Marjorie Montague

The Effects of Cognitive and Metacognitive Strategy Instruction on the Mathematical Problem Solving of Middle School Students with Learning Disabilities

This study investigated the effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of six middle school students with learning disabilities. Conditions of the multiple baseline, across-subjects design included baseline, two levels of treatment, setting and temporal generalization, and retraining. For Treatment 1, subjects received either cognitive or metacognitive strategy instruction. Treatment 2 consisted of instruction in the complementary component of the instructional program so that all subjects eventually received both cognitive and metacognitive strategy instruction. This design allowed a componential analysis of the content as well as sequence of instruction. Generally, subjects improved their mathematical problem solving as measured by performance on one-, two-, and three-step word problems. Discussion focused on effectiveness of treatment, acquisition and application of strategic knowledge, error pattern analysis, and the need to tailor instruction to the learners individual characteristics.

The Effect of Cognitive Strategy Training on Verbal Math Problem Solving Performance of Learning Disabled Adolescents

This study investigated the effect of an eight-step cognitive strategy on verbal math problem solving performance of six learning disabled adolescents. The cognitive strategy was designed to enable students to read, understand, carry out, and check verbal math problems that are encountered in the general math curriculum at the secondary level. Conditions of the multiple baseline desing included baseline, treatment, generalization, maintenance, and retraining. During treatment, students received strategy acquisition training, strategy application practice, and testing. Visual analysis of the data indicated this eight-step cognitive strategy to be an effective intervention for this sample of students who had deficits in verbal math problem solving. Overall, the students demonstrated impoved performance on twostep verbal math problems. Maintenance and generalization of the strategy were evident. This study has implications for an alternative teaching methodology that focuses on cognitive strategy training to improve the verbal math problem solving of learning disabled students.

Meeting the Challenge of Mathematics Reform for Students with LD

The purpose of this article was to examine the sustained effort to reform K through 12 mathematics instruction in this country over the last 10 years and the implications of this reform for students with learning disabilities. We begin by describing three forces that have driven mathematics reform: shifting theoretical paradigms, disappointing levels of mathematics performance of students in the United States, and the impact of rapidly changing technologies. We then discuss concerns about this reform from the special education community. In the second half of the article, we provide synthesized special education research relevant to mathematics reform, along with thoughts about future directions in mathematics education for students with learning disabilities.

SELF-REGULATION STRATEGIES TO IMPROVE MATHEMATICAL PROBLEM SOLVING FOR STUDENTS WITH LEARNING DISABILITIES

This article provides a review of research in cognitive strategy instruction for improving mathematical problem solving for students with learning disabilities (LD). The particular focus is on one of the salient components of this instructional approach — self-regulation. Seven studies utilizing this 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.

Middle School Students' Mathematical Problem Solving: An Analysis of Think-Aloud Protocols.

Using a cognitive-metacognitive theoretical framework, this study examined the verbalizations of middle school students as they thought aloud while solving three mathematical word problems. Middle school subjects who had been identified as learning disabled, average achieving, and gifted were given demonstrations and practice in thinking aloud and were then instructed to solve one-step, two-step, and three-step word problems while thinking aloud. A priori categories were developed based on information-processing theory and a cognitive-metacognitive perspective of mathematical problem solving. Verbalizations were coded, and between-group and grade comparisons of the number of verbalizations within categories were conducted. The relationship between type of verbalization and overall performance was also analyzed. The findings support Ericcson and Simons (1980) view of concurrent verbalization as a technique for assessing cognitive processes and Swansons (1988) notion that students with learning disabilities may use a qualitatively different approach to problem solving than their nondisabled peers.

Story Grammar and Comprehension and Production of Narrative Prose by Students with Learning Disabilities

This study investigated both quantitative and qualitative differences between subjects with and without learning disabilities (LD) across three grade levels on two tasks requiring active processing of story grammar. There was no evidence, for either task, of developmental differences in relation to either story comprehension or production. However, there were significant differences between students with LD and normally achieving students in the amount as well as the type of information included in the retellings and written stories. The results provide support for the hypothesis that students with LD have acquired a rudimentary but not fully developed schema for narrative prose.

Effects of Cognitive Strategy Instruction on Math Problem Solving of Middle School Students With Learning Disabilities

The purpose of the study was to improve mathematical problem solving for middle school students with learning disabilities by implementing a research-based instructional program in inclusive general education math classes. A total of 40 middle schools in a large urban district were matched on state assessment performance level (low, medium, and high performing) and socioeconomic status. One school from each pair was randomly assigned to the intervention condition, and one eighth grade math teacher participated at each school (n = 40). Because of attrition at the outset, 24 schools completed the study (8 intervention, 16 comparison). The intervention, Solve It!, a research-based cognitive strategy instructional program, was implemented for 7 months, and periodic progress monitoring was conducted. A cluster-randomized design was used, and the data were consistent with a three-level model in which repeated measures were nested within students and students were nested within schools. The results indicated that students who received the intervention (n = 319) showed significantly greater growth in math problem solving over the school year than students in the comparison group (n = 460) who received typical classroom instruction. Moreover, the intervention effects did not differ for students with learning disabilities, low-achieving students, and average-achieving students. Thus, the findings were positive and support the efficacy of the intervention when implemented by general education math teachers in inclusive classrooms.

Evaluating the Evidence Base for Cognitive Strategy Instruction and Mathematical Problem Solving

This review considers both the content and methodologies of 5 single-subject and 2 group experimental design studies investigating the effects of cognitive strategy instruction on the mathematical problem solving of students with disabilities, using quality indicators proposed by Horner et al. (2005) and Gersten et al. (2005). Findings indicated that the research base of both single-subject and group experimental studies did not meet the methodological criteria to support cognitive strategy instruction as an evidence-based practice for improving mathematical problem solving of students with disabilities. The shortcomings identified in the empirical literature supporting cognitive strategy instruction, however, can be addressed in future intervention studies bearing in mind the quality indicators and standards for determining evidence-based practices.

Metacognitive Strategy Use of Eighth-Grade Students With and Without Learning Disabilities During Mathematical Problem Solving A Think-Aloud Analysis

The purpose of the study was to investigate the metacognitive abilities of students with LD as they engage in math problem solving and to determine processing differences between these students and their low- and average-achieving peers (n = 73). Students thought out loud as they solved three math problems of increasing difficulty. Protocols were coded and analyzed to determine frequency of cognitive verbalizations and productive and nonproductive metacognitive verbalizations. Results indicated different patterns of metacognitive activity for ability groups when type of metacognitive verbalization and problem difficulty were considered. Implications for instruction are discussed.

Cognitive and metacognitive characteristics of eighth grade students' mathematical problem solving

Abstract The purpose of this study was to investigate the cognitive and metacognitive characteristics of eighth grade students in mathematical problem solving. Differences among high achieving (HA), average achieving (AA), low achieving (LA), and learning disabled (LD) students ( N = 60) on measures of mathematical achievement; reasoning; mathematical problem solving; and strategy knowledge, use, and control were studied. One-way analyses of variance and multivariate analyses of variance were employed to detect differences on a variety of dependent variables derived from a reasoning test, mathematical achievement tests, and a structured interview. Results indicated that LD and LA students differ significantly from AA and HA students in both general mathematical achievement and mathematical problem solving. Another finding suggested that poor problem solving performance of LD students may be related less to computational errors than to other factors such as prediction and selection of appropriate operations for solving problems. Finally, the results suggested that LD students are less aware of problem solving strategies than their peers and may be deficient in regulating strategy selection and application when solving mathematical problems.