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Gifted and Learning-Disabled Gifted Students' Knowledge and Use of Mathematical Problem-Solving Strategies

The purpose of this study was to investigate students' cognitive and metacognitive knowledge of mathematical problem solving. Six students who had been identified as gifted or learning-disabled gifted were interviewed about their math problem solving. Videotape-stimulated recall was used as part of the interview process to help students reconstruct their problem-solving activities and recall strategies they know about and use during mathematical problem solving. Students solved seven novel and textbook problems, viewed themselves solving the problems, and responded to questions pertaining to problem-solving processes and strategies. Observations of performance and examination of interview transcripts provided insight into students' strategies and performance patterns. The importance of understanding characteristics of good problem solvers for designing effective instruction for less proficient problem solvers is emphasized. Several instructional recommendations are provided.