Understand the basic concepts of mathematics: Understanding the basic concepts and principles of mathematics is the basis of cultivating mathematical thinking. For each concept, we should understand its definition, symbolic representation, nature and scope of application, and try our best to describe it in our own language. This will help to link new knowledge with existing knowledge, form a knowledge network, and improve the logic and systematicness of thinking.
Mastering problem-solving methods: On the basis of understanding and mastering basic concepts, we need to use what we have learned to solve problems. The process of solving problems is also a process of exercising thinking ability. Learn to look for clues from the conditions and conclusions of problems, identify the types of problems, and answer them according to the corresponding problem-solving methods.
At the same time, we should pay attention to summing up and accumulating experience. For frequently occurring questions, we can sum up the general steps and skills of solving problems.
Reflective summary: Reflective summary is an important means to improve thinking ability. After each problem solving, we should think about the knowledge points, ideas and methods used in the process of solving problems, whether there is a simpler solution, whether there are other possible variants, and whether this problem can be extended to a more general situation. Through reflection and summary, I will constantly improve the depth and breadth of my thinking.
Discussion and communication: It is an effective way to improve thinking ability to discuss and communicate with others on mathematical problems. Through discussion, we can learn different viewpoints, methods and ideas, broaden our horizons and learn to look at problems from multiple angles. At the same time, you can also exercise your expressive ability and logical thinking ability in the process of communication.
Be good at asking questions: Being good at asking questions is also an important way to cultivate thinking ability. When you encounter questions that you don't understand or have questions, don't be afraid to ask or pass by, but take the initiative to seek answers. By asking valuable questions, you can exercise your thinking ability and critical spirit.
In a word, to cultivate one's thinking consciously in the process of learning mathematics, we need to start from many aspects and constantly improve one's thinking ability and mathematical literacy.