The essence of mathematics is the ideological material that people get from the quantitative relationship in the real world through creative thinking in order to solve mathematical problems. Mathematics education is actually the education of mathematical thinking activities. Creative thinking is the highest quality, highest level and most valuable in the process of mathematical thinking. Creative thinking is a unique thinking activity in the process of people creatively solving problems and then inventing and creating. It is the sum of all thinking forms with brand-new content. It can not only reveal the essence of objective things and their internal relations, but also produce novel and unique ideas, at least put forward creative opinions. The ultimate goal of mathematics teaching is to let students use what they have learned to solve problems. Therefore, mathematics teachers should let students master basic knowledge, basic skills and basic methods, cultivate students' practical ability to solve problems from multiple angles, develop students' innovative thinking, and make students have keen observation, creative imagination, unique knowledge structure and active inspiration. In the process of solving problems, students are guided to break away from convention, think independently, make bold guesses, question and ask difficult questions, actively demonstrate, seek novelty and difference, let go of ideas, fully imagine, skillfully use intuition and explore various solutions or new ways, so as to solve mathematical problems quickly, simply and accurately. Next, I will talk about some ideas and practices in cultivating students' creative thinking ability.

1. Developing students' observation ability is the basis of cultivating students' creative thinking.

Observation is the most basic way to understand things, the premise of finding, analyzing and solving problems, and the basis of association and innovation. Any mathematical problem contains certain mathematical conditions and relationships. In order to solve the problem, we must observe the problem thoroughly and carefully according to its specific characteristics, and then seriously think about it, look at the essence through superficial phenomena, explore the problem-solving ideas and formulate the problem-solving strategies.

As the famous psychologist Rubins pointed out, "any thinking, no matter how abstract and theoretical, begins with observing and analyzing empirical materials." Observation is the gateway of intelligence, the outpost of thinking and the button to start thinking. The depth of observation determines the formation of creativity. Therefore, guide students to understand that a problem should not be solved in a hurry, but should be observed in depth, which not only lays the foundation for the final solution, but also may find opportunities for creative solution.

2. Improving students' guessing ability is the key to cultivate students' creative thinking.

Giorgia pointed out in the book Discovery of Mathematics: "Before you prove a mathematical theorem, you must guess the theorem, and before you know the details of the proof, you must guess the leading idea of the proof." Therefore, conjecture ignites the spark of creative thinking and plays a key role in the emergence and development of creative thinking. Many "discoveries" in science are intuitive and then proved or verified. In mathematical research, "guess first and then prove" is almost a law.

Suhomlinski, an educator in the former Soviet Union, said: "In people's hearts, there is a deep-rooted need to be a discoverer, researcher and explorer. In the spiritual world of teenagers, this demand is particularly strong. " Therefore, in mathematics teaching, according to the characteristics of teaching materials and students' cognitive rules, we should guide students to use their brains, stimulate students' desire to guess, cultivate students' interest in guessing, encourage students to observe diligently, boldly make guesses, allow students to raise various "objections" and inspire students to guess and think in many directions. In our mathematics teaching, cultivating students' conjecture is a necessary means to stimulate students' interest in learning, develop students' intuitive thinking and master the methods of exploring knowledge. We should be good at inspiring, actively guiding and enthusiastically encouraging students to guess, so as to truly achieve the purpose of inspiring thinking. Guiding students to imagine mathematics in teaching will often bring opportunities for mathematical discovery.