Reflections on Mathematics Teaching in Senior High School (I)
This semester, I am a math teacher in Class 1 (1) and Class 2 (2) of Senior High School. The main contents of this semester's teaching are: the concept of set and function, basic elementary function, application of function, straight line and equation, etc. The teaching work of this semester is summarized as follows:
I. Education and teaching
1. Use teaching materials rationally to improve classroom efficiency. The content of teaching materials needs to be properly handled in teaching, and the difficulty should be appropriately supplemented or reduced when preparing lessons. Only by using teaching materials flexibly can we avoid detours in teaching and improve teaching quality. For some problems existing in teaching materials, teachers should carefully understand the curriculum standards and make appropriate supplements to the key contents required by the curriculum standards; Appropriate adjustments should be made to the topics in the teaching materials that do not meet the actual situation of students. In addition, we should grasp the "degree" of teaching materials, and don't want to do it in one step, for example, the teaching of functional nature should spiral up several times and gradually deepen.
2. Cultivate students' self-study ability in the preparation before class. Preview before class is an important part of teaching. Judging from the teaching practice, whether students preview before class, the learning effect and classroom atmosphere are different. In order to do this well, I often ask students to do the following things in preview, urge them to read and use their brains, and gradually cultivate preview ability. (1). What are the basic concepts and precautions in this section? (2) What other theorems, properties and formulas are there in this section? How did they get it? Can you repeat them after reading them? (3) Can you answer the exercises in the textbook according to the examples in the textbook? (4) Write down any questions you have in the "Mathematics Excerpt Book" through preview. Never ask the students what to remember and what not to remember, but let the students evaluate what is useful and what is not (personally). The questions of a few students are representative and flexible. When these requirements were first implemented, there were still some difficulties, and some students were not conscious enough. Through a stage of practice, most students can form good habits.
3. Cultivate students' self-study ability in classroom teaching. Classroom is the main position of teaching activities and the main channel for students to acquire knowledge and ability. As a math teacher, it is very important to change the previous "centralized teaching" and "cramming" teaching methods. Instead, it adopts the methods of organizing and guiding, setting questions and problem situations, controlling and answering questions, forming a lively student-centered learning situation, stimulating students' creative passion, and thus cultivating students' ability to solve problems.
While respecting students' subjectivity, I also consider students' individual differences. It is necessary to teach students in accordance with their aptitude, tap the learning potential of each student, and try to achieve basic diversion and flexible management. In teaching, I adopt the method of classified teaching and hierarchical guidance, so that every student can make steady progress. Mobilize their learning enthusiasm. I am in no hurry to tell the students the answers to the questions, so that they can master knowledge in communication and improve their abilities in discussion. Try to let students find problems, try to let students question problems and try to make students different.
4. Cultivate students' self-study ability in homework and after-class feedback exercises. Homework, feedback exercises and tests are important means to check students' learning effect. Grasping the teaching of this link is also conducive to reviewing and consolidating old lessons, and also exercises students' self-study ability. After learning a lesson, a lesson and a unit, let the students sum up and ask them to finish it independently as much as possible, so as to feedback the teaching effect correctly. Through a series of practical activities, arouse each student's learning enthusiasm and become a participant and organizer of teaching activities.
Second, educational innovation.
Everyone knows that the teaching content of middle school mathematics is the basic knowledge of elementary mathematics with a long history. There can be no intellectual innovation. It is even more impossible to ask students to invent any new elementary mathematics conclusions. Therefore, I personally think that the innovation of mathematics education should focus on students constructing a new cognitive process, and the language of mathematics is "cognitive modeling". And the innovation of this process should be reflected in the following three aspects:
1. Think hard:
The premise of innovation is understanding. As we know, mathematics cannot be separated from concepts, and concepts derive properties, which are often presented in the form of theorems or formulas. Theorems and formulas must be demonstrated by logical reasoning, and the formation of these arguments requires a thinking process. To this end, students should first understand the object of study. Because the acquisition of mathematical knowledge mainly depends on the understanding after intense thinking activities, only a thorough understanding can be integrated into its cognitive structure. This requires abandoning the bad habit of memorizing the mathematical conclusions taught by teachers in class, and then applying these conclusions or mechanically imitating a model to solve problems. To understand, you need to be diligent in thinking. Ask more questions about knowledge and methods. Why? Why did this concept come into being? Why export this property? What is the function of this property, theorem and formula? How to apply? The performance of diligent thinking also lies in the continuous reflection and review of the cognitive process, and the continuous summary of the lessons of setbacks and successful experiences. Avoid conformism and be brave in innovation.
2. Be good at asking questions:
After observing and perceiving the object of study in math class, students should learn to analyze, have their own opinions, don't follow others' advice, be good at digging up unclear questions, explore and ask questions from multiple angles and in all directions. As a middle school student, you don't have to solve any problems by yourself. What we advocate is to be able to ask multi-angle questions to the research object, especially to be good at asking novel and unique questions. I think being able to ask questions is an important symbol of innovation.
Solve the problem:
Learning mathematics is inseparable from solving problems, which are applied on the basis of mastering the knowledge and methods learned. Solving problems can exercise skills and temper will. In the process of solving problems, we must first judge the general direction of solving problems and what the general idea is. In the process of guiding students to solve problems, they should pay attention to association, learn to think with different ideas, different knowledge and different methods, and be good at monitoring their behavior in the whole process of solving problems: Do you want to take a detour? Is it a dead end? Is there a mistake? It needs to be adjusted in time to remove obstacles. After forming a habit for a long time, you can often find a new way to solve the problem. This kind of thinking quality is also an important symbol of innovation. In order for students to reach this level, we must make it clear that we can't solve problems for the sake of solving problems, and we should constantly reflect and review after solving problems, accumulate experience, enhance our awareness of solving problems and improve our ability. From their experience, I realized the core of mathematics-problem; Summarize the solution to the problem-ask what, what, what else, what; Teach students how to learn-be diligent in thinking, be good at asking questions and be good at solving problems.
Reflections on Mathematics Teaching in Senior High School (Ⅱ)
People often think that mathematics teaching is only the explanation and application of formula axioms, but it is not. Mathematics classroom also has its own unique charm. The following is my teaching experience.
First, clarify mathematical thinking and build mathematical thinking
With the improvement of students' comprehensive ability in education and the deepening and popularization of interdisciplinary knowledge, the most important thing in learning mathematics is to learn to learn mathematical ideas and see the world from a mathematical perspective. For a teacher, he should not only be able to "do" but also teach students to "do", which requires teachers not only to have solid professional knowledge and ability, but also to have an overall understanding of mathematics subjects in order to build students' good mathematical thinking.
Second, respect students' ideas and understand individual differences.
In the past, the concept of education always ignored students' cognitive feelings, regarded students as containers carrying knowledge, constantly increased new knowledge, and at the same time consolidated old knowledge, resulting in a backlog of old and new, poor new learning and unsound old learning. At the same time, individual differences among students are also obvious. Crops in the same field are also high and low, and so are students. As a teacher, we should not only be good at sowing and fertilizing, but more importantly, we should understand students, give each student sufficient development space and motivation, and we should not lose sight of one thing and lose sight of another. This is the real people-oriented.
Third, the application of psychological tactics, starting with teaching
Starting from teaching, the most important thing is classroom introduction, because the introduction of new courses is not only the beginning of new teaching activities, but also the summary and generalization of old teaching activities. Good lead-in can often stimulate students' interest in learning, make them interested and have a higher desire for new knowledge, and teaching activities will certainly go smoothly.
J Piaget, a Swiss psychologist, believes that "all effective work must be based on certain interests". A strong interest can arouse students' enthusiasm for learning, inspire their intellectual potential and make them in the most active state. In teaching, due to the differences in teaching content, class types and teaching objectives, there is no fixed law to follow in the lead-in method. Below, I will talk about my superficial understanding of several commonly used classroom lead-in methods based on my own teaching practice.
1. Contradictions arouse interest
Contradictions are problems, and thinking begins with problems. Designing a suspense or interesting story that is difficult for students to answer in teaching can stimulate students' strong thirst for knowledge and play an enlightening role. When teaching the summation formula of arithmetic sequence, a teacher told a short story: Gauss, the "prince of mathematics" in Germany, when he was in primary school, the teacher gave a 1+2+3+…+ 100=? As soon as the teacher finished reading the topic, Gauss wrote the answer 5050 on his blackboard, while the other students were still adding it one by one. So, how can Gauss calculate so fast? When the students were puzzled, the teacher introduced the content of arithmetic progression's summation method.
2. Key and difficult issues
Some contents in the textbook are both boring and difficult to understand. For example, the concepts such as the limit of series and the sum of infinite equal ratio series terms are both abstract and difficult. In order to better explain the content of this lesson, a teacher inserted a story of "Analysis of the Legend of Divided Cattle" into his teaching. Legend has it that there was an old man in ancient India who left a will and gave 19 cows to his three sons. The oldest score is 1/2, the youngest score is 1/4 and the oldest score is 1/5. According to Indian canon, cows are regarded as gods and cannot be slaughtered. Only the whole head can be divided, and the will of the ancestors must be unconditionally obeyed. After the death of the old man, the three brothers racked their brains to divide the cows, but they couldn't figure anything out. Finally, they decided to turn to the government for help. The government was at a loss, so it pushed it off on the grounds that "it is difficult for honest officials to break housework." When Zhicuo, a neighboring village, knew it, he said, "This is easy to handle! I have a cow to lend you. So, there are 20 cows in all. If the boss scores 1/2, you can get 10 heads; The second child scored 1/4 and got 5 heads; Old three points 1/5 can get 4 cows. You wait for three people to divide 19 cows, and give me the rest! " It's wonderful! However, when people admire later, there is always a little doubt. It seems that the boss should only get 9.5 heads. How did he finally get the head of 10? In this way, it not only improves students' enthusiasm for inquiry, but also creates a good opportunity for teachers to introduce new courses, which invisibly brings students into their own teaching situation. In addition, we should pay attention to the continuity of teaching. The quality of a class not only reflects the process of prelude, but also reflects the ending, which is what we call the sublimation stage.
Music has profound meaning and endless lessons. At the end of a class, ask new questions according to the systematicness of knowledge. On the one hand, it can organically link old and new knowledge, and at the same time stimulate students' new desire for knowledge and make full psychological preparation for the next class. This fascinating psychological design is often used in Zhang Hui's novels in China. Whenever the story reaches a climax and the contradictions and conflicts of things intensify to a climax, readers are eagerly looking forward to the ending of the story, but the author ends with "I want to know what will happen next time", forcing readers to continue reading! If classroom teaching is like this, the two effects are the same.
As an invisible art, classroom teaching has its own space. How to grasp students' psychological characteristics and knowledge content is "religion". As long as teachers scientifically apply the laws of education and teaching to practical teaching, let students actively participate in classroom learning and feel the charm of knowledge and humanities, classroom teaching will certainly glow with charming colors.
Fourthly, the superposition of rationality and sensibility can improve students' cognitive style.
Teaching by example is not only the transfer of knowledge and skills, but also a kind of humanistic care and emotional voice. On the basis of experience, the transmitter makes learners feel frustrated by previous failures, and at the same time has a sense of success. This kind of education is more true, unconsciously let students enter the ideal situation, taste the ups and downs of life, then rise in failure and success, and then sublimate in rationality and sensibility.
Whether it is mathematics teaching or other subjects, our teaching can't just stay on the existing basis, understand the new laws of education and apply them to practical teaching in time, so that our teaching can be more effective and the investment in education can truly become the results of students. As educators in the new era, it is reasonable and reasonable to learn new theoretical knowledge for teaching, and of course, it also needs "thinking".
Reflections on Mathematics Teaching in Senior High School Part III
When I was in class, I often only cared about my own thoughts. I think the more topics we talk about, the better. I seldom care about students' thoughts and feelings. Slowly, I found that students can understand in class, but they can't. Horribly, they even lost confidence in learning mathematics. I've always been confused ...
Since 200 1, there is a learning theory that has strongly shocked me, that is, the constructivist learning theory-knowledge is not acquired by teachers, but by learners in a certain situation, that is, social and cultural background, with the help of others (including teachers and learning partners), using the necessary learning resources, through the way of meaning construction. Later, I learned that many new curriculum ideas we are advocating now come from this theoretical background, which also opened my confusion. Therefore, we must change the concept of education, take students as the foundation, take students' development as the starting point of teaching reform, and embark on a new road of high quality, high efficiency and sustainable development.
Based on the analysis and understanding of the above problems, through practice, I got the following teaching insights:
1 Pay attention to students' "preview" and downplay class notes.
For some easy-to-understand classes, students should preview in advance and give them a chance to learn independently; For some courses with strong concepts and high thinking ability, students are not required to preview. Why? For most students, their preview is to read the textbook once, and it seems that they have mastered the knowledge of this lesson. However, they lost their enthusiasm for studying problems in class; They lost the mathematical thinking method used when thinking about problems; What's more regrettable is that because I didn't fully participate in the process of solving problems, I lost my temper of facing difficulties and facing them directly!
As for downplaying class notes, it stems from a phenomenon-I found that students who take notes and remember well may not get good grades. Why is this happening? Because students who only know how to take notes, when the teacher asks them to think about the next question, they are often still taking notes on a question. ..... How can we talk about the development of thinking with such learning?
2 What should teaching be under the new concept?
The new curriculum standard points out that students' mathematics learning activities should not be limited to acceptance, memory, imitation and practice. High school mathematics curriculum should also advocate independent exploration, hands-on practice, cooperation and exchange, and pay attention to the cultivation of students' emotions, attitudes and values. This requires our teachers to lay down their authority and change the former "teacher-centered" to "student-centered", which fully reflects the subjectivity and initiative of students. The setting of teaching objectives has also changed the consistent wording: "Make students ……", which embodies the three-level objectives: knowledge and skills-process and method-emotion, attitude and values. Teachers should always have students in mind, design problems from the students' point of view, choose examples, become students' collaborators, promoters and guides, create a good classroom atmosphere and humanistic spirit, cultivate students' positive emotions and attitudes in learning mathematics, and form correct and healthy values and world outlook. Therefore, in teaching, I often insist on such a practice: teachers talk as little as possible in class, mainly to make a lot of time and space for students, so that students can learn more actively, actively and personally. It is precisely because of the deep participation of students that we can achieve the efficiency that teachers can't achieve in the past. Why? This can also be discussed from what is the essence of teaching.
What is the essence of teaching? What are the roles of teachers and students in the teaching process? Our teacher will now say that teaching is a special cognitive activity. In classroom teaching, teachers are the dominant, students are the main body, and so on. But the question is, does our teacher really understand the word "guide"? Have our students really become the main body of learning?
3 reflective teaching is imperative
Whether the above satisfactory results can be achieved in teaching depends on the change of teachers' concepts and teaching methods. From my personal experience, this is a rather painful thing and will not happen overnight. Teachers need to have a great sense of responsibility, patience and courage, constantly strengthen theoretical study and training with their accustomed teaching methods and teaching behaviors, and more importantly, strengthen reflective teaching, that is, the process in which teachers take their own teaching activities as the object of thinking and examine and analyze their own behaviors and the resulting results. It is the core factor of teachers' professional development and self-growth; The process of theorizing teaching experience; A powerful way to promote the transformation of teaching concepts (especially the implicit theory of self-existence).
Students should also reflect.
If teachers' reflection is for better teaching, then students' reflection is for better learning, and it is also the top priority of our whole teaching process. So, how do high school students reflect? I always take this question with me in teaching, thinking about the teaching design of each class and how to cultivate students' learning methods and habits. How to reflect? In order to achieve the ideal learning effect. Drawing the essence from predecessors and experts, especially the reflection on teaching and teachers, gave me a lot of scattered ideas, constantly thinking, constantly experimenting, constantly denying and correcting, and gradually formed a set of practices for high school students to reflect on.
4. What does1embody?
What should students reflect on in the process of mathematics learning? I think it can be roughly divided into: first, students are required to reflect on their own thinking process, including gains and losses and efficiency; Secondly, students are required to reflect on the knowledge and formation process involved in the activities, as well as the mathematical thinking methods involved; Thirdly, students are required to reflect on the related problems in activities, the process of understanding the meaning of problems, the process of thinking, reasoning and operation to solve problems, and the expression of language; Finally, students are required to reflect on the results of mathematical activities. Especially after finishing the problem, we should reflect on it in time, that is, take our own problem-solving process as the object of our own research and thinking, and draw conclusions from it.
4.2 How to reflect?
Some students are busy doing math homework as soon as they finish class, and they don't really understand the class content as a whole. When they do problems, they just imitate and copy. They are either full of loopholes, or they have blocked ideas and poor methods to solve problems. It is easy to dampen students' confidence in solving problems and learning efficiency. Therefore, students should reflect before solving problems. You can also reflect on your learning attitude, mood and will, such as your physical and mental state. Can you persist if you fail? Can you calm down when you encounter difficulties and complicated problems? Have the ability and confidence to solve it? Have you seen it before or have similar problems? What knowledge and skills need to be reviewed and consulted; Secondly, we should constantly supervise ourselves. The most important thing is to reflect after solving the problem. It mainly includes the examination of the results of solving problems, the review of the process, ideas and methods of solving problems, and the reflection on the thinking methods and related issues involved.
4.3 the habit of reflection
To improve students' reflective effect, in addition to the above points, we must also pay attention to scientific methods and improve students' reflective ability. It is a good form to ask students to keep reflective diaries;
First of all, students are required to write a reflective study diary after each class, so that students can go beyond the cognitive level, re-recognize this section of mathematics knowledge, urge students to form reflective habits, check their self-cognitive structure, and remedy weak links. Because of the time problem, we can't write down or understand all the essence of the class in time, so we can make up for it by taking notes and doing the aftermath. Do a good job in analyzing and correcting mistakes, improve cognitive structure and improve students' mathematical reflection ability.
Secondly, keeping a reflective diary is one thing, and how to achieve better results is another. Teachers should do a good job in students' ideological work, realize the importance of writing reflective diaries, and pay attention to browsing at any time, preferably spending 5- 10 minutes browsing every day. After a period, teachers should do a good job of supervision, as an assignment, understand students' learning situation, give individual guidance, and at the same time play a supervisory role in students' reflection work until they form conscious habits.
In short, as front-line teachers, only by actively participating in the new curriculum reform and constantly exploring and trying the connotation of new ideas can we better challenge the implementation of new textbooks.
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