1, cultivate the flexibility of thinking

The flexibility of thinking refers to the timeliness of being able to adapt to the changes of things without being too affected by the mindset. If we lack the flexibility of thinking, our thinking will be more inclined to a specific way and method, and it is easy to go into a dead end and unilaterally pursue the mode and procedure of solving problems, which will lead to the inertia of thinking in the long run.

Good at getting rid of the old model and general constraints and finding the right direction; Since knowledge can be used freely, dialectical thinking can be well used to balance the relationship between things, analyze specific problems and adjust ideas flexibly. These are the direct manifestations of the cultivation of thinking flexibility.

2. Cultivate the rigor of mathematical thinking.

The rigor of thinking refers to the rigor and justification of considering problems. To improve the rigor of students' thinking, we must be strict and strengthen training.

Implementing it in children's study life means starting with the basic ideas when learning new knowledge, steadily and steadily under the premise of clear ideas, developing the habit of serious thinking in this relatively slow process, and mastering enough reasons as the basis when reasoning; When practicing test questions, we should be good at paying attention to the hidden conditions in the stem, answering questions in detail, and writing out the ideas for solving problems without stint.

3. Cultivate the profundity of mathematical thinking.

Thinking depth refers to the abstraction and logical level of thinking activities, as well as the depth and difficulty of thinking activities. I believe that most students have experienced this situation. Sometimes, when teachers grade papers and hear wrong questions, it is easy to understand the problem-solving process, and suddenly they realize that they have made such a low-level mistake, but once they leave books and teachers, they can't understand the problem-solving methods and essence and realize independent problem-solving. This requires students to see the essence of mathematics through phenomena, master the most basic mathematical concepts and gain insight into the relationship between mathematical objects in their usual study, which is the main manifestation of profound thinking.

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4. Cultivate the openness of thinking

The broadness of thinking means that a problem can be considered from many aspects. Specifically, it can explain a fact in many ways, express an object in many ways, and put forward many solutions to a topic. In mathematics learning, paying attention to multi-directional and multi-angle thinking and broadening the thinking of solving problems can promote students' thinking broadening.

5. Cultivate critical thinking.

Critical thinking refers to being good at strictly estimating thinking materials and carefully examining the thinking process in thinking activities. In the process of mathematics learning, students should be good at extracting what they want from the existing answers and problem-solving ideas, and express their views. We should not blindly follow, but learn to reflect and test in various ways with critical thinking. Even if you completely accept something ideologically, you should try to improve it and put forward new ideas and viewpoints.

The above five kinds of thinking qualities are necessary ways to improve mathematical thinking ability, but they must not be ignored. These five kinds of thinking qualities are closely related and cannot be separated, otherwise they will be bound by the mindset and tend to mechanically apply the previous thinking mode. The more times the same method is used, the more obvious this tendency will be.