First, the content should be relevant.
Classroom teaching is the main position for students to learn cultural and scientific knowledge at school, and it is also the main channel for ideological and moral education for students. In today's new curriculum reform, the number of math classes has decreased, but the content and methods have not been cut too much, which challenges the old routines and methods that have been well taught. Teach students more content in 45 minutes, then every sentence should be to the point, practice accurately, and try to be within a limited time. Excellent completion of teaching tasks. Every class should have a key point, and the whole teaching is carried out step by step around this key point. In order to make students clear about the key points and difficulties of this class, teachers can write these contents briefly on the corner of the blackboard at the beginning of the class to attract students' attention. The focus of teaching is the climax of the whole class. Teachers should change their voices, gestures, blackboard writing, application models, projectors, etc. Stimulate students' brains, make them excited, be impressed by what they have learned, stimulate students' interest in learning and improve their ability to accept new knowledge. For example, in the first lesson of the second chapter of analytic geometry, the focus of teaching is to master the definition and standard equation of ellipse, and the difficulty is to simplify the equation of ellipse. Downloaded the video of the "Changmo" 1 lunar exploration satellite, and played it first in this class. That is, let students have an intuitive understanding of the ellipse and stimulate their interest in learning and patriotic enthusiasm. In order to emphasize the clarity of the ellipse, I prepared a thin line and two nails in advance. Before giving a strict definition of ellipse in mathematics, I prepared a small blackboard (foam can be used) and took two fixed points (the distance between the two fixed points is less than the length of thin lines), and then asked two students to draw an ellipse on the teaching aid according to the teacher's requirements. After drawing, the teacher takes two fixed points on the blackboard (the distance between the two fixed points is greater than the length of the thin line), and then asks the two students to draw according to the same requirements. Students sum up experience and lessons by observing the process of drawing twice, and teachers use situations to make students draw a strict definition of ellipse. Only in this way can students have a deep understanding of this definition, especially those two students who performed on stage, and they will never forget it. When further solving the trajectory equation, it is easy for students to come to the conclusion that the equation is easy to find and the coordinate system is successful, but the simplification is in trouble. At this time, the teacher can appropriately prompt: What methods do we usually have when simplifying the formula containing the root sign? The student replied: Both sides can be squared. The teacher asked: Is it better to square directly or square after proper arrangement? Through practice, students find that direct square is not conducive to the simplification of this equation, but square it after finishing, and finally a satisfactory result can be obtained. In this way, the difficulty of simplifying elliptic equation is solved, and the problem of simplifying hyperbolic standard equation is also solved.
Second, time should be spent on the cutting edge.
The meaning of "efficiency" refers to the workload completed and the income obtained in unit time. To measure the teaching efficiency of a class, we mainly look at the effective teaching time, that is, the time for students to learn knowledge, acquire skills, form abilities and raise awareness in the process of teaching activities. Therefore, teachers must do everything possible to improve the utilization rate of 45 minutes in class. For example, when I talk about linear problems in analytic geometry, I have to leave a few questions in each class for the next class, so that students can go back and do their homework. At first, the students felt a little hard, because the math scores of the students I taught were in the lower position in the science class, and then they were gradually cultivated. After a week, more than half of the students can finish this part of the homework independently. The reason for choosing a straight line is that students have learned function and proportional function once in junior high school. Knowing that their images are straight lines makes it easier to do it. This kind of teaching not only saves teaching time, but also enables students to think independently, analyze and solve problems, thus improving their ability.
Third, pay attention to ability training.
1. Choosing appropriate teaching methods is the key to cultivating students' ability.
Each class has its own teaching tasks and objectives. Teachers can use teaching methods flexibly with the changes of teaching content, teaching objects and teaching equipment. There are many methods of mathematics teaching. For new teaching, we often use teaching methods to impart new knowledge to students. In solid geometry, I try to show students geometric models or verify geometric conclusions by interspersed demonstrations. For example, before I talk about solid geometry, students are required to make a geometric model of a cube with lead wire, and observe the relative positional relationship between its sides, the angles formed between each side and the diagonal of the cube, and the diagonal of each side. In this way, when teaching the positional relationship between two straight lines in space, they can be explained intuitively through these geometric models. In addition, we can flexibly adopt various teaching methods such as talking, reading guidance, homework and practice according to the classroom content. Sometimes, in a class, we should use multiple teaching methods at the same time. As the saying goes, "There is no definite teaching method, it is important to get the correct method". As long as it can stimulate students' interest in learning, improve their enthusiasm for learning, help students develop their thinking ability and help them master and use what they have learned, it is a good teaching method.
2. It is the key to cultivate students' ability to give examples carefully.
Teachers should carefully select examples according to the requirements of classroom teaching content, and make comprehensive analysis according to the difficulty, structural characteristics and thinking methods of examples, instead of unilaterally pursuing the number of examples, they should pay attention to the quality of examples. According to the specific situation, the answering process can be written entirely by the teacher or partly by the students. The key is to let students participate in the explanation of examples, rather than being contracted by the teacher alone. Let the students fill the room. Teachers should set aside time for students to think about teachers' questions or answer students' questions, so as to further strengthen the teaching content of this lesson. If the content of the class is relatively relaxed, students can also be guided to preview and put forward appropriate requirements to prepare for the next class.
3. The choice of exercises is the guarantee of cultivating students' ability.
Basic exercise: This kind of pre-Protestant exercise has a clear purpose and strong pertinence, paving the way for new teaching. For example, when explaining the arrangement and combination, each class should have corresponding basic questions, only one or two questions, so that students can be more familiar with the key points of the last class.
Targeted exercises: targeted individual exercises after new lectures, and articles on how to break through difficulties. For example, when talking about the application of logarithmic function, students always don't know how to start. At this time, it is necessary to match the difficult questions, classify the type questions, and keep one homework in each class, so that the difficulties are broken.
Contrast exercise: seeking common ground while reserving differences can deepen understanding. For example, after finishing the basic content of permutation and combination questions, one or two special training sessions should be added. The topic is mainly a comprehensive application problem with existing permutation and combination, which can deepen understanding and consolidate knowledge through comparison.
Operation practice: Through drawing, cutting and spelling, education is put into practice, which not only cultivates hands-on ability, but also develops thinking in images. For example, in solid geometry, it is very difficult for a sphere to be tangent to a cone. At this time, students might as well go home and make three balls and put them in a cone to experience the conclusion of tangency.
Oral training: students can express their reasoning in language and cultivate their initial logical reasoning ability. In teaching, even if it is a difficult problem, the teacher should prompt the students first, and then try to make the next analysis, especially through physical projection, so that the students can explain the problem. For intermediate and basic questions, students must analyze independently, how to calculate the conditions from the questions, and have a complete understanding of the relationship between quantity.
Fourth, we should work hard on preparing lessons.
1. To optimize the teaching objectives of this class, the key and difficult point is the basis of preparing lessons.
Because preparing lessons is the basis and foundation of teaching. Only by delving into the teaching materials and carefully designing classroom teaching can teachers achieve good teaching results. There are many requirements for preparing lessons, but at least we should master the key points and difficulties of this lesson. Only by knowing what students should learn can we find out what they should teach, otherwise, we can catch sparrows with our eyes closed. Generally, it's just useless labor. Teaching objectives determine the direction of classroom teaching. Whether the preparation before class is sufficient or not directly affects the efficiency of classroom teaching, that is, we should grasp the teaching materials, make clear the purpose, connect with the students' reality, show the key points and difficulties in time, grasp the main line of thinking, prepare the teaching AIDS adequately and design the blackboard clearly. Grasping the difficulties and starting teaching can effectively overcome the randomness and blindness in teaching and enhance the pertinence of teaching.
Preparing lessons is not only for textbooks, but also for students.
To know the details of students' knowledge, if you want to know how students will react when you ask questions, such as the second class of binomial theorem, in order to cultivate students' transformation consciousness when choosing examples, I choose: the constant term in the expansion is -20, and the value of n is ().
A.3 B.4 C.5 D.7
After choosing this question, we should not only consider the problem of transforming three items into two items by matching, but also consider that it is impossible for all students to directly understand that a complete square is needed. If students think of pairs, how do you explain it? Only in this way, if there is a change in the classroom, the teacher will not directly say: your idea is not good, you should do what I mean. You are so arbitrary, just follow the students' thinking. For example, it is right to encourage students first, but this will lead to two binomial expansions, which will make the problem more complicated and make all students understand the truth. Although on the surface, the content of class hours is increased, but it also protects students' learning initiative and enthusiasm, satisfies students' thirst for knowledge, and can actually improve the efficiency of mathematics classroom in the future.
3. Pay attention to lead-in when preparing lessons to stimulate students' interest in learning.
Clever questions can attract students' attention. When giving lectures, proper questioning can add catalyst to abstract language, attract intentional or unintentional attention, stimulate the excitement center of the brain, and make students in an excited state. In my opinion, the purpose of classroom questioning is to inspire students to think positively around the goal and ask questions when in doubt; The second is to attract students' attention and urge them to listen carefully. Therefore, teachers should ask questions appropriately-in the exploration of key points, difficulties, turning points and laws, so that students can actively master knowledge through their own thinking activities such as perception, understanding, comparison, analysis and synthesis of teaching materials. Good lesson preparation design questions should stimulate students' interest in learning, cultivate students' interest in what they have learned, and gain happiness and comprehensiveness in learning. On the contrary, if you are not interested in what you have learned, you will feel that learning is a burden, which is manifested in class: listlessness and distraction, which eventually leads to boredom and giving up on mathematics. Mathematics is a highly abstract subject. If teachers teach in a straightforward way, it will easily cause students' boredom. This requires us not to talk and fill in the blanks in class, but to attract students to realize the important role of mathematics in life through various practical examples.
5. Be good at applying modern teaching methods.
With the rapid development of science and technology, three machines and one scene have entered the ordinary classroom. It is particularly important and urgent for teachers to master modern teaching methods. The remarkable characteristics of modern teaching methods are: firstly, it can effectively increase the class capacity of each class, thus solving the original 45 minutes in 40 minutes; The second is to reduce the workload of teachers writing on the blackboard, so that teachers can have the energy to explain examples in depth and improve the efficiency of explanation; Third, intuitive, easy to stimulate students' interest in learning, is conducive to improving students' initiative in learning. Fourth, it is helpful to review and summarize what you have learned in the whole class. At the end of the class, the teacher guides the students to summarize the content of the class, the key points and difficulties of learning. At the same time, through the projector, the content will jump to the screen in an instant, so that students can further understand and master the content of this lesson. In classroom teaching, for a large number of blackboard writing performances, such as some geometric figures in solid geometry, some simple but large number of small questions and answers, as well as application questions with more words, the summary of chapter content in review class, the training of multiple-choice questions, etc. Can be done with the help of a projector. For qualified schools, computer courseware can also be compiled with the help of computers to vividly display the contents taught. For example, the drawing of sine curve and cosine curve and the derivation of pyramid volume formula can all be demonstrated by computer.
In short, in this year's new curriculum reform, we must study hard and explore new teaching methods, so that students can master skills and develop their abilities while understanding knowledge. Because students' development in knowledge, skills and abilities is different, and there are individual differences among students, teachers should create conditions and teach students in accordance with their aptitude, so that each student can develop and improve in different degrees. In teaching, teachers should carefully design and create situations. Fully arouse students' learning enthusiasm, let every student participate in the whole process of teaching, actively think, ask questions and solve problems under the guidance of teachers, and develop students' wisdom potential, so the effectiveness of mathematics classroom teaching will be put forward.