First of all, we must understand the basic process of solving problems.
Mathematical problem solving refers to a thinking process of approaching the goal step by step according to certain thinking countermeasures and finally reaching the goal. In other words, solving problems in the field of mathematics not only pays attention to the result of the problem, but more importantly, pays attention to the process of obtaining the result. In order to solve the problem, it is necessary to find out the solution target, known conditions and unknown conditions, which is the first step to solve the problem. It puts high demands on the agility and profundity of thinking and creates excellent training opportunities for it. The second step to solve the problem is to design a solution, which requires a lot of analysis, synthesis, trial guess and analogy, which is of great benefit to the flexibility and originality of training thinking. The last step to solve the problem is to test and check the results obtained. At this time, the critical and profound nature of training thinking plays a very important role.
Second, specific suggestions.
1, pay attention to correctly understand the problem of "good".
The problem should be exploratory, and there are no ready-made methods and procedures to solve this problem, but students' various thinking and creativity need to be brought into play; The questions should be realistic, interesting and unpretentious, which can stimulate every student's curiosity; There are often many methods and strategies to solve problems, which require students to comprehensively use what they have learned and play a variety of mathematical thinking; Questions should be enlightening and help students master important mathematical thinking methods and problem-solving strategies, rather than so-called "off-topic" and "strange questions"; At the same time, questions should be properly open, which is not necessarily reflected in the diversity of answers. More importantly, problems can be solved by all students, and different students can develop in the process of solving problems.
2. Help students read the questions.
For solving problems, students' difficulties are, first, examining questions, and second, analyzing quantitative relations. Only after reading the questions can we lay the foundation for later analysis of quantitative relations. How to read the question? We can ask students: read it again and find out what it is; Read it twice, filter it and capture useful mathematical information. Who has anything to do with who? Read it three times and tell us what problem to solve. Only by understanding the problem can we solve it better. Teachers can help students understand the problem through gestures and scene reproduction when guiding students to read the problem.
3. On the basis of understanding the meaning of operation, analyze the quantitative relationship.
Solving problems requires students to have a mathematical vision, be able to identify the quantitative relationships in daily life, natural phenomena and other disciplines, refine them, analyze them by using the knowledge they have learned, and then comprehensively apply the knowledge and skills they have learned to solve them. Secondly, we should pay attention to the teaching of operation meaning. The meanings of addition, subtraction, multiplication and Divison are the core concepts. Only when students really understand the meaning of addition, subtraction, multiplication and division can they know when and what operation to use to solve problems. Third, we should pay attention to the analysis of quantitative relations. When solving specific problems, teachers should encourage students to find the implicit quantitative relationship in the problem through practical operation, thinking and discussion, and emphasize the practical and mathematical significance of truly understanding the problem.
4. Pay attention to solving problems with equations.
Equation is a good mathematical thinking, which can help people solve problems with forward thinking and the thinking process is relatively simple. Using equations is meaningful and helpful for reverse thinking. Some students don't want to use this equation because they think its format is very complicated. In teaching, teachers should have a sense of simplification and understand that the purpose of teaching is to train students to solve problems with the idea of equations.
5. Form some basic problem-solving strategies and experience the diversity of problem-solving strategies.
The value of problem-solving activities is not only to get the answers to specific questions, but more importantly, the development of students in the process of solving problems. One of the most important points is to let students learn some basic problem-solving strategies, experience the diversity of problem-solving strategies, and form some of their own problem-solving strategies on this basis. In teaching, we should pay attention to the guidance of students' problem-solving strategies and make the "hidden" problem-solving strategies "explicit". For example, before solving problems, teachers can encourage students to think about what strategies are needed to solve problems; In the process of solving problems, teachers can let students pay attention to whether to adjust the problem-solving strategies according to specific conditions; After solving the problem, teachers should encourage students to reflect on the strategies they use and organize the whole class to communicate. In short, teachers should take problem-solving strategies as an important goal and consciously guide and teach them. In addition, the strategies adopted by students may be good or bad in the eyes of teachers, but there is no good or bad in the children's thinking process, which reflects the students' understanding and efforts to the problem. As long as the students' problem-solving process and answers are reasonable, they are all worthy of recognition, because it provides a valuable opportunity to build students' self-confidence and cultivate their innovative spirit.