First, pay attention to the formation process of knowledge and cultivate students' exploratory thinking.

The value of mathematics teaching is not only limited to helping students acquire knowledge from books, but also helpful to the training of thinking and the improvement of cognitive ability, which requires studying the thinking process of knowledge, that is, how to ask questions, analyze problems and solve problems. In teaching, we attach great importance to showing the formation process of mathematical formulas, concepts, theorems and laws, so that students can seek the ins and outs of knowledge as much as possible, explore the ideas and methods of solving problems, summarize the laws of solving problems, understand the thinking methods contained in the process of knowledge formation, let them express themselves in participation, gain the joy of success, and improve their initiative and creativity in learning. For example, when learning the basic properties of inequality, let students try to answer the following questions: 1. Add (or subtract) 5 on both sides of the following four inequalities:17 > 4 ②-3 < 5 ③-4 >-5 ④-2.

Second, create a relaxed and happy situation and cultivate the enthusiasm of thinking.

Practice has proved that if students can maintain a relaxed and happy mood in their study, it will help to give play to their subjective initiative and creativity and release their great learning potential. Therefore, teachers should strive to create a relaxed and happy teaching situation, edify, infect and enlighten students with their own actions, expressions, language styles, temperament, ideals and beliefs, so as to create an emotional buzz between teachers and students, create a good classroom atmosphere, stimulate students to create beautiful enthusiasm and desire, and consciously carry out creative learning. Therefore, in teaching, teachers should encourage students to dare to speak and do, so that students can truly become the masters of learning. This can not only enliven classroom teaching, but also cultivate students' spirit of being outspoken and willing to take the initiative to explore, and at the same time strengthen the exchange of new ideas, new concepts, new theories and new plans, and improve students' enthusiasm for thinking.

Third, encourage students to be brave in questioning and cultivate the innovation of thinking.

Learning begins with thinking, thinking begins with doubt, doubt leads to exploration, thus discovering truth, and scientific invention and creation also begins with doubt. Therefore, questioning is the main way to cultivate students' creative thinking. In teaching, students should be encouraged to make bold guesses, dare to ask unusual questions and express their unique opinions. Some students' typical problems really play the role of "one stone stirs up a thousand waves".

For example, after learning the acute angle function, some students asked, "Is it only the acute angle of a right triangle that has sine and cosine?" "Are sine and cosine of acute angle related to side length?" Typical problems, such as teachers give affirmation first, and let students discuss, exchange doubts, express different opinions, and teachers summarize. In this atmosphere, students not only develop the habit of thinking and asking questions, but also cultivate the profundity, independence, challenge and innovation in solving problems.

Fourth, design open questions to cultivate the universality and flexibility of thinking.

Mathematics problem is the main content of mathematics learning and an important way to cultivate creative thinking ability. It is necessary to strengthen the connection between knowledge, consolidate and deepen basic concepts, reveal the essence of problems, enable students to master the law of solving problems and cultivate creative spirit.

1. Ask more questions. Problems are the starting point of thinking. Attractive questions can induce students to think positively. Design a set of in-depth questions for typical examples, and help students broaden their thinking through step-by-step guidance and inspiration, which is conducive to cultivating students' divergent thinking.

For example, the image of a linear function y = ax+b is shown in the figure, and the following problems are solved by combining graphics.

(1) Find the solution of equation AX+B = 0.

(2) Find the solution of the inequality AX+B > 1. (3) the value range of y when finding x

Through the above problems, we can fully tap the potential of exercises, cultivate students' logical thinking ability and stimulate students' thinking enthusiasm.

2. Multiple solutions to one problem. In the process of solving mathematical problems, students can be inspired to think from different angles, different ways and different ways, so that their thinking can be scattered in a "fireworks-like" way, and various solutions can be sought from different cognitive levels, which can broaden students' thinking and cultivate the breadth and depth of their thinking. For example, the outer angle of a regular polygon is 60. How many polygons are there? Let students use different solutions. On the basis of independent thinking, students come up with solutions through discussion and communication. Let's assume that it is an n polygon. Method 1: Considering the internal angle and internal angle, it is easy to get180 (n-2) = (180-60) n, and then we can get n. Method 2: Considering the external angles and aspects, we can get 60 n = 360, which makes it easier to find n ... This is of great benefit to broaden students' thinking and explore the law of solving problems.

3. One question is changeable. Properly changing the condition or question type of a topic can make a topic become multiple topics, communicate the connection between knowledge, and achieve the purpose of drawing inferences from one another, thus promoting the flexibility of students' thinking.

For example, △ABC, find a point P to make an isosceles triangle of △APB, △APC and △BPC. For this question, it is not difficult for students to find that the outer center of the triangle meets the conditions, and then ask further questions: "What if △ABC is an isosceles triangle? Is the answer unique? " Does this point p have to be in △ABC? Are there any other points that meet the requirements? Students' thinking naturally unfolds, and then they ask, "What if △ABC is an equilateral triangle?"

Guiding students to deepen their thinking through observation, conjecture and judgment, and exploring the internal and external relations of knowledge can cultivate the broadness and flexibility of thinking.

In short, in mathematics teaching, students' creative thinking will certainly develop well by giving full play to their main role, giving them the initiative in learning, giving them back their time and bringing their interest.