First, the connotation of critical thinking
There is no absolutely unified explanation about the connotation of critical thinking. However, it is generally believed that critical thinking is an advanced thinking skill, a reflective thinking and the core part of creative thinking. The author believes that critical thinking is a process in which a subject creatively uses dialogue and reflection to solve the problem of what he should believe. It combines the originality, critical thinking and problem-solving ability of the subject. The teaching of critical thinking must include three aspects: first, the subject's critical consciousness, which is the fundamental embodiment and soul of the subject's creativity. The second is critical personality, which is mainly manifested in the spiritual quality of independent thinking, dare to question and pursue objectivity. The third is the ability to think critically or solve problems. [3] It can be seen that critical thinking is an innovative thinking based on general thinking. But we should pay attention to the following aspects: first, critical thinking is not the same as intelligence. Although critical thinking is based on human intelligence, it is not the same as intelligence. Although a person with mental deficiency can't think critically, a person with high intelligence may not be good at critical thinking. In fact, not only critical thinking cannot be directly equated with intelligence, but all human thinking cannot be directly equated with intelligence. Debono pointed out that the relationship between intelligence and thinking is like the relationship between a car and a driver. The engine determines the innate ability of the car, but the performance of the car can't guarantee the driver's driving skills anyway. The performance of a car is equivalent to human intelligence, and the driver's driving skills are equivalent to thinking. It often happens that the worse the car is, the better the driver's driving skills are. Driving skills can be learned, practiced and improved. This is why we can often see that some people have average intelligence, but they show extraordinary knowledge when they speak and do things. Secondly, information can't replace thinking, and thinking can't replace information. Information is the material of thinking, and thinking is to get more information. Therefore, we cannot say that the more knowledge a student has, the better his critical thinking will be. Finally, critical thinking is not the same as logical thinking. Critical thinking, like any other thinking, must be logical, that is to say, critical thinking is first of all a logical thinking, and it also needs inductive reasoning and deductive reasoning. The place where critical thinking is higher than logical thinking is that it pays more attention to the authenticity, accuracy, significance and value of thinking, and emphasizes the knowledge and thinking of thinking. Perhaps the result of logical thinking is logical, but not necessarily meaningful. [4] It is often the case that the math teacher gives lectures on his proofs and theories. Although his concept was thorough and his reasoning was strict, it didn't interest the students. This is because students feel that his theory has no ideological and new ideas. Therefore, it cannot arouse students' critical thinking. Therefore, as a math teacher, in the teaching process, we should not only impart math knowledge, cultivate intelligence and exercise general thinking, but more importantly, we should be able to cultivate students' awareness, personality and skills of critical thinking through classroom teaching and appropriate exercises.
Second, some suggestions on cultivating students' critical quality of mathematical thinking
In mathematics teaching, there are often two situations. One is that teachers pay attention to the inference and teaching of principles and concepts, and require students to memorize relevant formulas, principles, theorems or inferences, but less guide students to think about how these formulas, principles, theorems or inferences come from. Over time, students no longer consciously think about their origins, and they gradually lose the consciousness of doubt and reflection. Another situation is that teachers emphasize the problem-solving process in the teaching process and guide students to pay attention to problem-solving thinking. Almost all the teachers' explanations are very logical, and they are strictly deduced step by step. What students have to do is to follow the teacher's ideas and finally sort out the teacher's logic, so that they feel that what the teacher said is reasonable and understand what the teacher taught. But after a long time, students form the same thinking mode as teachers and become "direct thinking" and "fixed thinking", while the opposite "bypass thinking" and "divergent thinking" are gone. Therefore, mathematics teachers should pay attention to using various methods to consciously cultivate students' critical thinking in teaching.
1. Encourage students to ask questions and guide students to ask questions and find problems conditionally.
First of all, we should guide students to question, stimulate and protect students' questioning spirit. Of course, the questioning mentioned here is not to doubt everything, but to critically accept the knowledge and thinking methods in textbooks or teachers. To guide students to dare to ask questions that they can't, students' questions are beyond the scope of the college entrance examination, and it is wrong not to prevaricate with the college entrance examination. These questions are sometimes easy and sometimes difficult. In either case, the teacher should encourage them. As for the difficult problems, on the one hand, it is normal for teachers not to solve them, so we should treat them correctly; On the other hand, teachers should also combine this problem to learn relevant knowledge. I think this is the so-called teaching and learning. Secondly, we should encourage students to dare to doubt the knowledge in books, especially some ideas and answers to problems, and encourage students to answer by themselves, so as to find problems by themselves, and then consciously solve problems by themselves, and gradually develop the habit of self-doubt.
2. Cultivate students' good reflective habits and critical psychology.
Teachers can often ask students to explain the solution and its rationality; Ask students to give as many solutions as possible, summarize and popularize these solutions and compare their advantages and disadvantages; Thinking about the internal relationship between conditions and conclusions, etc. [5] At the same time, the error-prone problems are classified and compared, so that students can reflect and solve them, sum up their similarities and differences and the key to solving problems. For some problems that students can solve, teachers should discuss them in classes or groups, so that students can get many different solutions to a problem through their own criticism.
3. Deliberately arrange some wrong questions or questions with insufficient conditions to train students' critical thinking ability.
Teachers can deliberately show mistakes in lectures, or deliberately leave loopholes for students to find, or appropriately arrange some wrong correction questions. In this way, students will consciously pay attention to whether the teacher has made mistakes in the learning process, and will take the initiative to explore, discover and solve them, thus training students' critical thinking ability. Teachers should also pay attention to the differences of different students when assigning homework, treat students with different abilities differently, and adopt different forms and difficulties of homework, so that each student can give full play to his own foundation and advantages, thus encouraging them to keep thinking and making progress, and gradually exercise their thinking ability at their own level.
4. Pay attention to creating a learning atmosphere and situation of critical thinking.
In order to cultivate critical and creative thinking, teachers must establish a learning environment that encourages adventure, enhances self-confidence and has a relaxed atmosphere. In order to create a learning environment that encourages adventure, teachers must have the following beliefs: finding mistakes is conducive to learning; Don't ask students to know everything from the beginning, pay attention to step by step; It is very important to attach importance to learning, improve the quality of learning and persevere; Good students also need teachers' help and feedback; Unremitting efforts and effective strategies are the decisive factors for success; Everyone can succeed. If a math teacher sets up the above ideas, he will really change his role, not only as an educator, but also as a friend, guide and demonstrator of students. When talking to students, he will not always use his index finger, but will be happy to use his thumb, and he will not always say what "you" should be, but what "we" should be. You will really become one with students and become their bosom friends.
Teachers should also pay attention to the cultivation of their own critical thinking.
Teachers are role models for students, and teachers' every move may be imitated by students. Therefore, mathematics teachers should pay attention to learning the relevant knowledge of pedagogy and psychology, understand the relevant connotation and performance of critical thinking, master the scientific methods of cultivating critical thinking, and pay attention to reflection and questioning from time to time in the teaching and work process. On the one hand, they can cultivate their own critical thinking, so as to better engage in teaching; On the other hand, it will also affect students unconsciously and play a good role as an example for the cultivation of students' critical thinking.