Teaching and learning are bilateral relations between teachers and students. Teaching should be effective and learning should be active. Initiative comes from interest, and interest needs to be cultivated. The same textbook is lively and interesting, and students never tire of listening to it, with endless aftertaste; Dogmatically speaking, boring, students are stupefied, get twice the result with half the effort. In order to enliven the classroom atmosphere, arouse students' learning enthusiasm, improve the art of lectures and enhance the teaching effect, the specific methods are as follows:
1, with kind attitude and humorous language.
Stroff, an educator in the former Soviet Union, said: "Humor is the most important and first assistant of educators." Amiable attitude can clear away students' fears, and humor can arouse students' interest in attending classes. For example, when some students apply simple equations to solve practical problems in algebra of senior one, they often forget to assume unknown quantities, which I call "a horse stumbles (a problem)". For another example, before speaking the axiom of straight line, I nailed a thin stick to the blackboard with a nail, and I found the stick turning around the nail. When I nailed the stick to the blackboard with two nails, I found that the stick was fixed. I read aloud while operating: a little sway is long, and two points are fixed for life. Through experiments and inspiration, it is concluded that there are countless straight lines behind a point; There is a straight line after two o'clock, and there is only one straight line. Through humorous ways and vivid language, students' interest in learning is doubled, their mood is high, and they enter a higher learning mood.
2. Clever questions to enlighten thinking.
Classroom questioning is an important means to organize classroom teaching and an important link to implement heuristic teaching. A good question can not only stimulate students' interest in learning, but also quickly concentrate students' attention, inspire students' thinking and develop their intelligence. The famous mathematician G Paulia pointed out: "Try to stimulate the reader through the choice, formulation and arrangement of questions and arouse him to deal with all kinds of research objects." It is difficult for freshmen to solve practical problems by solving equations. Example: How many grams of water should be added to dilute 30g 16% brine into 0. 15% brine? Several questions can be asked during the analysis: "How many basic quantities are there in the concentration problem? What is the quantitative relationship between them? " "How much salt does a gram of salt water with a concentration of 20% contain? How much water is there? " "In the process of adding water, what amount has changed and what amount has not changed?" "The salt content in the solution is constant. How to use this equivalent relationship to form an equation? " Students have strengthened their confidence in learning by thinking about a series of small problems and solving them one by one. Therefore, skillfully setting questions can give full play to the leading role of teachers and the main role of students, mobilize the enthusiasm of students to participate in classroom teaching and improve teaching effect.
3. Simple and easy.
In teaching, if teachers can quote some familiar and intuitive examples as metaphors, they can turn abstraction into concreteness and abstruse into conciseness. For example, the number axis is an abstract concept. Before talking about the number axis, first introduce the thermometer, and then abstract the thermometer to the number axis. Absolute value is a concept that is difficult for students to understand. Most of them just memorize | a | =-a mechanically when a < 0, but don't simplify | x-2 | when x < 2. Therefore, when teaching, I use specific figures to judge and guide, such as | x-2 | =|1.9 | = |-0.1| =-(-0.1) = 0.65438. It can be inferred that when x < 2, x-2 < 0, so | x-2 | =-(x-2) = 2-X. Such a simple description makes it easier for students to accept knowledge.
4, interesting teaching, increase the attraction.
One of the reforms of junior high school mathematics textbooks is to insert columns such as "think about it" and "talk about it" in the text, paying equal attention to knowledge and interest. It has a strong temptation to students who are eager for knowledge, stimulates students' interest in learning, and also cultivates students' thinking ability of reading, thinking, observing and imagining. For example, About π л embodies the infinite wisdom of our people and stimulates students' enthusiasm for learning science. Another example is the golden section, which not only introduces the proposal, practice and proof of the golden section, but also points out its role in geometric drawing. The book points out that making a circle inscribed with a regular decagon can also be summarized as the application of the golden section. In order to better reflect the consciousness of applied mathematics, this paper illustrates the universal application of golden section in photography and "optimization method", so that students can feel the charm of mathematics. Facts have proved that interspersed with interesting teaching can not only satisfy students' thirst for knowledge, but also improve students' initiative and enthusiasm in learning.
Second, advocate observation and discovery teaching.
Discovery method was put forward by Bruner, a representative figure of the American structuralist education school. Discovery method is a method to cultivate students' exploratory thinking. In classroom teaching, teachers should not regard themselves as the playback keys of tape recorders. No matter how students accept knowledge, they should continue to teach enthusiastically, mistakenly regard students as record keys, put them in a passive position and impose knowledge on them. This kind of "cramming" teaching, the classroom effect is good for the time being, but it can't stand the test of time, and the knowledge forgetting rate is high, which often gets twice the result with half the effort. Therefore, it is timely to adopt the discovery method in teaching.
In teaching, we should pay attention to guiding students to participate. The teacher is the director, the students are actors, not spectators, and the teacher's simple "starring" is transformed into the "performance" of teachers and students. There is a crucial "discovery method" in this kind of activity, which allows students to discover certain laws and conclusions after careful observation. When the teacher talks about "the sum of the internal angles of a triangle", he thinks through the trilateral relationship of the triangle he has learned: What is the relationship between the three internal angles of a triangle? Let the students draw a triangle on the prepared paper, and write down the three internal angles as 1, 2, 3. Try to fix one angle in the exercise book, draw the other two internal angles to be cut in the exercise book, and then cut the two internal angles together to see if they are right angles. Let the students "discover" that the sum of the angles in the triangle is equal to 180 through experiments. At the same time, in the process of spelling, guide students to find out how to prove the theorem with auxiliary lines (as shown in figure 1, figure 2).
Another example is to explain the following examples when teaching the subtraction rule of rational numbers: (+10)-(+3) =+7, (+10)+(-3) =+7, indicating (+10)-(+3) =+. Then let the students observe the similarities and differences between the two sides of the above formula and find that subtraction can be transformed into addition. Let the students express the rules and conclusions found in their own language, and then the teacher will comment and correct them. Through the guidance of teachers, the knowledge in books can be transformed into students' own knowledge through observation and discovery, which is helpful for students' understanding and memory, cultivating students' observation and discovery ability, cultivating students' expression ability and enhancing teaching effect.
Third, concentrate on speaking and practice more to improve the classroom teaching effect.
The combination of lectures and exercises will help students to think and study with their mouths, hands and brains, and make full use of the 45 minutes in class, which will not only reduce the burden on students, but also arouse their enthusiasm for learning. Psychologists' experiments show that teenagers, especially junior high school students, have a psychological characteristic that can not be ignored, that is, teenagers' concentration can not be sustained and has intermittent characteristics. The first concentration can only last for more than ten minutes before it begins to diverge. The second time is about ten minutes, decreasing in turn. In view of this characteristic of students, teachers should grasp the lecture time well. For example, the main content of "judgment of parallel lines" is the judgment axiom and theorem of parallel lines. I made such an attempt: lead the students to draw the judgment axiom of parallel lines, and then let the students complete the exercises suitable for the judgment axiom and give comments. In this way, students accepted the axiom of judgment when they were paying attention, relaxed their spirit in practice, eliminated the fatigue that had already appeared, and prepared for the following content. Then, the condition that the internal angles meet the judgment axiom is analyzed, and the judgment theorem is obtained: the internal angles are equal and the two lines are parallel, and the corresponding exercises are matched, and finally the conclusion is made. In the process of alternating speaking and practicing, the students are full of energy. They can not only quickly grasp the main points of knowledge, but also correctly apply knowledge to solve problems. This combination of teaching and practice can grasp the key points of the textbook and explain the knowledge thoroughly. On this basis, combined with practice, we can avoid listening fatigue, digest new lessons in class, further consolidate and understand new knowledge, and effectively improve the quality of classroom teaching.
Fourth, pay attention to job evaluation.
Homework evaluation is an important means of classroom teaching feedback and an important link to improve the quality of classroom teaching. Homework evaluation is the continuation of correcting homework. High-quality homework evaluation requires teachers to make full preparations in advance: correcting records, commenting on evaluation schemes, indicating details, sketchiness, not talking, and being good at grasping typical mistakes and representative topics. For example, "the quotient of A and B is 3 times", and many students will write 3, which is a mistake in writing habits. So, as long as you correct your mistakes in your comments and give one or two kinds of questions, this is a short conversation. For another example, when calculating (3x), some students got (3x) = 6x by mistake. This problem involves multiplication of products: (3x) = 3x, 3 = 9, so (3x) = 9x, which is a detailed talk about teaching students to apply laws to calculate.
Homework evaluation is also timely. As the saying goes: strike while the iron is hot. Timely comments can help students correct their mistakes in time, rethink on the basis of their original homework, find out their own knowledge gap and wrong thinking habits and methods, better grasp the accuracy of knowledge and deepen their mastery.
Homework evaluation needs students' active cooperation. For a long time, many students regard finishing homework as "homework" assigned by teachers. Homework handed down only depends on comment on writing, without checking the cause of the error, let alone correcting it. Some good students, although they notice mistakes, often correct them without delving into them. Over time, they have developed the bad habit of not thinking independently and muddling along. Therefore, when correcting homework, we should fully mobilize students' enthusiasm, not just give correct answers mechanically, but pay attention to teaching students how to solve problems. Controversial issues can be discussed by students and expressed by teachers. For example: "As shown in Figure 3, the equilateral △ABC, the side length is 2, D, B, C and E are on the same straight line, and DB = BC = CD, find the perimeter of △ADE." If we can find the length of AD and AE, we can find the perimeter of △ADE. The lengths of AD and AE can be obtained in many ways: (1) AD can be obtained in Rt△ADC. ⑵ Make height on BC side of △ABC, and get AD in R△ADC. ⑶ Using Rt△ADC, ∠ d = 30 ... There are various methods, and this problem combines the properties of special triangles and the application of judgment. Deepening the understanding of the old and new knowledge in the discussion and strengthening the connection between the old and new knowledge are conducive to filling the gap.
Five, for all students, pay attention to the cultivation of non-intellectual factors.
Intelligence factors and non-intelligence factors promote each other under certain conditions. Students with the same level of intelligence sometimes have a big gap in their academic performance. The main reason is that non-intelligence factors hinder the effective development of his intelligence, such as poor learning enthusiasm and poor self-discipline ability. Therefore, cultivating students' non-intelligence factors can effectively improve the quality of teaching, especially the quality of classroom teaching.
Some junior high school students are weak-willed, unable to bear hardships, love to imitate, lack the ability to distinguish right from wrong, and are easily disturbed by the outside world. Therefore, teachers should attach importance to their own personality cultivation and influence and motivate students in a positive way. Some students lack fighting spirit, their study enthusiasm is not high, and their grades are not ideal. They are easy to feel inferior and suspicious. In order to attract attention and satisfy vanity, they often like to "put on a show" in class. If we just criticize such students blindly, it will only increase the depressed mood, and even form a rebellious mentality, specifically targeting teachers and affecting classroom teaching. Therefore, the cultivation of poor students mainly starts with non-intellectual factors, takes "love" as the principle, grasps their own personality characteristics, tries their best to appease, care for and love, and gives more encouragement. Give patient guidance in learning, fully affirm their progress, help them build up confidence and focus on the classroom.