First, learn to preview new knowledge actively \x0d\ Before explaining, read the textbook carefully and develop the habit of previewing actively, which is an important means to acquire mathematical knowledge. Therefore, cultivate self-study ability, learn to read books under the guidance of teachers, and preview with teachers' carefully designed thinking problems. For example, if you teach yourself an example, you should find out what the example is about, what the conditions are, what you want, how to answer it in the book, why you answer it like this, whether there is a new solution and what the steps are. Grasp these important problems, think with your head, go deep step by step, and learn to use existing knowledge to explore new knowledge independently. \x0d\ Second, master the thinking method under the guidance of the teacher \x0d\ Some students are familiar with formulas, properties and laws. But I don't know how to apply what I have learned to answer practical questions. If there is such a problem for students to solve, "if the height of a cuboid is removed by 2 cm, it becomes a cube, and its surface area is reduced by 48 cm." What is the volume of this cube? " Although students are familiar with the formula for finding the volume, many students can't figure out the way to solve the problem because the problem involves a wide range of knowledge and requires students to gradually master the thinking method when solving the problem under the guidance of the teacher. In terms of units, this problem involves length units and area units; Graphically speaking, it involves rectangles, squares, cuboids and cubes; From the relationship of graphic changes: rectangle → square; From the perspective of thinking and reasoning, it is: a cuboid → reducing a part of a cuboid with a square at the bottom → reducing the area of four faces → finding the area of one face → finding the length of a rectangle (that is, the side length of a square) → the volume of a cube. Inspired by the teacher, after the analysis, the students can answer according to their ideas (they can draw pictures). Some students soon figured it out: if the length of the bottom of the original cuboid is x, then 2X×4=48 = 48 gives: x = 6 (that is, the side length of the cube), so the volume of the cube is 6× 6× 6 = 2 16 (cubic centimeter). \x0d\ III。 Summarize the law of solving problems in time \x0d\ Generally speaking, there are laws to follow in solving mathematical problems. When solving problems, we should pay attention to summing up the law of solving problems. After solving each exercise, you should pay attention to reviewing the following questions: (1) What is the most important feature of this problem? (2) What basic knowledge and graphics are used to solve this problem? (3) How do you observe, associate and transform this problem to achieve transformation? (4) What mathematical ideas and methods are used to solve this problem? (5) Where is the most critical step to solve this problem? (6) Have you ever done a topic like this? What are the similarities and differences between solutions and ideas? How many solutions can you find to this problem? Which is the best? What kind of solution is a special skill? Can you sum up under what circumstances? Put this series of questions into every link of solving problems, gradually improve and persevere, so that students' psychological stability and adaptability to solving problems can be continuously improved and their thinking ability can be exercised and developed. \x0d\ IV。 Broaden the thinking of solving problems \x0d\ In teaching, teachers will often set questions and ask questions for students to inspire them to think more. At this time, students should actively think and broaden their thinking, so that the broadness of thinking can be better developed. For example, a 2400-meter-long canal was built, and 20% was built in five days. According to this calculation, how many days will it take to repair the rest? According to the relationship among total workload, work efficiency and working hours, students can list the following formula: (1) 2400 ÷ (2400× 20% ÷ 5)-5 = 20 (days) (2) 2400× (1-20%). The teacher inspired the students to ask, "How many days will it take to repair 20% of them and the rest (1-20%)?" Students quickly thought of the method of doubling: (3) 5× (1-20%) ÷ 20% = 20 (days). If we think from the method of "knowing how many fractions a number has and finding this number", we can get the following solution: 5 ÷ 20%-5 = 20 (days). Enlighten the students again. Can you answer with proportional knowledge? Students will come up with: (6) 20%: (1-20%) = 5: X (assuming the rest will be completed in x days). This inspires students to think more, communicates the vertical and horizontal relationship between knowledge, changes the problem-solving methods, broadens students' problem-solving ideas and cultivates students' thinking flexibility. \x0d\ v. Be good at asking questions and asking difficult questions \ x0d \ Learning begins with thinking, and thinking comes from doubt. Students' positive thinking often begins with doubt, and learning to find and ask questions is the key to learning to innovate. Gu Mingyuan, a famous educator, said, "Students who can't ask questions are not good students." The concept of students in modern education requires: "Students can think independently and have the ability to ask questions." To cultivate innovative consciousness and learn to learn, we should start with learning to ask questions. For example, when learning to "measure the angle" and know the protractor, observe the protractor carefully and ask yourself, "What have I found? What questions can I ask? " By observing and thinking, you may say, "Why are there two semi-circular scales?" "What's the use of internal and external scales?" "Is it more convenient to measure with only one scale than with two scales?" "Why is there a central point?" Wait, different students will put forward different opinions. When measuring a shape like "V", you may think that it is not necessary to use one of the sides to coincide with the zero scale line of the protractor. In learning, we should be good at finding problems and dare to ask questions, that is, increase the subjective consciousness, dare to express our own views and opinions, stimulate the desire to create, and always maintain a high learning mood.