数学解题与元解题的训练策略

Training Strategies for Mathematical Problem-Solving and Meta-Problem Solving

解题在数学学习活动中具有不可替代的作用,解题不仅包括了对数学知识的应用,还包括了对解题过程的认知(即元解题)。要提高数学解题能力就必须进行解题和元解题的训练。解题训练的策略有:激活原有认知结构、表征问题、目标导向、拓展延伸等;元解题训练的方法主要有教师进行元解题思路示范、学生自我提问方式和写数学体会等。

Solving problem plays an irreplaceable role in mathematical studying activities. Solving problem includes not only the use of the mathematical knowledge, but also the cognition of the problem-solving process （i.e. meta-problem solving）. In order to improve the mathematical problem-solving ability, it is necessary to carry on training for problem-solving strategy and original problem-solving strategy. The strategies for problem-solving training include activating the original cognitive structure, symbolizing problems, expanding and extending and having a goal-oriented mind. The methods of meta-problem solving training mainly include the demonstration of the original problem-solving thinking by teachers, the self-questioning approach of students, learning from experience of solving mathematical problems, etc.