"Question" is the carrier of mathematics, and the designed question is the catalyst to stimulate students' thinking sparks.

Aristotle thought: "Thinking begins with doubt and surprise."

In the process of mathematics teaching, teachers should be good at setting doubts to stimulate students' positive thinking, and then help students to master knowledge, develop intelligence and form good thinking habits by solving doubts.

Second, guide conjecture and cultivate students' thinking quality

Conjecture is a creative thinking activity, which can produce novel and unique thinking results.

In mathematics classroom teaching, teachers should guide students to guess, dare to guess and be good at guessing, encourage students to think and let students imagine freely, thus cultivating students' creative thinking ability.

1. Cultivate the originality of thinking by guessing.

Modern teaching is a process of exchanging information between teachers and students. Therefore, in terms of teaching methods, teachers must mobilize students' learning enthusiasm to the maximum extent, encourage them to "be unconventional" and inspire them to guess better methods.

2. Cultivate divergent thinking through guessing.

Divergent thinking is an important part of creative thinking.

It is not bound by a certain problem-solving model, but looks for uniqueness and variability from the problem personality, and guesses, extends and develops along different directions and angles. In mathematics teaching, we can generally use the training of multiple solutions to one problem to cultivate and exercise the divergence of thinking.

Guiding students to think from different angles and directions can not only improve students' ability to use knowledge flexibly and solve problems, but also give play to students' unique views and enhance the radiation of divergent thinking. In addition, training such as changing more questions and filling more questions can also cultivate and exercise students' divergent thinking quality.

3. Cultivate the flexibility and agility of thinking by guessing.

"Active, thinking and curious" are the psychological characteristics of students. Teachers should grasp students' psychological characteristics, encourage students to make bold guesses, make students consciously communicate the vertical and horizontal connections of mathematics knowledge and explore hidden conditions; Construct a mathematical object skillfully and make a circuitous transformation; Flexible use of various ways of thinking and ways to find out various ways to solve problems.

Third, contact the old and the new to improve students' thinking level.

Mathematical knowledge has a strict logical system.

As far as students' learning process is concerned, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Students' cognitive activities are always based on existing old knowledge and experience.

In this kind of knowledge teaching, we should review the old knowledge as much as possible, make full use of the existing knowledge to pave the way, guide students to use the law of knowledge transfer, and improve their thinking level in the process of acquiring new knowledge.

Fourth, promote students' all-round development and cultivate their ability to solve problems.

To cultivate students' problem-solving ability, it is necessary to change students' learning methods, from a single passive learning method to a variety of learning methods, such as independent exploration, hands-on practice, cooperation and communication. In teaching practice, reflection is the most important step in the learning activity of "answering questions" and an "evaluation" of the problem-solving process.

Reflection on solving problems is not only aimed at "answers".

The focus of reflection is mainly on how to "examine" the "process" of answering questions.

Specifically, the content of reflection includes the following aspects:

Discuss the reasons for using a certain calculation method; Whether you can find other faster steps to solve the problem; Is there a better way to solve the problem? Can you simplify some steps? Is there a better and more interesting way to solve the problem? For the whole solution of the problem, what effect will it have if it is used in another way? What are the key points in the process of solving problems? Whether there are some "misleading" ideas in the process of solving problems is worth reminding others not to repeat the same mistakes.

In short, there are various ways to cultivate students' thinking ability. Teachers should be good at tapping students' potential and adopt effective teaching methods according to their specific conditions. In teaching, the cultivation of students' thinking ability runs through the whole process of teaching, thus optimizing students' thinking quality, developing students' learning ability and improving students' problem-solving ability.