1 How to improve the logical thinking of mathematics
In teaching, we should guide students to master mathematical laws on the basis of learning concepts well and pay attention to cultivating students' logical thinking ability.
In concept teaching, we should start from actual examples or students' existing knowledge and research methods, and gradually guide students to abstract and understand the meaning of concepts through observation, analysis and induction. For example, when learning the concept of score, we can distinguish the difference and connection between the concept of score and the concept of score by comparing the individual aspects or characteristics of the concept. For easily confused concepts, students should be guided to make clear their differences and connections through comparison. For example, when learning centrosymmetric and centrosymmetric graphs, let students know that their relationship can overlap after bypassing a point of 1800. The difference is that central symmetry refers to two figures, while central symmetry refers to one figure. For laws, we should find out their sources and distinguish their conditions and conclusions. Understand the process of abstraction, generalization or proof, and understand their purpose and scope of application. In the process of cultivating logical thinking ability, we should follow students' cognitive rules, from shallow to deep, from perceptual knowledge to rational knowledge.
In teaching, we should pay attention to improving teaching methods, insisting on heuristic and opposing injection.
We should attach importance to cultivating logical thinking ability in the process of acquiring and applying knowledge. In teaching, teachers play a leading role and students are the main body of learning. The mobilization of students' learning enthusiasm, the study of knowledge, the training of skills and the cultivation of ability all depend on the careful design, organization and implementation of teachers in the teaching process. Teaching process is also a process of students' cognition. Only when students actively participate in teaching activities can they receive good results. Teachers should pay attention to arouse students' enthusiasm and initiative in learning, and all teaching measures of teachers should proceed from students' reality.
Mathematics teaching should not only teach students mathematical knowledge, but also reveal the thinking process of acquiring knowledge, which is more important for developing ability. Mathematics teaching should focus on developing students' thinking activities, supplemented by necessary discussion and summary, and guide them correctly. In teaching, we should pay attention to the process of putting forward mathematical concepts, formulas, theorems and laws, the formation and development of knowledge, and the generalization of problem-solving methods and laws, so that students can develop their logical thinking ability in these processes.
In teaching, students' logical thinking ability is cultivated through correct organization exercises.
Practice is an organic part of mathematics teaching, which is very important for students to master basic knowledge, basic skills and ability development, and is a necessary condition for learning mathematics well. Therefore, the key knowledge must be designed and practiced repeatedly in time, with good knowledge points to exercise students' ability. In addition, we can use the methods of "teachers' reform, students' practice", "students' compilation, students' practice and teachers' evaluation" to practice, so that knowledge can be understood, deepened and applied, and students can consolidate knowledge, master skills, develop their abilities and cultivate their sentiments in the process of practice, thus truly achieving the purpose of quality education.
2 Mathematics teaching methods
Innovative idea of situation creation
The creation of teaching situation can also let students go out of the classroom, look for similar graphics in nature, take nature as the classroom for on-the-spot teaching, and constantly arrange the actual trees, clouds and people. Let the dynamic influence drive students' enthusiasm for solving problems.
Grasp the flexible teaching situation demonstration, so that students can not only learn textbook knowledge in the learning process, but also find the knowledge reflected by mathematics in real life, connect textbook knowledge with real life, seize better learning inspiration, show themselves in class, boldly demonstrate innovative situations in class, and let their ideas spread to other students better, so that the classroom atmosphere can be continuously driven and students can continuously form a kind of autonomous learning ability.
Application of suspense guidance method.
In the creation of actual teaching situations, teachers should strengthen the guidance of students' interests, effectively present key points, and adopt different methods to guide them, so that students' attention can be focused on solving mathematical problems, rather than just attaching importance to the rigid indoctrination of knowledge points.
For example, in the process of firm memory training of calculation formulas, teachers write key formulas on the blackboard, and let students do their own problems and replace the data of these problems, so that students can effectively use the unified formulas in different topics. Secondly, decompose students' problems, grasp the key points, leave students with suspense, and hide an important breakthrough in the problems for students to discover by themselves. In this way, students find hidden breakthrough points in their own problems, are very interested, and constantly enhance their interest in solving mathematical problems. After finding them, you can get the happiness of solving problems independently, but if you can't find them, you can also deepen your impression, so that they can constantly increase their experience in solving problems and learn lessons in the future learning process.
Application of consistent method.
In mathematics teaching, in order to make students fully master flexible problem-solving methods, it depends on teachers to deepen students' impression in the usual teaching process, repeatedly use different topics and the same formula, and combine the same topic with different formulas. In this way, it is necessary to simulate the presentation with the help of people or things in reality that students are interested in.
In the classroom, the teacher arranges experimental instruments, so that students can clearly understand what the figures arranged by these instruments are like, effectively grasp the key points, grasp the key links, solve with one formula, and then solve with other formulas. Then, the teacher transforms the figure into other shapes and transforms it several times, so that students can solve it with the same formula. In this way, students can find flexible inspiration to solve problems in actual situations and deepen their impressions.
3 Cultivation of interest in mathematics learning
Be good at connecting the past and the present. Stimulate students' desire to explore mathematics
In the process of mathematics teaching, we should be good at telling students some history of mathematics from ancient times to modern times, stimulating their desire to explore mathematics and increasing the connotation of mathematics classroom. For example, learning pi can tell students the history of pi, from Archimedes, the first person to find pi by scientific method, to Zu Chongzhi, a mathematician in the Northern and Southern Dynasties in China; From15th century, Arabian mathematician Kathy got the decimal value of pi17th place, which broke the record kept by Zu Chongzhi for nearly a thousand years. By 1706, British mathematician Mackin exceeded the decimal mark of100th place when calculating π value. Starting from 1948, Ferguson in Britain and Ronchi in the United States manually calculated the highest value of pi of 808 digits to 124 1 100 billion digits after the decimal point with electronic computers, which stimulated students' passion for exploring and learning the mysteries of mathematics.
It is necessary to teach students to draw inferences from others and let them find the right pleasure in success.
As we all know, the most important thing to learn mathematics well is to draw inferences from others. To solve mathematical problems, we should not only be good at logical reasoning, learn correct thinking and calculation methods, but also be good at comprehensively applying basic mathematical knowledge. Doing more exercise is of course a good thing, but there are endless problems and limited energy. If we can properly select some representative exercises, which are small in number but skillful, and draw inferences from each question, we can not only improve our ability to solve problems, but also enhance our confidence in learning mathematics. Let students experience the fun of learning mathematics. Therefore, every time they finish a problem, they should "reflect" on what the biggest obstacle is in the process of solving it, how to solve it, how many solutions there are, which solution is the best, whether it can be applied to other problems, and so on. So as to realize the organic combination of learning and acquisition, and finally form a problem with multiple solutions.
It is necessary to combine the reality of life and attract students' enthusiasm for learning mathematics.
Pay attention to connecting with practice in teaching, so that students can realize that what they have learned is closely related to the problems they are exposed to, as well as its value and wide application in production and life, and understand that mathematics is an indispensable basic tool for learning and studying modern science and technology, thus stimulating their interest in learning mathematics. For example, this paper introduces straight lines, rays, line segments and angles from the National Aquatics Center "Water Cube" and the National Stadium "Bird's Nest", which are one of the landmark buildings of the 2008 Beijing Olympic Games, and quotes China designer Zhao Xiaojun's explanation of the design concept of "Water Cube": "This is a water building" Water Cube ",which calmly expresses courtesy and respect for the main stadium with a pure square.
4. Students' divergent thinking ability
Cultivating students' divergent thinking ability by inducing differences.
Teachers properly choose specific cases, create problem situations, and carefully induce students' awareness of seeking differences. We should give affirmation and warm praise to the factors that appear from time to time in students' thinking process, so that students can truly experience the value of their own achievements in seeking differences. When students want to find different solutions but can't, teachers should carefully guide and concentrate on inducing success, so that students can gradually develop a conscious sense of seeking differences and develop a stable psychological tendency. When faced with specific problems, they will take the initiative to make "Is there any other solution?" "Give it a try and analyze it from another angle!" Thinking about seeking differences.
Combining with teaching practice, improve the training mode.
The particularity of mathematics teaching in primary schools requires teachers to pay attention to the acceptance process and psychological state of primary school students when organizing classes. First of all, we should pay attention to creating a relaxed and lively classroom atmosphere to avoid the scene of primary school students listening to math classes with trepidation. Such a state of psychological relaxation helps them to open the floodgates of thinking and carry out divergent thinking training. Secondly, it is necessary to guide students to mobilize divergent thinking to solve problems and form habits by means of "solving many problems with one problem". Although the knowledge problem in primary school mathematics is not profound, it is closely related to the reality of life. Teachers should teach primary school students to solve the same problem in many ways, let them learn to mobilize a variety of thinking senses, and train the breadth and freedom of thinking, so as to deal with the problem more harmoniously and efficiently. "Transforming thinking" and "variant expansion" are both good methods to improve the universality, association and activity of students' mathematical thinking and divergent thinking. Finally, teachers should first exercise divergent thinking. Cultivating primary school students' mathematical thinking is a difficult problem in itself, which requires teachers to use their brains and find multi-level methods to carry out experiments, which is also a test of cultivating divergent thinking.
Encourage innovation and cultivate students' divergent thinking ability.
In the process of analyzing and solving problems, students can creatively put forward new and different ideas and solutions, which is the performance of original thinking. For example, a toy factory produces a batch of children's toys. It was originally planned to produce 60 pieces a day and complete the task in 7 days, but it actually took only 6 days to complete it. How many more toys are actually produced every day than originally planned? "When solving a problem, according to the conventional solution, first find out how many pieces are in the total task and how many pieces are actually produced every day, and then find out how many pieces are actually produced every day and how many pieces are more than originally planned. The formula is 60X7÷6-60= 10 (pieces).