Abstract: This study compared mathematically gifted and mathematically disabled students in solving compare problems and the effects of metacognition on problem solving achievement with both experimental and clinical interview methods. Ss were 40 third graders of an elementary school. Compare problems were divided into consistent problems and inconsistent problems. Metacognition included metacognitive knowledge and metacognitive monitoring skills. The results showed that: (1) There were significant differences between the two group of students, mathematically gifted students performed better than mathematically disabled students in both consistent and inconsistent problems. These differences were due to the different representing strategy used by mathematically gifted and mathematically disabled students. (2) The main errors in solving compare problems were reversal errors, there were more errors in consistent problems than those in inconsistent problems. (3) There were significant differences between mathematically gifted and mathematically disabled students on metacognitive knowledge and metacognitive monitoring skills, metacognitive monitoring skill is a significant predictor in solving compare problems.

Key words: mathematics, problem solving, metacognition