1. Characteristics of Mathematics Education

(1) Abstraction: Abstraction is a basic feature of mathematics, and all objects in mathematics are the products of abstract thinking. (2) Simplicity: Simplicity of mathematics is mainly reflected in mathematical language and symbols, which is an abstract form of mathematics. (3) Formalization: The formal features of mathematics are mainly manifested in the formal symbol system applied in mathematics. Formal language is generally used in mathematics, and symbols are used to represent everything that can be expressed in the process of mathematical thinking, including a series of reasoning, axioms and theorems. (4) Logic: This is a major feature of mathematics. The important purpose of mathematics teaching in China is to improve students' logical thinking ability.

2. The connotation and characteristics of innovative thinking

The subject of thinking innovation is people, and other things outside the subject of innovation constitute the object of innovation. The cognitive process of innovative subject to innovative object is the formation process of innovative thinking. Several characteristics of innovative thinking: (1) initiative: the initiative of the thinking subject plays an important role in promoting innovative thinking. Without initiative, it is difficult to ensure a good innovation effect. (2) Originality: The originality of innovative thinking also emphasizes the difference and independence of innovative thinking. (3) Seeking the opposite sex: Seeking the opposite sex is the most essential feature of innovative thinking. It needs to take creative thinking as the theme and actively seek new breakthroughs and new ideas to solve problems on the basis of the existing theoretical system. (4) Divergence: It mainly refers to some related factors that should be fully connected with the thinking object in the process of forming innovative thinking.

Second, specific strategies to cultivate students' innovative thinking

1. Improve mathematics teachers' innovative consciousness and actively adopt innovative teaching methods.

Teachers play a key role in teaching innovation. If teachers do not have a good sense of innovation, then it is impossible to ensure the cultivation of students' innovative thinking. Only when teachers have innovative consciousness can they subtly influence the formation of students' innovative thinking. As the main body of learning, the formation and improvement of students' innovative thinking need the guidance of teachers.

2. Change the teaching concept and improve the problem consciousness.

(1) Take the problem as the starting point of teaching. When designing lesson plans, teachers should not directly copy the knowledge points in textbooks, but need to flexibly put forward some knowledge points in textbooks in the form of questions, such as formulas and theorems. Through this form, it is of great significance to stimulate students' desire to solve problems and root the problem consciousness in students' minds, so as to improve students' ability to solve problems independently. (2) Paying attention to the re-creation of mathematical problems and actively cultivating students' problem consciousness with innovative thinking are conducive to the formation of students' innovative thinking. However, the formation of students' problem consciousness not only needs enough professional knowledge as support, but also needs a long-term training and exercise process. Innovation cannot be completed in a short time, but it is a hard work. Therefore, in mathematics teaching, teachers should not only ensure students' rich knowledge, but also enhance students' inquiry spirit and problem consciousness in the form of problem re-creation, so that students can gradually form innovative thinking in such a process of continuous inquiry.

3. Grasp the psychological characteristics to stimulate students' innovative spirit.

Interest is the inexhaustible source and motivation of thinking. In teaching activities, teachers should actively adopt diversified teaching forms to cultivate students' interest in learning and enhance their thinking drive. Mathematics teaching content is rather boring, so teachers need to instill these mathematical knowledge into students in an interesting form, not only limited to the contents of textbooks, but also make full use of all teaching methods that can effectively stimulate students' interest in learning.

4. Make full use of mathematics textbooks to cultivate students' innovative thinking.

There are many materials in mathematics textbooks to train and cultivate students' innovative thinking. We should make full use of these materials and seize the opportunity to cultivate students' innovative thinking. In mathematics teaching, the cultivation of innovative thinking is a long-term and arduous task in the new period, which requires a long-term training and training process. This also requires math teachers to take all effective measures to make the greatest efforts for the formation of students' innovative thinking.