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.