解题思路与解题策略的教学研究

Teaching Research on Solving Thoughts and Solving Strategies

解决问题是数学教学中必不可少的一个环节,所有数学知识的学习都是为解决数学问题做铺垫的。因此,在解题教学中引导学生理清解题思路、制定解题策略并对题目反思迁移是一项重要的任务。以波利亚的"怎样解题"表为基础,提出四个解决数学问题的策略:从问题本身出发,理清思路,理解问题;借助画图列表建构思路,拟订计划;合理尝试和猜想,转化思路,实施计划;提高思维层次,迁移方法,回顾反思。通过对解题思路和解题策略的分析,找出培养学生解题能力的方法,提高学生的数学思维能力。

Problem solving is an indispensable link in mathematics teaching.All the learning of mathematical knowledge is to pave the way for solving mathematical problems.Therefore,it is an important task to guide students to solve problems in the teaching of problem solving,to formulate strategies for solving problems and to reflect on the transfer of problems.Based on Poolia’s“how to solve problems”table,this paper puts forward four strategies for solving mathematical problems:starting from the problem itself,clearing out ideas and understanding problems;drawing up ideas,lists,and plans;reasonable attempts and guesses,transforming ideas,and implementing plans;improving the level of thinking,transferring methods,review and reflection.It is hoped that through the analysis of problem-solving ideas and problem-solving strategies,the methods of cultivating students’problem-solving ideas and problem-solving strategies can be found,and the students’ability of thinking in mathematics can be improved.