1. Learn to proactively preview new knowledge\x0d\ Before explaining new knowledge, read the textbook carefully and develop the habit of proactive preview, which is an important means to acquire mathematical knowledge. Therefore, cultivate self-study ability, learn to read under the guidance of the teacher, and preview with the teacher's carefully designed thinking questions. For example, when self-study examples, you need to find out what the examples are about, what conditions are told, what is asked for, how the solution is in the book, why it is solved in this way, whether there are any new solutions, and what are the steps to solve the problem. Grasp these important issues, use your brain to think, go deeper step by step, and learn to use existing knowledge to independently explore new knowledge. \x0d\ 2. Master the method of thinking about problems under the guidance of the teacher \x0d\ Some students are quite familiar with formulas, properties, rules, etc., but when they encounter practical problems, they have no way to start and do not know how to apply what they have learned. knowledge to answer questions. For example, there is a question for students to solve: "Remove 2 centimeters from the height of a cuboid and it becomes a cube. Its surface area is reduced by 48 square centimeters. What is the volume of this cube?" Although the students remember the formula for finding the volume very well. However, because the question involves a wide range of knowledge, many students cannot understand the problem-solving ideas. This requires students to gradually master the thinking methods when solving problems under the guidance of the teacher. In terms of units, this question involves length units and area units; in terms of graphics, it involves rectangles, squares, cuboids, and cubes; in terms of graphic change relationships: rectangle → square; in terms of thinking and reasoning: cuboid → reduction Part of the rectangular base is a square → reduce the area of ??the four faces to be equal → find the area of ??a face → find the length of the rectangle (i.e. the length of one edge of the square) → the volume of the cube. After the teacher’s inspiration and analysis, the students based on their Ideas (can draw graphics) to answer. Some students quickly figured out the answer: Suppose the base length of the original cuboid is X, then 2X×4=48: 216 (cubic centimeters). \x0d\3. Summarize the problem-solving rules in a timely manner\x0d\ Generally speaking, there are rules to follow in solving mathematical problems. When solving problems, you should pay attention to summarizing the problem-solving rules. After solving each exercise problem, you should pay attention to review the following questions: (1) What is the most important feature of this problem? (2) What basic knowledge and basic graphics are used to solve this problem? (3) How did you observe, associate, and transform to achieve transformation in this question? (4) What mathematical ideas and methods were used to solve this problem? (5) Where is the most critical step in solving this problem? (6) Have you ever done anything similar to this question? What are the similarities and differences in solutions and ideas? (7) How many solutions can you find for this question? Which of them is the best? Is that solution a special technique? Can you summarize the circumstances under which it is adopted? By incorporating this series of questions into every aspect of problem-solving, gradually improving them, and persevering, students' psychological stability and adaptability in problem-solving can be continuously improved, and their thinking abilities can be exercised and developed. \x0d\ 4. Broaden problem-solving ideas \x0d\ During teaching, teachers will often set doubts for students, ask questions, and inspire students to think more. At this time, students should think actively and broaden their ideas so that the broadness of thinking can be obtained better development. For example: to build a 2,400-meter-long canal, 20% of it was built in 5 days. Based on this calculation, how many days will it take to complete the rest? According to the relationship between the total workload, work efficiency, and working time, students can list the following formulas: (1) 2400÷(2400×20%÷5)-5=20 (days) (2) 2400×(1- 20%)÷(2400×20%÷)=20 (days). The teacher inspired the students and asked: "It will take 5 days to complete 20% of it. How many days will it take to complete the remaining (1-20%)?" The students quickly thought of a doubling method and listed: (3) 5× (1-20%) ÷ 20% = 20 (days). If you think from the method of "you know what fraction of a number is, find this number", you can get the following solution: 5 ÷ 20% -5 = 20 (days). Inspire students, can they use proportion knowledge to solve the problem? Students will come up with: (6) 20%: (1-20%) = 5: End). This inspires students to think more, communicates the vertical and horizontal relationships between knowledge, changes problem-solving methods, broadens students' problem-solving ideas, and cultivates students' thinking flexibility. \x0d\5. Be good at questioning and asking questions\x0d\Learning starts with thinking. , Thinking comes from doubts. Students' positive thinking often starts with doubts. Learning to discover and ask questions is the key to learning innovation.

The famous educator Gu Mingyuan said: "A student who cannot ask questions is not a good student." The student outlook of modern education requires: "Students can think independently and have the ability to ask questions." Cultivating innovative consciousness and learning to learn should start with learning to ask questions. . For example, when learning "Measurement of Angles" and getting to know the protractor, carefully observe the protractor and ask yourself: "What did I find? What questions can I ask?" Through observation and thinking, you may say: "Why are there two semicircles? What about the scale? "What is the use of the inner and outer scales?", "Is it more convenient to measure with only one scale?", "Why should there be a central point?" and so on, different students will ask. Propose various opinions. When measuring a shape such as a "V", you may think of ways to avoid having one of its sides coincide with the zero mark of the protractor. During learning, you must be good at discovering problems and dare to ask questions, that is, increase your subjective awareness, dare to express your own views and opinions, stimulate your desire to create, and always maintain a high learning mood.