the teacher (Swanson, 1999).

In contrast, strategy instruction focuses on processes; for example, metacognition or self-regulation. The following procedures characterized strategy instruction: (a) systematic and direct explanations and/or verbal descriptions of the performance of a task; (b) verbal modeling, questioning, and demonstrations by the teacher of the steps and processes in the cognitive routine; (c) systematic prompts and cues to use the processes, strategies, and procedures; and (d) cognitive modeling using "think aloud" to model task completion or problem solving (Swanson, 1999).

Although the two instructional approaches were found to operate independently, they share many components and procedures, such as drill and repetition, distributed practice, task analysis, small-group instruction, and strategy cues, all of which were found to increase the predictive power of treatment effectiveness. Direct instruction was associated more with effective instruction for teaching basic skills such as decoding and math fact recall, as opposed to strategy instruction, which was associated more with effective instruction in higher order learning (e.g., reading comprehension and mathematical problem solving) that utilized higher order skills such as metacognition, self-monitoring, rule learning, and self-awareness (Swanson, 1999; Swanson & Sachs-Lee, 2000).

Likewise, Kroesbergen and van Luit (2003), in their meta-analysis of mathematics intervention studies conducted with students with disabilities, found that self-instruction, a self-regulation strategy, as a component of instructional models, is most effective generally for mathematics learning, but direct instruction appeared more effective for basic skills acquisition.

Following a comprehensive search of the literature, seven intervention studies were located that investigated the effects of cognitive strategy instruction on mathematical problem solving for students with disabilities. The five single-subject design and two group-design studies were evaluated individually using previously identified quality indicators to determine whether they qualified as "high quality" or "acceptable" and then to determine if the instructional practice, in this case, cognitive strategy instruction for improving mathematical problem solving, qualified as "evidence-based" or "promising" (Gersten et al., 2005; Homer et al., 2005).

For the single-subject studies, the benchmarks included (Homer et al., 2005):

1. Sufficient description of the participants and setting

2. Sufficient description of the measures and measurement procedures, including interrater agreement

3. Sufficient description of the intervention and procedures for determining

fidelity of implementation

4. Sufficient description of the baseline phase and evidence of a pattern prior to intervention

5. At least three demonstrations of experimental effect, explanations of how internal and external validity were controlled, and established social importance and cost-effectiveness of the intervention

For the group-design studies, the benchmarks included (Gersten et al., 2005):

1. Research based on previous studies or a compelling argument for its importance

2. Sufficient description of the participants, setting, attrition, and intervention agents

3. Sufficient description of the intervention, procedures for determining fidelity of...

NOTE: All illustrations and photos have been removed from this article.



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