1 Research on ideas and skills of solving mathematical problems; Research on the thinking and skills of solving mathematical problems: research on the thinking and skills of solving mathematical problems: review; Review; Review; After sorting out the above materials, I intend to write this paper from the following aspects with reference to the above materials. 2. Several common mathematical problem-solving ideas Several common mathematical problem-solving ideas Research on several common mathematical problem-solving ideas When introducing various mathematical problem-solving ideas, I borrowed several common mathematical problem-solving ideas from the following three reference books: Elementary Mathematics Research, Mathematical Methodology-Problem-solving Theory, and Senior High School Mathematics Problem-solving Methods and Skills to discuss mathematical problem-solving ideas. 3. Cultivation of mathematical problem-solving skills and applied mathematical problem-solving skills. 4. When discussing the cultivation and application of mathematical problem-solving skills, I borrowed several Wan Fang periodical materials collected from the campus network library: Cultivation of Mathematical Problem-solving Skills and Practice and Discussion of Cultivating Teachers' and Students' Mathematical Problem-solving Ability. Borrowing the above data and my own understanding, I summed up the following exploration methods: overall substitution method, reduction method, collocation method, clever use of non-negative numbers, clever construction of equations, clever design of elements and so on. How to integrate mathematical problem-solving ideas into problem-solving skills, how to integrate mathematical problem-solving ideas into problem-solving skills, how to integrate mathematical problem-solving ideas into problem-solving skills, and how to write research on integrating problem-solving ideas into problem-solving skills are a major focus of this paper. Referring to the relevant contents in two periodicals, On the Multi-purpose of One Problem in Mathematics Problem-solving Teaching and Thinking of Solving Mathematical Problems with Multiple Solutions, collected by the campus network library of the school, this paper discusses the skills of problem-solving thinking through multiple solutions to one problem. First of all, I used the following solutions to an inequality: the idea of classified discussion; The idea of combining numbers with shapes; The idea of transformation and transformation; Concepts of functions and equations. With the help of four different solutions of inequality in the above periodicals, it can be understood that mathematical thought is the abstraction and generalization of mathematical knowledge at a higher level, which is contained in the process of the occurrence, development and application of mathematical knowledge. Therefore, the study of mathematical ideas must be combined with mathematical knowledge, and through the study of mathematical knowledge, students' understanding and mastery of mathematical ideas can be continuously fed back. Thus, it is beneficial to establish concepts from the overall and ideological significance of mathematics, pay attention to general methods, improve problem-solving skills, and effectively test students' mastery of mathematical ideas contained in middle school mathematics knowledge.

5. Cultivate the experience of problem-solving ideas and skills, cultivate the experience of problem-solving ideas and skills, and study and study. When expounding the experience of cultivating problem-solving ideas and skills, I borrowed three kinds of periodical materials collected from the campus network library in Wan Fang: How to Cultivate Students' Problem-solving Skills in Junior Middle School Mathematics Teaching, Click Problem-solving Skills and How to Guide Students to Learn Mathematics Well. By borrowing the essence of these three journals and combining what I have learned, I summarized the following three points to emphasize how to improve the ability of problem-solving skills. First of all, we should strengthen the teaching of basic mathematics knowledge and the training of basic skills. Second, we should vigorously improve students' observation ability. Third, we should improve students' ability to use basic knowledge flexibly.