1. Find a breakthrough to cultivate mathematical thinking ability.
Psychologists believe that cultivating students' mathematical thinking quality is a breakthrough in cultivating and developing mathematical ability. Thinking quality includes profundity, agility, flexibility, criticism and creativity, which reflects the characteristics of different aspects of thinking, so there should be different training methods in the teaching process.
The profundity of thinking is the essence of mathematics, which determines that mathematics teaching should be student-oriented and cultivate students' profundity of thinking. The difference of mathematical thinking depth reflects the difference of students' mathematical ability. To cultivate the profundity of students' mathematical thinking in teaching is actually to cultivate students' mathematical ability. In mathematics teaching, students should be educated to look at the essence through phenomena, think about problems comprehensively, and form the habit of asking questions.
The agility of mathematical thinking is mainly reflected in the speed problem under the correct premise. Therefore, in mathematics teaching, on the one hand, we can consider training students' operation speed, on the other hand, we should try our best to let students master the essence of mathematical concepts and principles and improve the abstraction of the mathematical knowledge they have mastered. Because the more essential and abstract knowledge is, the wider its scope of application and the faster its retrieval speed will be. In addition, the operation speed is not only the difference in understanding mathematical knowledge, but also the difference in operation habits and thinking generalization ability. Therefore, in mathematics teaching, students should always be asked about speed, so that they can master the essentials of quick calculation. In order to cultivate students' thinking flexibility, we should strengthen the variability of mathematics teaching, provide students with a wide range of thinking association space, enable students to consider problems from various angles, quickly establish their own ideas, and truly "draw inferences from others." Teaching practice shows that variant teaching plays a great role in cultivating the flexibility of students' thinking. For example, in concept teaching, let students describe concepts in equivalent language; In the teaching of mathematical formulas, students are required to master all kinds of variations of formulas, which is conducive to cultivating the flexibility of thinking.
To cultivate the quality of creative thinking, students should first learn knowledge comprehensively and form the habit of independent thinking. On the basis of independent thinking, we should also inspire students to think positively and let them think more and ask more questions. Being able to ask high-quality questions is the beginning of innovation. In mathematics teaching, students should be encouraged to put forward different opinions and guide them to think positively and identify with themselves. The new curriculum standards and textbooks have opened up a broad space for us to cultivate students' creative thinking.
The cultivation of critical thinking quality can focus on guiding students to check and adjust their thinking activities. Guide students to analyze the process of finding and solving problems by themselves; What are the basic thinking methods, skills and techniques used in learning, how reasonable and effective they are, and whether there are better methods; What detours have you taken, what mistakes have you made and why?
2. Teach students how to think
To be good at thinking, students must attach importance to the study of basic knowledge and skills. Without a solid foundation, their thinking ability cannot be improved. Mathematical concepts and theorems are the basis of reasoning and operation, and accurate understanding of concepts and theorems is the premise of learning mathematics well. In the teaching process, we should improve students' cognitive ability of observation and analysis, from outside to inside, from here to there.
Mathematical concepts and theorems are the basis of reasoning and operation. In the teaching process, we should improve students' cognitive ability of observation and analysis, from outside to inside, from here to there; In the example class, the discovery process of solving (proving) problems should be regarded as an important teaching link, so that students should not only know how to do it, but also know why and what prompted you to do it. In mathematics practice, we should carefully examine the questions, observe them carefully, have the ability to dig out the hidden conditions that play a key role in solving problems, and use comprehensive methods and analytical methods to express them in mathematical language and symbols as much as possible in the process of solving problems (proofs). In addition, we should strengthen the training of analysis, synthesis and analogy to improve students' logical thinking ability; Strengthen the training of reverse application formula and reverse thinking to improve the ability of reverse thinking; Solve mistakes and omissions through analysis and improve the ability of identifying thinking; Improve divergent thinking ability through the training of multiple solutions to one problem (syndrome).