How to break through the difficulties in 1 high school mathematics teaching
How to determine the key points and difficulties in teaching
To determine the important and difficult points of the textbook, we must first grasp the teaching content as a whole, understand the relationship between chapters, and understand the reasons arranged by editors. Secondly, we should understand the logical relationship between the unit contents in each chapter and finally implement it in the content of each lesson. From the overall layout, according to the actual situation of students, to determine the important and difficult knowledge of this textbook, so as to facilitate the effective decomposition of the important and difficult knowledge in future lesson preparation, so as not to make the important and difficult knowledge in the textbook too concentrated and increase the students' academic burden. In short, the focus and difficulty of teaching are generally determined by the teaching materials, but students' factors should also be taken into account. Once the key and difficult knowledge in the textbook is determined, this knowledge point should be the key and difficult point for every student.
In view of the current cognitive level of students, it is generally difficult to start from the key points and break through the difficulties. The emphases and difficulties of teaching are often directly related to students' cognitive level and cognitive structure, which is caused by the contradiction between the new learning content and the original mathematical cognitive structure. The process of properly integrating new knowledge into the original mathematical cognitive structure and expanding the original mathematical cognitive structure is an assimilation process; When the newly learned knowledge cannot be integrated into the original mathematical cognitive structure, it is necessary to reconstruct the mathematical cognitive structure at this time to adapt the newly learned knowledge to this cognitive structure. Judging from students' cognitive level, it is the focus of teaching to master new knowledge points by absorbing old knowledge, which is both the focus and the difficulty in our teaching. However, in practice, each student's cognitive level is different from the original cognitive structure, which leads to a different starting point of learning. Some students may find it relatively easy to learn what they think is difficult because of their different cognitive structures, and vice versa. In short, in teaching, according to the actual situation of students, the difficulties should be determined on the basis of grasping the key points.
Strategies to highlight key points and break through difficulties
Grasping the key points and difficulties of knowledge is the premise of highlighting the key points and breaking through the difficulties, which requires teachers to fully analyze and prepare according to students' actual cognitive level. In this process, we should grasp the differences of different students' cognitive structure and grasp the key and difficult points of teaching. Careful preparation and accurate positioning before class provide good conditions for the breakthrough of teaching.
Finding the growth point and correlation point of knowledge is the key to highlight the difficulties of the problem. High school mathematics is a subject with high difficulty coefficient and strong systematicness. As we all know, mathematics learning is inseparable from mathematics logic and thinking, and students' learning must also guide them to a new self with the help of mathematics logic and thinking structure; Actively organize students' knowledge transfer, from known to unknown, from simple to complex, so as to improve the cognitive structure. Therefore, in teaching, we can effectively combine old and new knowledge and explore unknown knowledge from known content: (1) Use the similarities and differences between old and new knowledge to explore their "* * * similarity" and simplify the complex. (2) Find the connection point between old and new knowledge, that is, the new knowledge consists of multiple old knowledge, and turn the unknown into the known. (3) Explore the evolution point of old and new knowledge, that is, some new knowledge evolved from some old knowledge in some form to break through the difficulties. Although the relevant strategies to break through the difficulties are summarized, they are not uniform in application. According to specific topics and students, appropriate breakthrough strategies should be adopted. Make breakthroughs in key and difficult knowledge according to local conditions.
2 innovative teaching in mathematics classroom
Pay attention to cultivating students' innovative thinking.
For primary school students, the process of using the knowledge, methods and life experience they have learned to acquire new knowledge and methods independently can be understood as the creative process of students. Although the knowledge formed in this process lacks certain social value, the ability formed in it will have an inestimable impact on the student's life and even on his whole career in the future. Therefore, cultivating students' innovative thinking is an important teaching goal of modern primary school mathematics teaching. For example, in the lesson of "Lines and Segments", I asked students to straighten a part of a group of lines from one end and feel what a straight line is from the change of shape. Then, one hand pulls the thread, and the thread ball in the other hand keeps releasing the thread, and both hands slowly move to both sides at the same time until the arms are completely open. And asked: "If the arm is longer, how does this straight line change?" How about a little longer arms? A little longer ... imagine, where is the line now? What about now? ..... can it grow? "In this way, students gradually feel that the straight line can be infinitely extended and permeated with infinite thoughts. The problem is the core of mathematics. Students are brave and good at revealing their own cognitive conflicts and actively exploring the concrete manifestations of unknown psychological needs.
Stimulate students' innovative consciousness.
One of the goals of mathematics curriculum standards is to cultivate students' innovative spirit. Mathematics education should change from taking knowledge acquisition as the primary goal to paying attention to people's development as the primary goal, creating an educational environment conducive to students' lively and positive development and providing students with sufficient development space. Therefore, primary school mathematics, as an important subject of basic education, should not only let students master mathematical knowledge, but also cultivate students' learning ability to acquire knowledge independently and innovative subject consciousness. Democratic and harmonious classroom teaching atmosphere is the premise of cultivating innovative consciousness. The democratic and harmonious classroom teaching atmosphere shortens the distance between teachers and students, and can make students feel that teachers are their amiable and respectable friends. Pupils often like this course because they like a teacher, and then they have a strong interest in learning the knowledge and content of this course, forming a good psychological foundation of "innovation". If the teacher's teaching is not democratic, it will make students feel "afraid", thus killing students' interest in learning and innovative consciousness. Therefore, in mathematics classroom teaching, we must always pay attention to creating a democratic and equal relationship between teachers and students and a good relationship of harmony, friendship, competition and mutual assistance among students, so as to lay a good foundation for stimulating students' innovative consciousness.
Pay attention to cultivating students' problem consciousness.
"Learning is expensive and suspicious, small doubts are small, and big doubts are big." Asking a question is often more important than solving a problem. The process of learning revolves around the word "doubt". Only when there is doubt will there be problems, which will make people think deeply. Asking questions is the beginning of questions and the basis of innovation. Innovation is possible only if students dare to question, will question and will question. The consciousness of innovation comes from questioning. Only those who are good at finding and asking questions love innovation and can innovate. "Doubtful learning" is a sign of learning progress and a prerequisite for innovation. For example, when teaching "Year, Month and Day", after writing on the blackboard, let the students ask, "How many months are there in a year?" "What is a normal year and a leap year?" "A child of 12 years old has only had three birthdays. What is this? " Then let the students read books and encourage them to talk about the problems found in self-study. The student asked again, "Why are there 12 months in a year?" "Why are there 365 days in a normal year and 366 days in a leap year?" "Why is there a big month and a small month? Why is December also called the twelfth lunar month? " ..... Teachers firmly grasp several key issues, let students discuss and dispel doubts, and students' desire to solve problems is mobilized.
3 mathematics interest teaching
Set up interesting exercises to consolidate interest.
Practice is the basic way to consolidate what you have learned. The clever and reasonable design of exercise questions is more conducive to students to master new knowledge, deepen their impressions, expand their thinking, and turn monotonous and abstract math exercises into interesting exercises that students love to do. For example, when I finished teaching the Comparison of Fractions of Different Denominators, I made up such a question for my students. One day, the weather was sultry, and Tang Priest and his disciples were on the way to learn from the scriptures, thirsty. Wukong finally found a big watermelon, and Bajie made his mouth water. Tang Priest said that in order to be fair, everyone should eat a quarter. Bajie was very unhappy. He stood up with a big belly and said, "No, no! You should eat more when you are pregnant. I have to eat a sixth, at least a fifth. "
Wukong laughed and quickly cut one-sixth of the melon for Bajie, and gave the rest to the master and the apprentice. Everyone is happy to eat melons. Pig looked at his three disciples while eating melons and thought, "They ate one-sixth of the melons and were very happy. Do they eat less? There must be a problem. " Please think about it. Did Bajie eat too much or too little? After listening to this story, the students became interested. First there is a heated discussion, and then there is a rush to answer. The atmosphere is extremely active. Interesting exercises make students have fun in learning, learn in fun, get fun from it, and have endless fun, which not only increases their knowledge, but also cultivates their interest.
Clever introduction to attract interest
As the saying goes, "A good beginning is half the battle." As long as a class starts well and arouses students' interest, it is at least half the battle. Pupils love to listen to interesting things in daily life. As long as teachers try to skillfully introduce these interesting things into the classroom, they will certainly arouse students' interest and their attention will soon be concentrated. For example, that's what I did when I was teaching interest. Teacher: Students, your parents have been busy all day for you, and have worked hard to earn a lot of money, but they don't need it for the time being. What do you suggest? Are they all at home or elsewhere?
The students scrambled to speak after listening, and the most common thing they said was to deposit money in the bank. I then asked: Why did you put the money in the bank? Do you know the benefits of doing so? The student replied: this is both insurance and interest, and money is long. I guided the topic according to the situation and wrote "interest" on the blackboard. At this time, the students suddenly understand that what they have learned today is very useful for their future life and work. So that their strong desire to learn was aroused at once, full of energy and confidence, and their interest in learning was mobilized.
4 Mathematics self-study ability training
The connection between old and new knowledge;
(2) The main concepts, theorems and formulas of this lesson; (3) Formula derivation or theorem proving; (4) Ask students to summarize the types, methods, rules and error-prone places in the operation. For example, the reading outline of the section "Determination of isosceles triangle": (1) What are the topics and conclusions of the determination theorem of isosceles triangle? What does it have to do with the property theorem of isosceles triangle? (2) Is there any other way to prove the isosceles triangle judgment theorem? (3) What are the methods to judge the isosceles triangle? (4) When proving that two line segments are equal, how do you generally consider the proof method?
After the teacher shows the reading outline, let the students read according to the outline. On the basis of reading the textbook repeatedly, think about the exam and answer questions and write them down, waiting for the next step. At the same time, write down the difficult questions and wait for the next step.
This step is decisive for a good self-taught course. Let students taste the sweetness of self-study through their own efforts. Doing so can not only cultivate students' self-study ability and develop their intelligence, but also enable students to learn actively. Using this method, students can gain more knowledge than teachers.
Stimulate students' interest in self-study according to their actual situation.
Influenced by the traditional teaching methods, students are accustomed to the learning methods of teachers' speaking, students' listening, teachers' writing and students' taking notes. Therefore, teachers should first change their ideas, explain the characteristics and benefits of new teaching methods to students, and build their confidence that new teaching methods and learning methods will enable them to acquire better knowledge and ability. At the same time, stimulating students' interest in learning, mobilizing their enthusiasm for learning and giving full play to their main role are the fundamental guarantee for the success of classroom teaching. Interest is the best teacher, with interest, there will be motivation to learn; Once students are interested in what they have learned, they naturally internalize from the objective "I want to learn" to the subjective "I want to learn". Make them give up the idea of waiting for an injection, adapt to new learning methods, and be willing to acquire knowledge through their own efforts.
Mathematics is everywhere in life. In the process of teaching, we should try our best to link mathematics knowledge with real life, let students observe and think, discuss some topics they like with students, and let students worship and like you. In class, the teaching methods should be flexible, the language should be humorous and the speed should be slow. We should fully understand students' problems, lower the focus of knowledge, face most students, take care of their individual differences in cognitive level, string knowledge together with one question, constantly ask questions for students to think about, let them solve some problems within their power, let students experience the joy of success, and thus arouse their enthusiasm for learning.
How to break through the difficulties in high school mathematics teaching;
1. Summary of teaching experience of senior high school math teachers
2. Improve high school mathematics teaching methods.
3. Effective teaching methods of high school mathematics
4. How to improve the math foundation of senior two?
5. How to effectively improve the classroom teaching of senior high school mathematics?
6. Summary of personal teaching experience of senior high school mathematics teachers
7. How to improve the quality of high school mathematics teaching?
8. What are the teaching methods of high school mathematics?
9. How to do a good job in mathematics teaching in senior two?