First, create a situation, arouse interest by setting doubts, and grasp the opportunity to introduce.
Psychological research shows that a wonderful beginning often brings freshness to students, which not only makes students' thinking quickly change from inhibition to excitement, but also makes students take learning as a self-need and naturally enter the situation of learning new knowledge. There are many ways to introduce junior high school mathematics classroom, such as opening the way through experiments, introducing stories and introducing suspense. For example, when teaching the "denominator is physics and chemistry" section, the teacher wrote a question on the blackboard after class: "Calculate 1∕√2 (accurate to 0.0 1)". Assign two students to act in two different ways. First, multiply both the numerator and denominator by √2, and quickly calculate the result. The other is to directly divide 1 by the approximate value of √2 1.4 14, and the calculation is very complicated. After the two students finished speaking, the teacher asked the students: which method is simpler? The students unanimously affirmed the former solution, which naturally introduced the topic of denominator rationalization. For another example, to talk about "the mutualization of coordinates", let's give an example to show that the weights and measures systems in different countries are not unified. We should not only master the market system, but also learn the metric system, and be able to integrate them. Then turn to the topic: Cartesian coordinate system and polar coordinate system have their own advantages in establishing the corresponding relationship between functions and images, but sometimes it is necessary to transform the equations in one coordinate system into those in another. This is why we should learn "the mutual transformation between rectangular coordinates and polar coordinates". In this way, the introduction of the topic is effortless and the purpose is clear, which makes students have a strong thirst for knowledge and desire to learn new knowledge, and their attention is immediately attracted to classroom teaching, which stimulates their strong desire to actively participate in the research.
Second, cultivate students' new ideas and concepts in mathematics teaching.
New ideas include not only new understanding and new ideas about things, but also a process of continuous learning. Therefore, as a new talent, we must learn to learn. Only by continuous learning can we acquire new knowledge, renew our concepts and form new understandings. In the history of mathematics, Descartes, a great French mathematician, liked reading extensively when he was a student and realized the disadvantages of the separation of algebra and geometry. He studied the drawing problem of geometry by algebraic method, and pointed out the relationship between drawing problem and solving equations. Through specific problems, he put forward the coordinate method, expressed geometric curves as algebraic equations, asserted that the number of curve equations had nothing to do with the choice of coordinate axes, and classified curves by the number of equations, thus realizing the relationship between the intersection of curves and the solution of equations. It advocates a new viewpoint of combining algebra with geometry and applying quantitative methods to geometry research, thus creating analytic geometry. As a math teacher, we should not only teach students to learn, but also teach them to learn. In the teaching of inequality proof, I mainly teach students how to analyze problems, flexibly use three basic proof methods: comparison method, analysis method and synthesis method, and guide students to learn and prove inequalities with new methods such as triangle, complex number and geometry.
Example a & gt=0, b & gt=0, and a+b= 1, verification (A+2) (A+2)+(B+2) > =25/2.
There are many ways to prove this inequality. In addition to the basic proof, it can also be proved by finding the maximum of quadratic function, triangle substitution and constructing right triangle. If a+b =1(a >; =0, b & gt=0) as a line segment in the plane rectangular coordinate system can also be verified by analytic geometry knowledge.
The proof is as follows: Take straight line segment x+y= 1, (0 = = 1), (a+2)+(b+2) (b+2) as point (-2, -2), and straight line segment X+Y = 1. Because the distance from a point to a straight line is the minimum of the distance from this point to any point on the straight line. And d*d=( -2-2- 1|)/2=25/2, so (a+2) (a+2)+(b+2) > =25/2. "It is better to teach people to fish than to teach people to fish". Only by mastering methods and forming ideas can students benefit for life.
Third, strengthen perseverance and study hard.
In order to succeed, one must have strong perseverance, determination and courage, not afraid of difficulties and go forward bravely. Some underachievers always think that they are born stupid and have no mathematical cells, so they can't learn. I often educate and encourage these students. Practice has proved that good study habits can be gradually transformed into strong will. When I cultivate students' will, I first let them gradually form good study habits in their study life. I mainly start with the following points: (1) preview before class and review after class. Ask students to develop: read what they want to learn word by word before class, and mark what they don't understand or don't understand (or carefully complete the introduction outline); Listen attentively in class, think seriously, and actively participate in group discussions; Review after class, and then finish your homework (or "introduction outline"). (2) Standardization of operation. Students are required to develop: before starting to do homework, they should revise the last homework, complete it in strict accordance with the writing format, write neatly, carefully examine the questions and complete the homework independently. If you persist in this way, you will gradually develop good habits. (3) Set an example and enhance confidence. Remember "good" for those who get an A in every assignment, and each unit will evaluate who is "good" the most times. Poor students should also be praised and encouraged for their progress in their homework, so that they can slowly overcome bad habits and catch up. (4) Persuade patiently and persuasively. Underachievers sometimes have some difficulties in finishing their homework. I often use my spare time to help them, carefully analyze difficult problems, criticize their homework problems as much as possible when conditions permit, and repeatedly encourage them to finish their homework independently, so their grades will definitely improve.
Fourth, create an activity process to cultivate students' practical ability.
Fourth, create an activity process to cultivate students' practical ability.
Piaget, a famous psychologist, said: "Children's thinking begins with action. If we cut off the connection between action and thinking, thinking cannot develop. " It can be seen that activities are the bridge between subject and object, and the direct source of students' understanding and development. Therefore, teachers should create more activity situations, let students operate, observe, think and express, guide students to participate to the maximum extent, and inspire students' thinking by "moving". In fact, the classroom should be the "activity field" for students, and the teaching process should be the "activity process" for students. One of the leading roles of teachers is to create "activity points". For example, the teaching design of "exercise homework" in junior high school mathematics: (1) students make their own inclinometers; ⑵ Let students design experiments; (3) Students use inclinometers, scales and other equipment to do experiments and explore ways to solve practical problems with right triangle knowledge; (4) Students try to summarize by themselves, and teachers summarize and explain; 5] This paper introduces the use of inclinometer to measure the height of other buildings that cannot be reached at the bottom, such as buildings and chimneys. During the internship, the teacher observed and guided on the spot and answered the questions raised by the students. In the whole teaching process, students actively participate in activities, allowing students to study, explore, design and analyze independently. Teachers are only the guides and organizers of students' learning, and their teaching effect is very good.
Fourth, create an activity process to cultivate students' practical ability.
In a word, how to improve the quality of mathematics teaching has become a problem that the majority of mathematics teachers study and discuss. I think to improve the quality of junior high school mathematics teaching, we should not only pay attention to the development of students' intelligence, but also pay attention to the cultivation of students' non-intelligence factors, and at the same time pay more attention to reforming the traditional classroom teaching mode. Only in this way can we improve the quality of junior high school mathematics teaching.