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On Classroom Teaching of Mathematics in Senior High School

Senior high school students are more mature physically and psychologically than junior high school students. Therefore, self-control is strong and learning is relatively active. How to improve students' learning efficiency for 45 minutes in class as much as possible is a problem worthy of consideration for me who just came into contact with senior high school teaching. To teach high school mathematics well, we must first have an overall understanding and grasp of high school mathematics knowledge; Secondly, we should understand the cognitive structure of students; Thirdly, the relationship between teachers' teaching and students' learning should be handled well in classroom teaching. Classroom teaching is the main position for students to learn cultural and scientific knowledge during school, and it is also the main channel for ideological and moral education for students. Classroom teaching should not only strengthen double basics but also improve intelligence; We should not only develop students' intelligence, but also develop their creativity. Not only students but also parents should learn, especially self-study; Not only should we improve students' intelligence factors, but also B? Hey? Why did you steal Ruilong 6? This burden? What happened to yttrium? Desalinate overseas Chinese? 5 minutes classroom teaching and education efficiency, try to complete the teaching task well in a limited time. Let's talk about some of my own views:

1 has clear teaching objectives.

Teaching objectives are divided into three areas, namely, cognitive area, emotional area and motor skill area. Therefore, when preparing lessons, we should choose teaching strategies, methods and media around these goals and reorganize the necessary content. In mathematics teaching, through the joint efforts of teachers and students, students can achieve the predetermined goals in knowledge, ability, skills, psychology, ideology and morality, so as to improve their comprehensive quality. For example, the lesson "Introduction to Complex Numbers" is the first lesson of the whole complex number chapter. When preparing lessons, we should pay attention to the fact that through the teaching of this course, students can explain the formation and development of complex numbers from the perspective of dialectical materialism, and realize that contradictions are the driving force for the development of things, and the resolution of contradictions promotes the development of things. In real life, when we encounter contradictions, we should face them bravely, have the determination and confidence to solve them, promote the transformation and solution of contradictions, and improve our ability to analyze and solve problems.

2 can highlight key points and resolve difficulties.

Every class should have a key point, and the whole teaching is gradually carried out around this key point. In order to make students clear about the key points and difficulties of this class, teachers can simply write these contents on the corner of the blackboard at the beginning of the class to attract students' attention. The key content of the lecture is the climax of the whole class. Teachers should stimulate students' brains by changing sounds, gestures, writing on the blackboard, application models, projectors and other visual AIDS, so that students can get excited, have a strong impression on what they have learned, stimulate students' interest in learning and improve their ability to accept new knowledge. For example, in the first lesson of Chapter 8 Ellipse, the focus of teaching is to master the definition and standard equation of ellipse, and the difficulty is the simplification of elliptic equation. Teachers can talk about the direct view of the circle, the slice of radish, the shadow of the disc on the ground in the sun, the earth and artificial earth satellites, so that students can have an intuitive understanding of the ellipse. In order to emphasize the definition of ellipse, the teacher prepared a thin line and two nails in advance. Before giving a strict definition of ellipse in mathematics, the teacher first takes two fixed points on the blackboard (the distance between the two fixed points is less than the length of thin lines), and then asks two students to draw an ellipse on the blackboard 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. By observing the process of drawing twice, students sum up their experiences and lessons, and the teacher guides them according to the situation, so that students can draw a strict definition of ellipse. In this way, students will have a deep understanding of this definition. When further solving the standard equation, students are prone to encounter such a problem: 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 squared after sorting out, and finally got a satisfactory result. In this way, the difficulty of simplifying the elliptic equation is solved. At the same time, it also solves the simplification problem when solving hyperbolic standard equation in the future.

3. Be good at applying modern teaching methods.

With the rapid development of science and technology, it is particularly important and urgent for teachers to master modern multimedia teaching methods. The characteristics of modern teaching methods are: firstly, it can effectively increase the class capacity of each class, thus solving the original 45-minute content 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, it is intuitive, easy to stimulate students' interest in learning, and conducive to improving students' initiative in learning; Fourth, it is helpful to review and summarize what the whole class has learned. 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, there are a lot of contents, such as some geometric figures in solid geometry, some simple but large number of small questions and answers, application questions with a large number of words, summary of chapters in review class, training of multiple-choice questions, etc. Can be done with the help of a projector. If possible, we can make our own computer courseware for teaching, and use computers to show what we teach vividly. For example, the drawing of sine curve and cosine curve and the derivation of pyramid volume formula can all be demonstrated by computer.

4. According to the specific content, choose the appropriate teaching methods.

Each class has its own teaching tasks and objectives. As the saying goes, "there is a method for teaching, but there is no fixed method". Teachers should be able to 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, we often show students geometric models or verify geometric conclusions by demonstration. For example, before teaching solid geometry, students are required to make a geometric model of a cube with lead wire, and observe the relative positional relationship between the sides, the angle formed by each side of the cube and the diagonal line 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, exercises, etc. in combination with the classroom content. Sometimes, in a class, multiple teaching methods should be used at the same time. "There is no fixed method in teaching, what is important is proper method". As long as it can stimulate students' interest in learning and improve their enthusiasm for learning, it will help to cultivate students' thinking ability and help them master and use what they have learned. This is a good teaching method.

5. Summarize students' performance in class in time and give appropriate encouragement. In the teaching process, teachers should keep abreast of students' mastery of the content. For example, finish a concept and ask students to repeat it; After an example, erase the solution and let the middle-level students perform on stage. Sometimes, for students with poor foundation, we can ask them more questions and give them more exercise opportunities. At the same time, teachers should encourage them in time according to their performance, cultivate their self-confidence and let them love and learn mathematics.

Give full play to students' main role and teachers' leading role, and mobilize students' learning enthusiasm.

Students are the main body of learning, and teachers should start teaching around students. In the teaching process, we should always give full play to the leading role of students, so that students can change passive learning into active learning, so that students can become the masters of learning and teachers can become the leaders of learning.

7. Deal with the accidental events in the classroom and adjust the classroom teaching in time.

Although teachers are fully prepared for each class, sometimes they may encounter some unexpected things. For example, when I taught the concept of complex numbers in the second class, I came to the conclusion that "when two complex numbers are not both real numbers, the sizes are incomparable", but I didn't prove it. There is no requirement for proof in the teaching plan. When I was brought to this question in class, a student with good grades asked me to write an answer. I introduced the comparison principle of numbers to students, and used this principle to explain why "I > 0" could not be established. Then, once, I told that classmate that I would interview you after class about the detailed proof process. Although this increases the content of class hours, it also protects students' learning initiative and enthusiasm and satisfies students' thirst for knowledge.

We should elaborate on examples, do more classroom exercises and leave more time for students to practice.

Teachers should carefully select examples according to the requirements of classroom teaching content, and make a 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 teachers to fill students' rooms. Teachers should set aside ten minutes for students to do exercises, 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.

Pay attention to basic knowledge, skills and methods.

As we all know, in recent years, the novelty and flexibility of mathematics test questions are getting stronger and stronger. Many teachers and students focus on the more difficult comprehensive problems, thinking that only by solving difficult problems can they cultivate their abilities, thus relatively ignoring the teaching of basic knowledge, basic skills and basic methods. Come up with formulas and theorems in a hurry in teaching, or train students through a large number of topics by telling an example in a hurry. In fact, the process of deducing theorems and formulas contains important problem-solving methods and laws. Teachers did not fully expose the thinking process and explore its inherent laws, so they asked students to do problems and tried to "realize" some truths by asking students to do a lot of problems. As a result, most students can't "understand" methods and laws, and their understanding is superficial, their memory is weak, they can only imitate mechanically, their thinking level is low, and sometimes they even copy mechanically; Draw a gourd ladle and complicate simple problems. If the teacher is too careless in teaching or the students don't know much about the basic knowledge in learning, they will make mistakes in the examination. Many students said that there are too many test questions now, and they often can't solve all the test papers. The speed of solving problems mainly depends on the proficiency and ability of basic skills and methods. It can be seen that while paying attention to the implementation of basic knowledge, we should also pay attention to the cultivation of basic skills and methods. 10 permeates teaching thinking and methods, and cultivates comprehensive application ability.

Commonly used mathematical thinking methods include transformation, analogy induction and analogy association, classified discussion, combination of numbers and shapes, method of substitution, undetermined coefficient method, reduction to absurdity and so on. These basic ideas and methods are scattered in the chapters of middle school mathematics textbooks. In normal teaching, teachers should consciously and properly explain and infiltrate basic mathematical ideas and methods while imparting basic knowledge, so as to help students master scientific methods, so as to achieve the purpose of imparting knowledge and cultivating ability. It's the only way. Students can use what they have learned flexibly and comprehensively.

In a word, in mathematics classroom teaching, if we want to improve students' learning efficiency and teaching quality in 45 minutes, we must think more and prepare more, fully prepare teaching materials, students and teaching methods, improve our teaching wit and give play to our leading role.

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On the Function and Application Strategies of Thinking Set in Mathematics Teaching

Abstract: There are two aspects of mindset, namely, suitable mindset and wrong mindset. For learners, it is of great significance to correctly master and use the mindset to solve mathematical problems. Through analysis, this paper studies its advantages and disadvantages, analyzes its correct and effective application value in mathematics teaching, and puts forward practical and effective mathematics teaching and learning strategies from the aspects of flexible learning, weakening the cognition of rigid laws and paying attention to the establishment of creative thinking.

[Keywords:] mathematical teaching mindset

In psychology, mindset refers to a state of psychological preparation formed by certain psychological activities when people know things, which affects or determines the trend or formation of similar follow-up thinking activities. Simply put, this state is a phenomenon that people show because they are limited to the existing information or understanding. When people work and live in a certain environment, they will form a fixed mode of thinking over time, which will make people accustomed to observing and thinking things from a fixed angle and accepting things in a fixed way.

Thinking mode may help to solve new problems, but sometimes it will hinder new problems. In mathematics learning, high school students often unconsciously apply their familiar ways of thinking to the new situation of mathematics problems, and are not good at changing the perspective of understanding problems, which leads to the inability to solve mathematics problems correctly. Therefore, the study of mindset is of great significance to mathematics teaching.

First, the role of mindset in mathematics teaching

(A) the formation and analysis of mindset

There are usually two forms of mindset: mindset and mindset. The former means that people form a certain set in the process of thinking. Under the same conditions, people can quickly perceive things in the real environment and make correct responses, which can promote people to better adapt to the environment. The latter refers to people's wrong perception and explanation of things in the real environment due to unconsciousness or mental activity obstacles.

The mindset emphasizes the similarity and invariance between things. In solving problems, it is a kind of thinking strategy of "changing with constancy". Therefore, when the new problem is the leading role of its similarity with the old problem, the mindset formed by solving the old problem often helps to solve the new problem. When the difference between new problems and old problems plays a leading role, the mindset formed by the solution of old problems often hinders the solution of new problems.

In the teaching process, teachers should purposefully, systematically and step by step help students to form a mindset suitable for the mindset and prevent students from forming illusions. This plays an important role in learning and flexible use.

(B) the advantages and disadvantages of fixed thinking in teaching

Thinking set can make us quite skilled in some activities, even realize automation, which can save a lot of time and energy; However, the existence of mindset will also bind our thinking, so that we only use conventional methods to solve problems without seeking other "shortcuts", which will also bring some negative effects to solving problems. Stereotype effect will be produced not only when thinking and solving problems, but also in the process of understanding and interacting with others.

1, suitable for positive-minded characters.

Thinking set is an objective phenomenon. Psychological research shows that people use certain cognitive ways to think in the process of learning. The more times they repeat, the better the effect. Then, in new similar situations, this method will be given priority. This is an unconscious behavior. It is the "inertia" phenomenon of thinking and the expression of a special instinct and internal drive of human beings.

Thinking set is of great significance to the solution of problems. In problem-solving activities, the role of mindset is: according to the problems faced, associate similar problems that have been solved, compare the characteristics of new problems with old problems, grasp the similarities between the old and new problems, connect the existing knowledge and experience with the current problem situation, use the knowledge and experience of dealing with similar old problems to deal with new problems, or turn new problems into solved familiar problems, and make positive psychological preparations for solving new problems.

Thus, fixed thinking is the main form of problem-solving thinking. Many times, the fixed thinking is manifested in the tendency and concentration of thinking. Insufficient or bad set will hinder the progress of solving problems. From another point of view, the process of students' understanding and solving problems always happens on the basis of existing stereotypes. We should make use of the existing experience and solve problems according to a certain model (orientation, definition and sequencing) to complete the "double-base" task in teaching.

2. The negative effects of mindset.

The mistakes of fixed thinking often make us psychologically defensive and form a dull, mechanical and rigid problem-solving habit. When the old and new problems are similar in appearance but different in nature, fixed thinking often leads the problem solver into a misunderstanding.

When the conditions of the problem change qualitatively, the mindset will make the problem solver stick to the rules, and it is difficult to pour out new ideas and make new decisions, resulting in negative transfer of knowledge and experience. Teaching practice shows that many mistakes made by students in solving problems are caused by bad thinking patterns.

Second, the application strategy

(1) mindset plays an important role in improving mathematics learning skills. In study, work and teaching, we should consciously overcome the mindset and make our thinking more open, deeper, more flexible and agile. The experiment of American psychologist Mike well illustrates the application value of mindset in life.

(2) In psychology, the transfer theory of learning should also be effectively applied to mathematics teaching. This theory tells us that existing knowledge and experience will always have various influences on the solution of new problems, that is, old knowledge will act on new knowledge. There is always a connection between old and new problems. In a sense, the success or failure of problem solving and its efficiency depend on the quantity and quality of knowledge and experience that can be transferred in problem solving to a considerable extent. A good attitude can effectively promote the positive transfer of knowledge and experience, which enables problem solvers to extend the results of solving several problems to many similar problems.

(C) the correct use of mentality

1, pay attention to the mindset tendency and guide it reasonably. Thinkers have a tendency to reduce various problem situations to familiar problem situations, which is manifested in the contraction of thinking space. There are traces of concentrated thinking. If we study solid geometry, we should emphasize the basic idea of solving problems: that is, transforming space problems into plane problems and finding inner special relationships.

2. Strengthen the regularity of learning. Students are required to master conventional problem-solving methods and attach importance to the training of basic knowledge and skills. For example, when learning the knowledge points of functions, we should first firmly grasp the basic knowledge of functions, and remember and use them on the basis of understanding.

3. Strengthen the procedural nature of thinking set in learning, that is, the steps of solving problems should meet the requirements of standardization. For example, how to draw, describe and discuss solid geometry problems, planes and line segments, and how to describe and prove the actual process must be clear, step by step and reasonable in format, otherwise it will be chaotic.

(D) Some issues that need attention

1. Strengthen the function and application guidance suitable for mindset. The purpose of mathematics teaching is to establish a philosophical thinking pattern that meets the requirements of mathematical thinking itself. This stereotype is not only an important part of mathematical concept system, but also a concrete embodiment of mathematical thinking ability. The role of mindset is not the mindset itself, but how it is formed. For example, in concept teaching, if we talk about concepts and give them to students hastily, then we can only form a rigid concept set; If students' learning enthusiasm is fully mobilized, starting from actual cases and students' existing knowledge, through analysis and comparison, starting from students' internal needs, the self-application value of knowledge, rather than its fractional significance, is emphasized. In the step-by-step teaching, a positive learning state and learning atmosphere are presented.

2. Strengthen the flexible use of learning in mathematics teaching, pay attention to solving practical problems, and eliminate students' dead state. In mathematics teaching activities, it is necessary to train with appropriate exercises. It is unscientific to highlight the so-called "law of solving problems", which will undoubtedly make students form rigid thinking. In the case that students can't understand, even if they recite it, they can't make knowledge play its greatest role. Although the teaching method of rote learning can achieve good results temporarily in some occasions, it is not conducive to the development of students' thinking ability in the long run, so we should pay attention to this point from both students' and teachers' perspectives.

3. Besides paying attention to the wrong mindset, we should also pay attention to the application of creative thinking in mathematics teaching. The teaching of some teaching contents may be divorced from the syllabus, violate the law of students' cognitive development, and pursue "high difficulty, high skill and wonderful methods", resulting in most students being confused and at a loss, not only unable to form their own creative ability, but also unable to master the knowledge they want to learn. Therefore, the training of creative thinking should be moderate, teachers should pay attention to the stage, coherence and consistency of students' knowledge, properly handle the relationship between them, and strive to do both, and strengthen the correct methods and significance of learning from learners themselves.

References:

1. Zhang Naida. Pedagogy of mathematical thinking. Jiangsu Education Press, 1990.4.

2. Online paper: Analysis of the relationship between thinking set and creative thinking in mathematics teaching.

3. Peng Yuling and Zhang Biyin. Zhejiang Education Press, 2004+02.38+0.