递归原理的思维特性及其数学应用

Theoretical Analysis and Practical Attempt of Recursion Principle

递归原理的基本思想隐含于数学知识或解题过程中,构造递归结构是运用递归方法进行解题的关键步骤,也凸显了递归方法解题的策略性和技巧性。递归原理具有结构化、条件性、有限性和辩证性等思维特性,在数学实践中,结合数学课程内容,通过强化递归原理的数学观念、思想方法、策略模式等进行解题思维训练,可引导学生达成思维自控,不断提升思维能力,完善数学认知结构。

The basic idea of recursion principle is implicit in mathematical knowledge and problem-solving process.Constructing a recursive structure is the key step in using recursive method to solve problems.It is also the strategy and technique of recursion in problem-solving.Characterized with structuring,conditionality,finiteness and dialectic,recursion principle can be used to train and develop students’thinking ability effectively by strengthening the mathematical concepts,thinking methods,and strategic models underlying the recursive principle.Thus,the teaching approach can gradually move from teacher-led thinking to student self-control thinking,and students’thinking ability and cognitive structure of mathematics can be constantly improved.