First, use teaching materials to update students' ideas and cultivate their innovative consciousness.
Students are the masters of learning, not passive listeners; Students are active seekers of knowledge, not containers for instilling knowledge. Teachers should give full play to students' main role in teaching, arouse their enthusiasm and initiative, guide them to think actively, explore actively and practice consciously, and strive to create an innovative teaching atmosphere.
1, inspire students to be good at asking questions. Professor Li Zhengdao said to his students, "The most important thing is to be able to ask questions, otherwise you will never be able to do first-class work in your life." As we all know, questioning is a common link in classroom teaching, but it is not a teacher's "patent". Teachers should be good at asking challenging new questions to students, paving the way for innovation. When I am teaching, students can ask questions on their own initiative. In the whole teaching activity, teachers encourage them in time, mobilize each student's sense of participation, and let each student have the joy of success.
2. Guide students to think positively. When talking about the image of function y=kx+b, some students in the class asked: does the function have an image when k=0? There is no special introduction in the textbook. However, in the quadratic function y=ax2+bx+c(a≠0), the symmetry axis x=-b/2a appears, which is difficult for students to understand and easy for teachers to ignore in teaching. For this kind of problems, we should be good at stimulating and catching students' innovation sparks, encouraging students to explore, publishing unique (even wrong) views, not superstitious about "standard answers", protecting innovation desire and developing innovation potential.
3. Encourage students to make bold guesses. In teaching, teachers should encourage students to put forward different opinions and don't jump to conclusions about the opinions put forward by students. They should take the initiative to accept students' mistakes and failures, help students understand where they are wrong, and let students get learning opportunities in an atmosphere of care and support. At the same time, encourage and praise students who dare to imagine and innovate, and promote the development of students' innovative thinking. For example, when I watched the teaching video of "Cone" in a middle school, the teacher first asked the students to guess the shape of the side expansion diagram of the cone, and the students answered that it was round, semi-circular, fan-shaped and so on. One student even replied that it was a trapezoid. The teacher actively guided and analyzed the situation, and asked the students to try to cut a trapezoid when they got home. When the students knew that the cone contour was a fan, the teacher did not cut it according to the bus line, but cut it into a curve to form an irregular figure. At the same time, ask students to find out its area. This kind of teaching is conducive to cultivating students' innovative consciousness.
Second, the use of teaching materials to stimulate students' desire and motivation for innovation
Innovation motivation is the internal driving force that directly pushes people to engage in creative activities, and it plays a guiding, stimulating and strengthening role in people's creative behavior. Achievement motivation is the source of students' innovation. Students with achievement motivation have strong perseverance and are full of challenges. Teachers should let students experience happiness from their academic performance, and let students get satisfaction in answering a question correctly, completing an assignment and getting better academic performance. Only in this way can teachers better stimulate students' innovative motivation, inspire students' creative thinking and better cultivate students' innovative ability.
Third, create a lively classroom atmosphere.
In mathematics classroom teaching, only when teachers do everything possible to guide and stimulate students' positive emotions, and strive to create a classroom atmosphere of mutual respect, mutual encouragement, solidarity and mutual assistance, democracy and harmony between teachers and students, can teachers give full play to their leading role and students' main role, so that students can enter a happy and relaxed thinking realm, spread their imagination wings, actively think about problems and boldly express their different ideas, thus achieving the goal of truly and efficiently participating in the whole process of classroom teaching.
Such as using modern teaching methods to enhance novelty (introducing "parabola" through multimedia demonstration of basketball trajectory) and using real-life phenomena to increase interest (introducing "probability" through lottery winning prediction).
Fourth, pay attention to the teaching of mathematical thinking process.
In mathematics classroom teaching, on the one hand, teachers should pay attention to properly expose and reproduce their own thinking process, and develop the formation process of mathematics knowledge through observation, comparison, classification, specialization, induction, speculation, analysis and synthesis, so that students can understand the ins and outs of knowledge, know what it is and know why. At the same time, they can be trained in mathematical thinking and influenced by mathematical thinking methods, so as to learn to ask questions and learn how to ask questions. To realize the essential function of mathematics education, on the other hand, we should pay attention to effectively exposing students' thinking process, finding out students' thinking methods and habits of mathematics problems in time, finding out their real thinking obstacles in the process of solving problems, and improving the pertinence of thinking training. For example, the textbook introduces the method of measuring pond width with "congruent triangles" or "similar triangles". We might as well let students try to measure tall buildings, big trees and flagpoles, put forward the measurement scheme, complete the measurement task and write the measurement report. This not only consolidates the knowledge learned, but also cultivates students' practical ability to solve practical problems.