Problem Solving Toward Mathematical Understanding : instructional design for students with learning disabilities

Over three decades of data continue to show a lack of mathematical achievement for students of color, minority language speakers, students living in poverty, or those who have learning disabilities (LD). Problem Solving Toward Mathematical Understanding (PSTMU) is designed to teach LD children multiple ways to represent and solve problems, improve reasoning skills, and persevere. Through the use of higher-order questioning, students develop metacognitive awareness helping them monitor the effectiveness of a strategy and to consider different options. PSTMU is designed to develop a deeper understanding of mathematical concepts through scaffolded instruction, peer-talk, teacher-talk, and group discussions. Students come to a shared understanding of the material and observe multiple approaches to solving problems. The curriculum was implemented, evaluated, and revised over seven weeks with a group of nine middle school students in an urban school setting. The students were of low socio-economic background, diverse ethnicities, and all had one or more learning disabilities. Qualitative and quantitative measures were used to determine the effectiveness of this approach. Students' problem solving skills, ability to reason, provide proof, effectively communicate mathematically, and create and use representations in their work was evaluated through a rubric scored by two raters. Observations, class work, and audio recordings were used to support the findings. Surveys and questionnaires were used to rate metacognitive awareness and attitude. The data indicated that all students increased their abilities in two or more of the areas evaluated. The attitudes of six out of the nine students improved and overall students became more flexible in their use of strategies to solve problem