1 How to develop children's mathematical thinking
Discussion on the method of developing students' thinking
Generally speaking, mathematical thinking is people's essential understanding of mathematical content, a further abstraction and generalization of mathematical knowledge and methods, and belongs to the category of rational understanding of mathematical laws. If you want to learn mathematics well, you must have agile mathematical thinking. Here are several ways to train thinking: (1) memory training. Our brain is equivalent to a storage machine, and thinking is also based on memory. Knowledge is interlinked. If you only have a single knowledge point, how can you make knowledge collide with sparks? (2) Think hard in life. Any science is for life. And our life also contains great wisdom, so we should develop the habit of asking more questions in life, such as why water boils. Why go home to travel and so on.
(3) Do more intelligence games. People often say that you can't learn to be a nerd, that is, one must learn to play, spend time playing, find time to play, play cards, play video games, play chess, watch late-night phone calls, participate in tug-of-war competitions and so on. It doesn't matter what you play. You just have to play! It's good for your mind and brain. It gives your brain a chance to think strategically and keep running. Games are the activities that can develop people's thinking most. (4) concentrate. Doing anything seriously is the most terrible thing. It is obvious that concentration can improve your brain, but the factors that interfere with your attention are not always so obvious. Learn to pay attention when you are distracted, and learn to control your own thoughts.
Reasonably plan the classroom content and stimulate students' interest in learning.
Mathematics knowledge is complicated, and theorem after theorem seems puzzling, so it is very important to plan the course content reasonably, stimulate students' interest in learning and help them regain their confidence. Then let's take the chapter "sine theorem of trigonometric function" as an example to analyze it concretely: first of all, we know that sine theorem is the relationship between the three sides of any triangle and the sine value of the corresponding angle. It is related to triangles, so at the beginning of the class, let's ask a question like "A mountain is too high for us to climb, or there is a river blocking it, how to calculate the height of the mountain". The first step is to arouse students' curiosity with practical questions;
Then we introduce the concept of sine theorem. After introducing the concept and formula, let students make a guess, encourage them to question boldly, and let them reason whether this sine theorem is correct or how to draw this conclusion according to the formula. The second step is to change the role of scientists and make their own inferences. In the process of students' own reasoning, there must be different ways of thinking, and what is right will naturally be wrong. At this time, teachers need to participate and help, listen to students' opinions and ideas, and give correct guidance to mathematical thinking in time to prevent them from falling into the misunderstanding of thinking and ignoring the blind spot of knowledge. The third step is to give students timely guidance and attach importance to mathematical thinking. Then at this time, we can do some examples to let everyone feel the application of the theorem, which is convenient for deepening.
2 How to cultivate students' creative thinking in mathematics
1. Do a good job in "two basics" teaching, guide students to discover and apply rules, and lay a good foundation for forming creative thinking ability.
In the process of mathematics learning, students' creative thinking is mainly manifested in the discovery, generalization or creative application of existing mathematical knowledge, and takes existing knowledge as the growth point of new knowledge. In teaching, teachers must attach great importance to the "two basics" teaching, so that students can firmly grasp the basic knowledge and skills of solving problems, and guide students to be good at discovering laws and applying them to cognitive activities, thus laying a solid foundation for cultivating students' creative thinking.
2. Cultivate students' creative thinking ability in the process of solving problems.
Whether from the perspective of quality education or examination, creative thinking ability is a very important ability in the process of students' growth. In the teaching process, exercise teaching takes up a lot of class hours, so it is particularly important to cultivate students' creative thinking ability in exercise teaching.
3. Guide students to study independently and cultivate creative thinking ability.
The creation of creative thinking needs an intrinsic motivation, which is triggered by students' successful experience in completing a learning task. Therefore, teachers must create conditions for students to study, explore and display their talents independently, let students perceive the formation process of knowledge themselves, and guide students to reveal the internal relations and the essence of things through induction and generalization, and "discover" the laws. Doing so may be troublesome and time-consuming, but the students' gain is not only to draw a conclusion, but more importantly, to cultivate their creative thinking ability in the process.
summary
Cultivating innovative spirit and practical ability is the core of quality education. Therefore, cultivating innovative spirit is the sacred duty of every teacher in the new era. Therefore, every teacher should reflect on the advantages and disadvantages of various practices in our past education, dialectically think and analyze some traditional practices and understandings in education, update educational concepts, and try their best to cultivate students' creative thinking.
3 How to cultivate primary school students' innovative thinking
First, create problem scenarios to introduce thinking realm. In the process of teaching, if you just talk about it, students will get bored and lose interest. In this case, teaching will not achieve good results. If we first create a problem scenario for students, guide them into the scenario, give them vitality, and let students seek ideas and boldly innovate in the excitement aroused by the scenario. As far as the content situation is concerned, there are story method, life case method, experimental operation method, contact with old knowledge method and accompanying problem solving method. As far as its intention is concerned, there are interesting problems to stimulate students' enthusiasm for learning, analogy problems to strengthen practice by reviewing what they have learned, and practical problems to combine with reality. For example, when I was reviewing the relationship between the parts of division, the students themselves had deduced the relationship between the parts. When they were experiencing success, I suddenly calculated a division with remainder to find the dividend. At first, students feel that there is no way to doubt, but after thinking about it, they are "promising".
Second, reproduce the innovation process and cultivate innovative thinking. Mathematics classroom teaching should not only pay attention to the proof and application of conclusions, but also pay attention to the process of exploration and discovery. Students should follow a "rediscovery" road carefully designed by teachers to explore and discover the causes and internal relations of things, find out the laws and concepts through induction, analogy and migration, and then try to demonstrate or solve problems. For example, when teaching practical problems with fractions, I summed up the problem-solving methods through the transfer method, so that students can know that the quantitative relationship of such application problems is consistent with the "multiple" problem, and the unit "1" is defined as who X is, so that students can still explore and innovate in this way when they encounter new math problems in the future.
Third, grasp the psychological characteristics of students and stimulate their interest in innovation. Interest is the source of innovation and the driving force of thinking. In teaching activities, teachers should stimulate students' interest in innovation, enhance the internal driving force of students' thinking, and solve the motivation problem of students' innovative thinking. Pupils are curious and eager to learn. Teachers should grasp these psychological characteristics of students, give appropriate guidance, stimulate their thirst for knowledge and cultivate their interest in learning.
4 How to develop mathematical thinking
Cultivating Mathematical Thinking in Multimedia Teaching
Mathematics is the gymnastics of thinking. Modern media can vividly simulate the thinking world, reproduce the thinking process, promote students' transition from image thinking to abstract thinking and divergent thinking, and gradually develop students' logical thinking ability. For example, when teaching "lateral area of a cylinder", first show a cylinder on the screen with multimedia courseware, so that students can imagine and think "What is the shape of the side of the cylinder after expansion?" Then slowly expand the side of the cylinder on the screen, so that students can clearly see that the side of the cylinder after expansion is a rectangle.
At this point, the teacher asked this question again: "What do you think is the length of a rectangle equivalent to the length of a cylinder? What is the width of a rectangle equivalent to a cylinder? " Let the students think, watch the demonstration just now, and then deduce the formula for calculating the side area of the cylinder. At this point, the students' thinking has further diverged. They think that if you don't expand the edge along the height of the cylinder, you will get a parallelogram, the bottom of which is equivalent to the circumference of the cylinder bottom, and the height of which is equivalent to the height of the cylinder. They are trying to verify it.
Develop thinking in practical operation
Mathematical problems and mathematical thinking must be understood and mastered by students in practical activities, which requires teachers to carefully design all aspects of teaching in classroom teaching and guide students to acquire knowledge and develop their thinking independently through practical operation. For example, in the teaching of "Understanding the Circle", take the objects that belong to the circle in real life as an example to let students understand the difference between the circle and other plane figures. As for how to draw a circle, the teacher doesn't need to demonstrate, let the students try it themselves.
"Can you draw a standard circle? Who has the best way to see it? " Students cooperate with each other, and everyone uses their hands and brains to explore boldly. Soon, most students learned to draw circles with round objects (such as coins and ink bottle caps) or compasses. Then, the teacher further encouraged the students to explore, "If you want to build a big round flower bed, can you draw it with compasses?" This kind of teaching provides students with practical opportunities, encourages students to seek novelty and innovation, boldly explores, and maximizes students' practical ability, thinking ability, exploration spirit and interest in learning.
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