| Summary: | 碩士 === 臺北市立教育大學 === 數學資訊教育學系碩士班 === 96 === The purpose of this study is to investigate the difference of representing problem; devising and carrying out problem-solving strategies and control the process of problem-solving, and how the difference effect the devising and carrying out the plan of problem-solving when the different ability children face non-routine problem.
The study selected four 6-th grade students (two high abilities; two low abilities) from Taipei private school, and used “non-synchronic thinking-aloud” method interview students about six mathematical problem individually, then analyze, discuss, and sort the characteristics and difference. The following conclusions are provided:
In representing problem, divide into three levels: wrong representation, direct representation, and relational representation. High abilities tend to relational representation, they can transform the difference form of representation, and select material which help themselves thinking. Using direct representation and relational representation can express full meaning completely, so the difference of devising the plan of problem-solving is not obvious, but when carrying out the plan, the process of reaching aim is fluent or not depends on which level he belongs to.
In devising and carrying out problem-solving strategies, High abilities have devised and carried out feckless, complex, effective strategies; but low abilities often can’t devise and carry out effective strategies. High abilities have more strategies and they can use more than one strategy at the same time. When high abilities can’t solve problem successfully, they can transform strategies by themselves, using effective strategies to solve problem.
Six levels in control: level 1 non-control; level 2 unclear control; level 3 result control; level 4 process control; level 5 relational control; level 6 reflective control. Low abilities belong to level 1 to level 3; High abilities belong to level 3 to level 6.
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