Before explaining new knowledge, students are required to read the textbooks carefully and form the habit of previewing actively, which is an important means to acquire mathematical knowledge. To cultivate students' self-study ability, we must first guide students to learn to read, carefully design and think about problems, and let students preview. For example, to preview a division example with a remainder, we must first find out what this example is about, what conditions it is about, what questions it asks, how to answer it in the textbook, why to answer it like this, whether there is a new solution, what are the steps to solve it, and so on. Grasp these problems, use your head to think, and gradually learn to use existing knowledge to explore and solve new knowledge independently.
2. Guide students to master thinking methods.
Some students are familiar with formulas, properties and rules. However, when encountering practical problems, I always feel at a loss and don't know how to answer with what I have learned. For example, when students learn the knowledge of angles, they know that an angle has a vertex and two sides, and they also know how to judge whether a graph is an angle. But in the process of counting how many angles a complex figure has, they feel that they can't start and can't count. This is how teachers should guide students to think about such topics, and how to avoid omission and repetition. Through the guidance of teachers, students can go through the process of groping and trying, and finally find out the law, or they can solve similar problems with the same problem-solving ideas.
3. Guide students to broaden their thinking of solving problems.
In the process of solving problems, there are many times when a problem will be solved in many different ways. In the teaching process, teachers are required to set questions for students frequently, so as to inspire students to think more, guide students to think actively and broaden their thinking, and make the broadness of students' thinking develop better.
4. Guide students to summarize the law of solving problems in time.
The answers to mathematical questions are usually regular. Guide students to learn to summarize the law of solving problems when solving problems. What is the most important feature of reviewing this problem after each problem is solved? What basic knowledge is used to solve this problem? When solving this problem, how to observe and associate them to realize the transformation? What mathematical ideas and methods are used to solve this problem? What is the key point to solve this problem? Have you ever done a similar problem, and what are the similarities and differences between the solution and the current problem? There are several different solutions to this problem, which one is the best? This series of questions will run through the whole process of solving problems, gradually improve and persevere, so that students' adaptability in the process of solving problems will be continuously improved and their thinking ability will be exercised and developed.