1 how to improve the ability of mathematical analysis
Lack of accumulation of typical topics and methods that have been learned: some students have done a lot of exercises, but the effect is little and the effect is not good. The reason is that they are forced to do problems passively in order to complete the task, lacking the necessary summary and accumulation. On the basis of accumulation, we can strengthen the "theme" and "sense of theme", gradually form a "module", and constantly draw intellectual nutrition from it, thus realizing the mathematical thinking method hidden in the model. This is the process from quantitative accumulation to qualitative change, and only "accumulation-digestion-absorption" can "sublimate".
When solving new problems, there is a lack of exploration spirit: "learning mathematics without doing problems is equivalent to entering Baoshan and returning to empty space" (Chinese). In the society we are facing, new problems appear constantly and everywhere, especially in the information age. Learning mathematics requires constant exploration in problem-solving practice. Fear of difficulties and excessive dependence on teachers will form the habit of not learning actively over time. We adopt the method of "thinking before speaking, doing before commenting" in classroom teaching, precisely to stimulate learners' enthusiasm for active exploration. It is hoped that students will enhance their self-confidence, be brave in guessing, actively cooperate with teachers, and make mathematics classroom teaching a communication process of learners' thinking activities.
Ignore the standardization of problem-solving process and only pursue the answer: the process of mathematical problem-solving is a process of transformation, and of course it is inseparable from standardized and rigorous reasoning and judgment. In solving problems, jumping too much, scribbling letters and drawing by hand, it is difficult to produce correct answers with such an attitude towards slightly difficult problems. We say that the standardization of problem-solving process is not only the standardization of writing, but also the standardization of "thinking method". Students should learn to constantly standardize their own thinking process and strive to solve problems perfectly.
Do not pay attention to arithmetic, ignore the choice and implementation of operation methods: mathematical operation is carried out according to rules, and the general rules and methods must of course be firmly grasped. However, the relativity of stillness and the absoluteness of motion determine that the general methods to solve mathematical problems cannot be fixed. Therefore, when using generality, generality and general principles to solve problems, we should not ignore arithmetic, but pay more attention to guessing and inference, and choose reasonable and simple operation methods. The method of solving problems without thinking must be improved. Replacing "doing" with "seeing" or "thinking" is the root cause of poor computing ability and complicated calculation.
2 Mathematics teaching methods
Using multimedia to implement open teaching and improve classroom teaching efficiency
The application of modern educational technology in the teaching classroom is becoming more and more mature, which has had a great impact on the classroom teaching in primary schools and prompted earth-shaking changes in classroom teaching. The teaching method of "chalk and blackboard" in traditional teaching shows obvious disadvantages in the face of multimedia teaching. Therefore, in teaching, our teaching methods should be open to multimedia, give full play to the advantages of multimedia, solve the difficulties in teaching with multimedia, highlight the key points of teaching with multimedia, and stimulate students' interest in learning with multimedia, thus effectively improving the efficiency of classroom teaching.
For example, when we teach the content of "reasonable time arrangement" in grade four, I ask students to read the topics carefully first: it takes Xiaoming 8 minutes to make tea for Aunt Li, 1 minute to wash the kettle, 2 minutes to wash the teacup, 7 minutes to fetch water, 1 minute to find tea and 1 minute to make tea. How to make Li? What would you do if you were Xiao Ming? How long will it take? Then, I organize students to have a heated discussion and make clear the order of doing things reasonably. Finally, I will show students the courseware about reasonable time arrangement. In the whole process of watching how to wash the kettle and make tea, students intuitively feel the ingenuity of reasonable time arrangement, which deeply stays in students' minds, letting students know how to pay attention to reasonable time arrangement when doing other things, and also improving classroom efficiency.
Strengthen the life experience in mathematics classroom, and let students experience and apply mathematics.
Primary school mathematics knowledge is widely used in daily life, such as shopping in life, calculation of house size and so on. In today's modernization, even after zero, primary school students "have never heard of or seen" all kinds of things in life. Therefore, strengthening the life experience in mathematics classroom can let students know the usefulness and value of primary school mathematics knowledge and let them learn to use mathematics knowledge to solve practical problems in daily life. In addition, strengthening life experience in mathematics classroom can not only broaden students' horizons and understand primary school mathematics, but also make students like mathematics in life experience.
As the saying goes, "Interest is the best teacher". Let students study with interest in primary school mathematics class, which can not only improve students' enthusiasm for classroom learning, but also promote the mathematics learning atmosphere of the whole class, so that students can learn mathematics more actively, and teachers' enthusiasm for teaching can also grow by leaps and bounds. In this way, Mr. He Chou's primary school mathematics classroom teaching can't improve students' mathematics level.
3 math classroom interest
Through intuitive teaching. Stimulate students' interest in learning mathematics
Mathematics itself is abstract, which is the direct reason why many students are afraid of mathematics. It is not enough for teachers to solve mathematics knowledge only by language, but also to stimulate students' interest in learning mathematics by strengthening intuitive teaching. Intuition has the advantages of being visible and tangible, which will leave a deeper impression on students. For example, when teaching "the surface area of cuboids and cubes", students can prepare physical objects of cuboids and cubes such as matchboxes, erasers and puzzles before class.
Before deriving the formula, guide students to observe the difference between the six faces of a cuboid and the six faces of a cube. Through intuitive observation, students quickly found that the opposite sides of a cuboid are the same, while the six sides of a cube are the same, which laid the foundation for the derivation of the surface area formula of a cuboid and a cube. In the eyes of students, I think mathematics is not as difficult as I thought, and my interest is high. Raise your hand and speak. Then ask the students to discuss and summarize the calculation methods of the surface area of cuboids and cubes. Finally, the teacher will make a more accurate summary. In the process. Students' knowledge is sublimated from perceptual knowledge to rational knowledge, which gives full play to students' learning enthusiasm and makes students understand what they have learned more deeply. Intuitive teaching is not limited to physics teaching. It can also be done by drawing line segments and watching videos.
Educate students in the beauty of mathematics.
Let students realize the beauty of figure, symmetry and logic in mathematics, so as to improve their interest in learning mathematics. Plocque Ras has long asserted: "Where there are numbers, there is beauty." In nature, no matter the sky or the earth, the wonderful light of mathematics is everywhere; In social life, whether it is literature or art, mathematics is full of agility and beauty. For a long time, in middle school mathematics teaching, people only pay attention to the teaching and training of basic knowledge and skills, while ignoring the infiltration of aesthetic education. Not good at discovering the unique beauty of mathematics itself, not paying attention to infecting and inducing students' desire for knowledge with mathematical beauty and stimulating students' interest in learning; Do not pay attention to guiding students to discover and appreciate the beauty of mathematics.
"Successful teaching gives people a kind of beautiful enjoyment", and there are a lot of aesthetic contents in mathematics. Teachers should dig out these aesthetic essences in mathematics, stimulate students' experience of mathematical beauty through mathematics teaching, and cultivate students' interest in and understanding of mathematical beauty. In teaching, teachers can solve multiple problems (proofs) through one problem and change one problem. The beauty of changes in mathematics, such as using one method for multiple purposes and changing one picture, encourages students to think in many directions, guides them to compare and summarize what they have learned, and forms an orderly structural system, thus improving the teaching quality. For example, in the study of trigonometric function and function image transformation, students can see the image of beauty, appreciate the charm of beauty, feel the wonder of the combination of numbers and shapes, and form an orderly knowledge structure and method system in the process of feeling and appreciating beauty. The great French mathematician H Poincare once said: "Feel the beauty of mathematics, the harmony of numbers and shapes, and the elegance of geometry. This is the real aesthetic feeling that all real mathematicians know."
4. Cultivate divergent thinking in mathematics
Change the angle of thinking and let the students' divergent thinking wings see the light.
To carry out divergent thinking activities, it is very important to overcome the mindset and think about problems from all angles in order to solve them. For example, make full use of the positive and negative use of the formula; The application of theorem and inverse theorem, such as Pythagorean theorem and Pythagorean inverse theorem; Proof methods include reduction to absurdity, algebra or geometry.
Step by step, close to life, let students spread their thinking wings and fly happily.
Cultivating the enthusiasm of thinking is an important basis for cultivating divergent thinking. In teaching, teachers should fully stimulate students' strong interest in learning and thirst for knowledge, so that they can learn with high emotions. For example, when summarizing the multiplication formula with the same base number, the author first puts forward 102× 103 to make students think, and many students write:102×103 =100×1000 =/. Therefore, the author further suggests that there are other methods to calculate the results in the form of power. Based on the meaning of power, students quickly wrote:102×103 = (10×10 )× (10×10) = 65438+. Then the author asks how to calculate 10m× 10n if the letters m and n are used to represent indices 2 and 3 respectively. This step-by-step training allows students to taste the "sweetness" brought by learning, which effectively stimulates students' thirst for knowledge.
Carry out "multiple solutions to one question", "multiple changes to one question" and "multiple thoughts to one question", so that students' divergent thinking wings can fly over mountains and sweep across the sea.
Carry out "multiple solutions to one question", "multiple changes to one question" and "multiple thoughts to one question", guide students to observe and think from different angles, seek various solutions, compare them, choose the best solution, and then explore the inherent law of the problem. Through this kind of training, we can draw inferences from others, draw inferences from others and have a comprehensive effect. It can broaden our horizons, broaden our thinking and cultivate students' innovative ability and divergent thinking.
Encourage students to "associate and guess" and let students' divergent thinking wings fly over a new world.
In solving problems, association is an important method. Through the thinking process from one thing to related things and from one concept to another, the connection from the starting point to the end point of the problem is effectively completed. With the help of association, we can find a breakthrough in thinking, thus improving the flexibility of students' thinking.