First of all, the innovative consciousness of mathematics teachers is the first condition to cultivate students' innovative ability.
Education itself is a process of innovation. Teachers must have innovative consciousness, change the teaching concept centered on knowledge transmission, aim at cultivating students' innovative consciousness and practical ability, make bold breakthroughs in teaching concepts and teaching methods, and establish innovative teaching principles.
1. Overcome the misunderstanding of innovation. When it comes to innovative education, we often think of activities that are divorced from teaching materials, such as small production and small inventions. Or with the help of questions, let students think freely and say casually that this is innovation, which goes to the other extreme. In fact, every reasonable new discovery and unique observation angle is innovation. Whether a person's solution to a problem is innovative or not lies not in whether the problem and its solution have been mentioned by others, but in whether the problem and its solution are novel to the person. Students can also innovate and must have the ability to innovate. Teachers can fully control the teaching materials through the excavation of the teaching materials, introduce new knowledge and new problems that adapt to the development of the times into the classroom, organically combine with the content of the teaching materials, guide students to explore again actively, and let students master more methods and know more knowledge, thus cultivating innovative ability.
2. Establish a new relationship between teachers and students, create a relaxed atmosphere, a competitive and cooperative class spirit, and create an environment for creative thinking. Rogers put forward: "The general conditions conducive to creative activities are psychological safety and psychological freedom."
First of all, in order to let students actively explore knowledge and give full play to their creativity, we must change the old teaching model, that is, teachers are the protagonists, a few students are supporting roles, and most students are spectators and listeners. Because this kind of classroom teaching often gives full play to the leading role of teachers and limits the development of students' creative thinking. Teachers should aim at cultivating students' innovative ability, reserve students' own space, respect students' hobbies, personality and personality, treat students with an equal, tolerant and friendly attitude, and let students participate in teaching and learning together with teachers in the process of education and teaching, and be masters of learning, thus forming a relaxed and harmonious educational environment. Only in this atmosphere can students give full play to their intelligence and creativity.
Secondly, the class group can brainstorm, which is conducive to multi-directional communication and mutual learning between students. In classroom teaching, teachers should consciously do a good job in cooperative teaching, so that the roles of teachers and students are in dynamic change at any time, and design collective discussion, leak detection and group work to cultivate students' cooperative ability. Especially for some difficult problems, it is very helpful to create a democratic teaching environment and let students have group discussions in class. In a relaxed environment, students can speak freely, express their own opinions, dare to express their own independent opinions, or correct others' ideas, or combine several ideas into a better one, thus enhancing the collective innovation ability. It is worth noting that any cooperation can not make some students in an obvious subordinate position, but should be carefully grasped, assign responsibility to each student, and maximize the potential of students.
3. Teachers should fully encourage students to discover, ask, discuss and solve problems, and let students have innovative thinking, innovative personality and innovative ability through questioning and resolving doubts. Teachers use profound language to create situations, encourage students to break their own thinking patterns, ask questions from a unique angle, and encourage students to ask critical questions. Critical questioning is the concentrated expression of innovative thinking, and scientific invention and creation begins with critical questioning. Let students dare to question the content of the textbook and the teacher's explanation, especially the students' views, especially because there is a lot of room for discussion. Innovative students are also required to break away from convention, critically question, be brave in practice, verify and seek solutions.
Cultivate students' ability to judge complex problems. In classroom teaching, teachers should design some complicated and changeable problems for students to solve by their own judgment, or train students' judgment ability in the form of debate to make their thinking more fluent and agile, so as to express their views.
In the process of classroom teaching, teachers should make all kinds of summaries in each class, and also consciously let students summarize. Summing up ability is the embodiment of comprehensive quality. Cultivating students' summing-up ability can well train students' ability of concentrated thinking, which is complementary to cultivating students' thinking of seeking differences. Practice has proved that concentrated thinking can enable students to master all kinds of knowledge accurately and flexibly, and summarize and refine them into their own opinions, which can be used as the basis of thinking differently, ensuring the breadth, novelty and scientificity of thinking differently. In addition, in classroom teaching, students should be given as many opportunities as possible to sum up, such as summing up a problem; Summarize the content of a lesson; Summarize the results of the discussion; Summarize the pros and cons of the debate. Every time you summarize, you should select a number of students to speak and ask them to express their unique understanding, instead of echoing with one voice. After summing up, students can also be encouraged to ask deeper questions they have found in order to further extend them.
Second, students' interest in innovation is the key to cultivate and develop innovative ability.
Educator ushinski said: "Compulsory learning without the slightest interest will stifle students' desire to seek truth. "Interest is an important driving force for learning, and interest is also an important driving force for innovation. The process of innovation needs interest to maintain.
1. Use the psychology of "students are eager for unknown problems that they can do" to cultivate students' interest in innovation. Interest comes from thinking, which requires a certain knowledge base. Show appropriate questions in teaching and let students "jump up and pick peaches". Moderate questions, students want to know, will attract students, stimulate their cognitive contradictions, cause cognitive conflicts, and arouse strong interest and curiosity. Students learn because of interest, but because of thinking, and put forward new problems, consciously solve and innovate.
2. Reasonably satisfy students' competitive psychology and cultivate students' interest in innovation. Students have a strong competitive psychology. If they fail repeatedly in their studies, they will lose confidence in their studies. It is necessary for teachers to create suitable opportunities for students to feel the joy of success and cultivate their innovative ability. For example, for different groups, geometric design competitions, math joke parties, logical reasoning story speeches, etc. They are all held, so as to spread the wings of imagination, give full play to their different specialties, fully show themselves in the activities, find the combination of life and mathematics, feel their own victory psychology, experience the success opportunities and happiness brought by mathematics, and cultivate their own interest in innovation.
3. Cultivate students' interest by using the beauty of graphics in mathematics. There are a large number of geometric figures in life, some of which are produced according to important theories in mathematics, and some are geometric figure combinations, which have strong aesthetic value. In teaching, we should make full use of the beauty of lines and colors of graphics to give students the greatest perception and fully appreciate the beauty brought by mathematical graphics to life. In teaching, we should try our best to connect beautiful graphics in real life with classroom teaching, and then apply graphics to artistic creation and the design of living space, so as to make students have the desire to create graphic beauty, drive them to innovate and maintain their long-term interest in innovation.
4. Use historical figures, allusions, interesting stories of mathematicians' childhood and the generation of a conclusion in mathematics to stimulate students' interest in innovation. Students generally like to listen to interesting stories, and tell stories about the history of mathematics development and mathematicians in history, such as the vicissitudes of mathematical theory, the deeds of mathematicians' growth, the contributions of mathematicians in scientific and technological progress, the origin of some conclusions in mathematics, etc., which can not only make students understand the history of mathematics and enrich their knowledge, but also increase their interest in mathematics and learn innovative spirit.
Third, teachers are the "guardians" to protect the development of students' innovative ability.
1. Treat students' mistakes correctly. Students are immature individuals in the process of seeking knowledge, and it is inevitable and permissible to make mistakes of one kind or another in exploration. Teachers should not be eager to evaluate and show their own conclusions, but should help find out the reasons for the mistakes and let them admit and correct them with a positive attitude. As teachers, we should make a diversified developmental evaluation of developing individuals from a dialectical point of view and a developmental perspective. This objectively protects the enthusiasm of students' thinking and urges them to devote themselves to learning with a positive attitude.
2. Give students more encouragement and support and praise their correct behavior or good grades. Students' self-evaluation ability is low, they often acquiesce in the teacher's evaluation, and often use the teacher's evaluation to measure their position in the group. At the same time, judging from the expression or language of adults, this is one-sided. Therefore, teachers should clearly praise students' correct behavior, so that students can understand the teacher's evaluation of them, thus enhancing their self-confidence and letting them see the hope of success.
3. Protect students' curiosity. Curiosity is the innate nature of children, and curiosity is the source of thinking and the driving force of innovation. Because of curiosity, students have the desire to innovate and try to uncover the mystery of things. This kind of desire is the thinking spark ignited by the knowledge-seeking behavior in children's minds, and it is one of the most valuable innovative psychological qualities. So we should look at the whole world with curious eyes and psychology, and teachers should affirm students' curious performance in teaching. For example, we should cherish and cultivate students' spirit of "ask what's next".
In short, in teaching practice, the cultivation of students' innovative ability is multifaceted, which requires both teachers' leading and students' main body. Only with the cooperation of teachers and students can teaching learn from each other.