The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD, n = 25), low-achieving students (LA, n = 30), and average-achieving students (AA, n = 29). The primary interest was to analyze the processes students use to translate and integrate problem information while solving problems. Paraphrasing, visual representation, and problem-solving accuracy were measured in eighth grade students using a researcher-modified version of the Mathematical Processing Instrument. Results indicated that both students with LD and LA students struggled with processing but that students with LD were significantly weaker than their LA peers in paraphrasing relevant information. Paraphrasing and visual representation accuracy each accounted for a statistically significant amount of variance in problem-solving accuracy. Finally, the effect of visual representation of relevant information on problem-solving accuracy was dependent on ability; specifically, for students with LD, generating accurate visual representations was more strongly related to problem-solving accuracy than for AA students. Implications for instruction for students with and without LD are discussed.

The effects of a mathematical problem-solving intervention on students' problem-solving performance and math achievement were measured in a randomized control trial with 1,059 7th-grade students. The intervention. Solve It!, is a research-based cognitive strategy instructional intervention that was shown to improve the problem-solving performance of 8th-grade students with and without leaming disabilities (LD). The purpose of the present study was to determine whether the effectiveness of the intervention could be replicated with younger students. Forty middle schools in a large urban school district were included in the study, with one 7th-grade math teacher participating at each school (after attrition, n = 34). Solve It! was implemented by the teachers in their inclusive math classrooms. Problem-solving performance was assessed using curriculumbased math problem-solving measures, which were administered as a pretest and then monthly over the course of the 8-month intervention. Students who received the intervention (n = 644) embedded in the district curriculum showed a significantly greater rate of growth on the curriculum-based measures than students in the comparison group (n = 415) who received the district curriculum only. Results of the Bayesian analyses indicated that the intervention effect was somewhat stronger for low-achieving students than for averageachieving students. Overall, findings from the present study as well as the previous study with 8th-grade students indicate that the intervention was effective across ability groups and is an appropriate program to use in inclusive classrooms with students of varying math ability.

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.

This study investigated the effectiveness of Solve It! instruction on students’ knowledge of math problem-solving strategies. Solve It! is a cognitive strategy intervention designed to improve the math problem solving of middle school students with learning disabilities (LD). Participants included seventh- and eighth-grade students with LD (n = 77) and average-achieving students (n = 77). We examined treatment effects of the intervention, as well as differential effects of treatment across ability levels, on students’ knowledge of problem-solving strategies using the Math Problem-Solving Assessment. Results showed that students across ability levels who received Solve It! instruction reported using significantly more strategies than students in the comparison group. Implications for instruction are discussed as well as directions for future research.

Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research.

The purpose of this article is to offer teacher training and professional development recommendations in mathematics based on the findings of a federally funded 3-year intervention study that improved the problem solving of middle school students with a focus on students with learning disabilities. Over the 3-year project, 29 seventh and eighth grade teachers implemented a problem-solving intervention based on cognitive strategy instruction. Though the intervention was successful in improving students' problem-solving performance, several issues related to teaching effectiveness and teacher training came to light. The article will: (1) describe the intervention and its implementation, (2) present the findings of the study, and (3) discuss the issues of effectiveness and possible solutions via teacher education and professional development.

Students with learning disabilities (LD) consistently struggle with word problem solving in mathematics classes. This difficulty has made curricular, state, and national tests particularly stressful, as word problem solving has become a predominant feature of such student performance assessments. Research suggests that students with LD perform poorly on word problem-solving items due primarily to deficits in problem representation. Therefore, it is imperative that teachers provide these students with supplemental problem-solving instruction that specifically targets the development of representational strategies. This article describes how one representational strategy, using number lines, can be used to model word problems as part of a comprehensive problem-solving intervention to improve the conceptual understanding of math word problems and, subsequently, the problem-solving performance of students with LD.

Título: Hipatia: un entorno de aprendizaje hipermedia en matemáticas. Resumen: La literatura existente señala los beneficios de diferentes herramientas dirigidas al desarrollo de la competencia matemática, la solución de problemas y los aspectos afectivo-motivacionales y la intervención en estudiantes con dificultades específicas de aprendizaje en matemáticas. Sin embargo, no existe una herramienta que combine todas estas variables. El objetivo de este estudio es presentar y describir el diseño y desarrollo de una herramienta hipermedia llamada Hipatia. Los ambientes hipermedia son, por definición, sistemas adaptativos de aprendizaje que son habitualmente empleados para proporcionar ambientes personalizados de aprendizaje. Este trabajo describe los principios en los que se basa la herramienta hipermedia Hipatia, así como, una revisión de las tecnologías disponibles desarrollas en diferentes áreas académicas. Hipatia fue creada para potenciar la autorregulación del aprendizaje y desarrollar habilidades específicas matemáticas y la resolución de problemas. La herramienta está dirigida a estudiantes de quinto y sexto curso de Educación Primaria con y sin dificultades de aprendizaje en matemáticas. Tras el desarrollo de la Hipatia, se puede concluir que efectivamente subyace los principios dela aprendizaje autorregulado. En investigaciones futuras será necesario poner a prueba la eficacia de la herramienta a través de metodologías empíricas. Palabras clave: Hipermedia; pizarras interactivas; ambientes de aprendizaje; aprendizaje autorregulado; matemáticas.Abstract: Literature revealed the benefits of different instruments for the development of mathematical competence, problem solving, self-regulated learning, affective-motivational aspects and intervention in students with specific difficulties in mathematics. However, no one tool combined all these variables. The aim of this study is to present and describe the design and development of a hypermedia tool, Hipatia. Hypermedia environments are, by definition, adaptive learning systems, which are usually a web-based application program that provide a personalized learning environment. This paper describes the principles on which Hipatia is based as well as a review of available technologies developed in different academic subjects. Hipatia was created to boost self-regulated learning, develop specific math skills, and promote effective problem solving. It was targeted toward fifth and sixth grade students with and without learning difficulties in mathematics. After the development of the tool, we concluded that it aligned well with the logic underlying the principles of self-regulated learning. Future research is needed to test the efficacy of Hipatia with an empirical methodology.