Multi-solution to a problem refers to encouraging students to think independently and solve problems in their own way in the process of solving problems, so that there will be many ways to solve problems in the group, and then report and communicate with each other in the group. It is not difficult to find that in this learning process, students can solve problems through independent thinking, exercise their independent learning and inquiry ability, and deepen their thinking. More importantly, in the process of communicating and reporting their own methods, students compare, analyze and understand various methods, obtain a variety of problem-solving methods, promote students' multi-angle thinking, break the original thinking mode and habits, and expand the breadth of students' thinking. In the teaching of multiple solutions to one problem, teachers should pay attention to the selection of materials, so that students can obtain a variety of problem-solving methods. In addition, teachers should also stimulate students' intellectual resources to the maximum extent, so that students' thinking can be expanded to the maximum extent.

Second, pay attention to the diversity of topics and promote the development of thinking breadth.

Changing the topic is to change the conditions or problems in the topic. In the process of solving problems, students' thinking direction, angles and skills are constantly changing according to the development and changes of conditions, and new directions and methods for solving problems are sought from multiple angles. For example, it is known that every inner angle of a polygon is equal to 135. What is the degree of this polygon? Variant 1, it is known that the sum of the inner angles of a polygon is equal to 1080. What is the degree of this polygon? Variant 2, knowing that the number of sides of a polygon is 8, find the sum of the inner angles of this polygon? Variant 3, it is known that the outer angle of a regular polygon is equal to 45. What is the sum of the internal angles of this regular polygon? Variant 4, it is known that the sum of the degrees of the inner and outer angles of a polygon is equal to 1 180. How many sides does this polygon have? Through the variability of a topic, it provides rich materials for students to observe and think about the problem from different angles and solve the problem in different ways. It is very valuable to let students' thinking break through the stereotype and get broader development.

Third, cultivate the habit of tracing back to the source and develop the depth of thinking.

Mathematics is a very logical subject. Be good at thinking and ask "why" more, so as to master its internal laws. Asking more questions has been valued by many sages since ancient times. Tao Xingzhi said in his poem: "He, He, He, When, He, Where, Where to Go, Like Brothers, There is also a Western learning, whose surname is reverse, called Geometry. If you ask the Eight Sages for advice, you can't be wrong again. " Mr. Li Zhengdao, a famous physicist in China, also pointed out in many speeches in China that learning should not be "learning to answer", but "learning", that is, learning to ask questions first. Mastering the basic knowledge of mathematics such as basic concepts, formulas and theorems is the basis of learning mathematics well. There is no value in memorizing them. We should really understand them. How to really understand them? We should not only understand their connotation and extension, but also understand the necessity of introduction and the connection with other knowledge. Ask more "why" when you do the problem. If you can't finish the problem, you should know how to do it, why to do it, what to do, and whether the analysis method and solution of this problem have been used in other problems. Only by asking why can we not stop at the superficial and superficial understanding of knowledge, truly grasp the essence of knowledge and develop the depth of students' thinking.

Fourth, pay attention to the systematization of knowledge and expand the depth of thinking.

There are profound internal relations between mathematical knowledge, including the vertical relationship between each part of knowledge in their respective development process and the horizontal relationship between each part. Being good at discovering the relationship between them is helpful for students to think about the problem from a systematic perspective and grasp the essence of the problem. For example, when learning the positional relationship between circles, it is easy to get the positional relationship between circles by analogy with the positional relationship between points and circles and the positional relationship between straight lines and circles that have been learned. Learning knowledge in the system is easy to remember and understand. The most important thing is to cultivate the profundity of thinking in the process of classifying, combing, synthesizing and finding the law of knowledge. Mathematics is the science of thinking, and thinking ability is the core of mathematics discipline ability. Some studies have found that the thinking quality of mathematics is based on profundity and extensiveness. Therefore, mathematics teachers take mathematics knowledge as the carrier in the teaching process, create opportunities to improve students' thinking ability and open the door to students' wisdom.