First, pay attention to the cultivation of students' mathematical basic ability, and lay a solid foundation for the emergence of students' innovative thinking.
Among all mathematical abilities, mathematical thinking ability is the core, and the cultivation of mathematical operation, logical reasoning, spatial imagination, problem analysis and problem solving ability can not be separated from mathematical thinking ability. Therefore, it is very important to cultivate students' basic mathematical ability in peacetime teaching.
1. Cultivate students' logical reasoning ability.
Mathematics is characterized by strict logic, and the ability of logical reasoning should be one of the basic mathematical abilities that students must possess. To cultivate students' reasoning ability, we must master the basic laws such as logical identity, law of contradiction, law of excluded middle and law of sufficient reason, so teachers should train in a planned and step-by-step manner.
2. Cultivate students' intuitive thinking ability.
(1) Encourage students to guess. Cultivating the thinking habit of daring to guess and being good at exploring is the basic quality of forming intuition. Let students guess, not only can stimulate them to solve problems, but also can teach them an applied way of thinking, so students should be encouraged to make reasonable guesses in class.
(2) The discovery, induction and application of knowledge chunks are the knowledge basis for training intuitive thinking. In mathematics teaching, we should attach importance to the teaching of basic graphics and basic patterns to help students form knowledge chunks. There is a lot of information about basic graphics, patterns and methods. When solving problems, these knowledge and methods are used repeatedly to form knowledge chunks. When encountering related problems, we can quickly associate knowledge chunks, identify and analyze them intuitively, and form a comprehensive judgment on the problems, so as to get methods and ideas to solve the problems.
Second, open the way of thinking and cultivate students' innovative thinking
In mathematics teaching, opening students' thinking mode can effectively stimulate students' innovative thinking, broaden their innovative horizons, make students actively participate in innovative activities, develop their innovative potential, and continuously improve their innovative spirit and creativity.
1. Cultivate students to question boldly.
(1) Ask questions to stimulate students' learning interest and thinking motivation. In the process of teaching, teachers should consciously ask enlightening and inducing questions and create problem situations, so that students are often in the contradiction between exploring and solving problems, resulting in curiosity, thirst for knowledge and desire for creation.
(2) Guide students to form a good habit of asking questions. Teachers should encourage students to dare to ask questions and question classmates and teachers boldly; At the same time, teachers should arouse doubts in key places, guide students to find, refute and correct mistakes, and guide students to find and solve problems that are easy to be confused and wrong.
(3) Questioning and answering the mistakes in students' homework to stimulate students' thinking motivation.
2. Cultivate students' exploratory thinking.
To cultivate and train students' innovative thinking, it is necessary to improve students' cognitive level and develop it into inquiry understanding.
(1) The key point is to be brave and good at providing students with certain conditions and opportunities for independent thinking and finding problems in classroom teaching.
(2) Cultivate classified thinking, educate students not to be satisfied with mastering the teaching knowledge (concepts, theorems and laws), but also to attach importance to and emphasize the use of mathematical ideas and methods for generalization and classification, so as to achieve understanding and mastery of knowledge.
(3) Cultivate the habit of "review" and "reflection", review, sort out and reflect on math problems in a planned way, and arrange pioneering, multi-solution and expanding exercises in a planned way to cultivate students' inquiry spirit.
3. Cultivate students' multi-directional thinking and divergent thinking.
Divergent thinking has the characteristics of fluency, flexibility and uniqueness, that is, it pays attention to multi-channels and multi-schemes when thinking about problems and draws inferences when solving problems, so it is very important to cultivate and develop students' divergent thinking correctly. Common methods are:
(1) How to solve a problem and cultivate the fluency of thinking. Example: Change a RMB with a face value of 1 yuan into small change, and RMB with a face value of 50 cents, 20 cents and 1 minute will be enough. How many ways are there?
Analysis: First, try to find out the answer through experiments, which is easy for ordinary students to accept and be interested. However, the disadvantage of experimental methods is that it is not easy to find all the methods, and it is not easy to miss the solution with ternary heuristic equations. Let RMB with a face value of 5 cents, 2 cents and 1 minute be x, y and z respectively, and list the equations:
5x+2y+z= 10 From 5x≤ 10, we know that 0≤x≤2.
If x=2, y=0 and z=0.
If x= 1, when y=0, z = 5；; When y= 1, z = 3；; When y=2, z= 1.
If x=0 and y=0, z =10; When y= 1, z = 8；; When y=2, z = 6；; When y=3, z = 4；; When Yy4, z = 2; When y=5, z=0.
* * * There are ten alternatives. Such divergent thinking training can not only broaden students' thinking of solving problems, but also help them overcome the rigidity and rigidity of thinking, which plays an important role in cultivating students to explore new methods and theories.
(2) Solve a problem skillfully and cultivate the flexibility of thinking. In teaching, students are required to give full play to the flexibility of thinking and solve problems in an all-round and multi-angle way without being influenced by factors such as mindset.
Third, create an innovative atmosphere for students' growth
American psychologist Rogers said: "Successful teaching depends on sincere respect and trust between teachers and students, as well as a harmonious and safe classroom atmosphere." In a relaxed learning environment, students can be open-minded, quick-thinking, and actively participate in learning activities, thus creating a spark of innovation in creation. In teaching, teachers should establish friendship with students and put the "podium" among students. In classroom teaching, teachers will never do what students can do for them. Through group discussion, intra-group communication and cooperative inquiry, we can discover the rules and learn new knowledge. Through games and competitions, stimulate students' interest in learning, fully make students move, and change "teachers need to learn, teachers teach everyone to learn" into "everyone wants to learn, everyone will learn"; Every word and every look of the teacher gives students trust and care, so that a "zero" distance space can be formed between teachers and students and between students in this new space. Arouse the courage of "everyone dares to innovate", enhance the consciousness of "everyone is willing to innovate", and show unique innovative talents. Let each student walk out of the growth path of different personalities in such an atmosphere.
In short, no matter what method is adopted to cultivate students' innovative thinking, teachers should be the guiders of students' thinking, guide students to clarify the direction and basis of thinking, and more importantly, change teachers' teaching methods and students' learning methods, build an open learning environment for students, provide multi-channel access to knowledge, comprehensively apply what they have learned to practice, and effectively cultivate students' innovative ability and spirit.