Narrative case of mathematics education 1 It is said that I have been engaged in mathematics teaching in senior high school for more than several years. Talking about my own teaching experience and teaching methods, I feel a lot. Now I pay more attention to comprehensively considering students' cognitive factors and emotional factors in every link of teaching, so that I can successfully complete my teaching goals. The implementation of this measure has improved the teaching effect in an all-round way, my classroom is full of vitality and vitality, and students' interest in learning is getting stronger and stronger.
I remember once in class, I was talking about the problem of series, asking students to master the general formula of series through observation. In class, I set out several questions for students to practice and asked them to sum up the general formula of series through the laws of the first few items. When I checked, I found that these questions were generally not well done, and even the good students in the class were puzzled. I was very confused at that time. After class, I made careful thinking and investigation, and found that students were at a loss when they encountered such incomprehensible topics. It really felt like a blind man touching an elephant. Even the top students feel a little lost. But students are very interested and can think seriously. They all think it seems simple to solve this problem, but why is it so difficult? I am really happy to see students learning their own emotions and positions. I remind students that math problems can be divided into two categories, one is to apply math laws, and the other is to discover math laws. The problem of applying mathematical laws refers to the problem that students need to explain and answer by applying the mathematical laws they have learned before. Inventing the problem of mathematical laws has nothing to do with the mathematical laws that students have learned before. Students need to find patterns from known things in order to explain the answered questions. Most of the math exercises done by students belong to the first class. Finding the topic of mathematical laws is related to one or several variables. The so-called finding the law, in most cases, refers to the changing law of variables. Therefore, grasping variables means grasping the key to solving problems that you don't understand. Through my tips, their curiosity and thirst for knowledge have been aroused. I asked my classmates to collect our related exercises and extracurricular questions, because some students wanted to "embarrass the teacher" and show themselves accurately. So I deliberately inquired a lot of information and found many problems they thought. I also adjusted my teaching plan, and planned to solve this incomprehensible topic in one class, so I made substantive preparations for it.
Another class has begun, and the children are looking forward to it. They all dug their brains, argued with each other, and finally explained their answers, with happy smiles on their faces. Some students asked me questions directly, and I thought hard. Some students are very worried about me. In fact, I want to guide students to learn to think, learn how to solve problems and learn to think on the basis through this process. When I explained and answered the questions that my classmates didn't understand one by one, and affirmed their questions, their happiness seemed beyond words. Next, I pushed the boat and showed the students a series of sequences, so that they could try to find the rules. Although there are some difficulties in solving them from time to time, these problems are finally solved by the students. At this time, I sincerely admire them and give them the most sincere encouragement: you are amazing! Then, I put forward a new problem: I tried to sum up the laws from the solved problems and form my own "axiom". The students were very happy and began to sum up. The whole learning process must be so relaxed and lively. After about ten minutes of induction, the students reached their own conclusions, and then they had a heated discussion. After a fierce struggle, some students who were skeptical about the conclusion also withdrew their doubts.
A new class has started. One group of students asked questions first, and other groups of students were not to be outdone. They dug their brains, argued with each other, and finally explained their answers. There was a happy smile on their faces. Some students asked me questions directly, and I thought hard. Some students are very worried about me. In fact, I want to guide students to learn to think, learn how to solve problems and learn to think on the basis through this process. When I explained and answered the questions that my classmates didn't understand one by one, and affirmed their questions, their happiness seemed beyond words. Next, I pushed the boat, let the students look at the questions of function law and graphic law, and get the characteristics of the regular questions. Soon they came to the conclusion that many of them are quadratic functional relationships and there are higher functional relationships. This conclusion is very accurate and beyond my expectation. At this time, I sincerely admire them and give them the most sincere encouragement: you are amazing! Then, I put forward a new question that I don't understand: So how do we judge that this law is a quadratic function relationship? With this incomprehensible topic, students are eager to explore again. The real answer is found in several questions that don't understand the law of quadratic function: when the difference between the dependent variable divided by the corresponding independent variable is constant, it is a linear function relationship. Then, other situations are generally quadratic functional relationships.
With the students' own conclusions, we launched a big discussion. After a fierce struggle, some students who were skeptical about the conclusion also withdrew their doubts.
The real search for laws is, of course, the search for mathematical laws. Mathematical laws are mostly analytical expressions of functions. Analytic expressions of functions often include mathematical operations. Therefore, to find the law, to a great extent, is to find a mathematical expression that can reflect the known quantity. Therefore, starting from the operation, trying to make some comparisons is also a good way to solve the problem of finding the law. After this teaching experience, I really realized that the needs of students are the first. In the next teaching, we should start from the actual needs of students, stimulate students' desire to explore knowledge and inquiry, and let different students have different growth in mathematics, so as to lay a solid foundation for enriching mathematics classroom teaching.
Mathematical education narrative case 2 case description:
When I was teaching Simple Algorithm of Addition and Subtraction, I created the following situations in both classes: In the class, I chose the best and worst math students recognized by the whole class to have a verbal contest, and the two groups of topics were as follows:
Eugenics: 324+ 198 5968—3999 396+498.
Poor students: 324+200 5968—4000 400+500
The result of the game is of course the winner with poor grades. Suddenly, the whole class became enthusiastic and raised their hands to express their meaning. The competition of "atmosphere" is unfair: among the two groups of questions, it is certainly easier to add and subtract 100 thousand.
The development of the course is as smooth as the design, but the performance of the students in the competition still makes me uneasy: two excellent students cried sadly without expressing any opinions, while two poor students behaved exactly the same: there was a flash of pride in their eyes, but no smile on their faces, and their "honor and disgrace" was fresh in my memory. Isn't that what many great men pursue?
When students do their homework, I immediately teach Eugenics and give him a brief explanation. After class, I want students to apologize (the teacher didn't consider your feelings) and focus on helping to analyze the reasons for crying. I hope he will become strong and calm when he encounters difficulties. As for the poor student, I asked him why he was unhappy to win. I praised his progress and encouraged him to continue his efforts. At that time, I saw his happy smile
Case reflection:
Reflection 1: Teaching should pay more attention to aesthetic feeling and students' emotion.
There is a passage in Interpretation of Mathematics Curriculum Standards: As the general development of students, mathematics learning should pay more attention to students' emotional factors. In fact, healthy and progressive learning activities, independent thinking and cooperative communication, self-confidence and opposing and respectful learning atmosphere are very conducive to the coordinated development of students' non-intelligence factors and intellectual factors, and to the formation of healthy personality. This shows that it is very important to pay attention to students' emotions in teaching.
The purpose of scenario creation in this lesson is to arouse the emotional resonance of the whole class, attract students' attention, stimulate students' interest in learning, actively think about the characteristics of finding topics, and understand that the essence of simple algorithms is "rounding". Educator zankov said, "Once the teaching method touches students' emotional and will fields and their spiritual needs, it will play a highly effective role." But the design achieved the expected effect, but when I saw the crying expression of the gifted students and the honor and disgrace of the poor students, I knew that I had failed them. Obviously, this was not their spiritual need.
Reflection 2: Encourage students more in teaching, and their advantages will be frustrated.
When the poor students showed their sense of honor and disgrace, I thought of a profound story circulating on the Internet: an old teacher went to the market to buy food and met a student he had educated in the past, who was making a fortune in a small business. The student selling eggs warmly invited the teacher to dinner. The teacher said, "Isn't it embarrassing to sell eggs?" The student said, "This is nothing compared with what you taught me in those years."
This story mainly satirizes the teacher's educational behavior towards poor students, which deserves our reflection. Just as students dare not stretch after winning the competition, yes, we really should give them more sunshine, so that they can not only bear setbacks, but also bathe in the bright sunshine and have a healthy personality.
On the other hand, what students benefit most is the concern of teachers. He became strong in the face of numerous setbacks and blows, and this quality will benefit him for life. Therefore, frustration education is an important tree in life, and gifted students who are successful in their studies rarely encounter setbacks, so they will cry in an informal competition. Someone specially studied the biographies of 293 famous foreign writers and artists, and found that 127 of them had suffered serious setbacks in their lives. As the saying goes, "since ancient times, heroes have dreamed, and men are not too handsome." Most people who have achieved something on the surface have suffered. Mencius pointed out: "If God wants to be a great man, he must first suffer from his mind, his bones and muscles, his body, and his body ..." All these show that frustration education is an indispensable nutrition for children's growth, as well as for gifted students.
Looking back on the previous teaching clips, the teacher showed accommodation to his unconscious behavior of ignoring and respecting students, but his psychological activities obviously tended to eugenics. In the family environment and school environment, "gifted students" almost all grow up in "preferential treatment". Have the characteristics of fear of difficulties, poor endurance and so on. In fact, it is impossible for children to encounter setbacks in life. Teachers have the responsibility to immunize them early. Let them take their time in the face of difficulties and setbacks, and don't have nervous and negative emotional reactions. In order to prevent setbacks from being unhurried and unattainable, children must experience setbacks in order to surpass them. Therefore, teachers should pay attention to the design of educational environment in education and teaching, and should not blindly create an educational environment with cold demand and easy satisfaction for students, let alone prevent them from correctly accepting difficulties and setbacks.
Narrative case 3 of mathematics education I remember that when teaching a number multiplied by two or three numbers, I arranged for students to complete a seemingly ordinary problem of correcting mistakes (that is, the following problems).
12 52 476
× 7 × 2 × 8
74 104 3808
Because the students in the class were very lively and outgoing, and the classroom atmosphere was very active at that time, I turned the topic around: "Today, several math patients suspected that they were sick, so they came to our class to see which math doctor was skilled and solved their illness?" As soon as the voice fell, the classroom atmosphere suddenly entered a new climax. Immersed in serious analysis, the students quickly raised their hands one by one and shouted, "Teacher, I know how to treat them. Let me do it! " Some students sitting in the front row even left their seats and put their hands in front of me, as if afraid that I would not let them "treat the disease." So, I called a student named Zhang: "Dr. Zhang, please come up and see the first patient." When Zhang heard me call her that, she was shocked at first. Later, she immediately understood my intention to call her that. She was very happy to go on stage and began to analyze the "illness": "The cause of this patient is that she forgot to bring it here." As he spoke, he pointed to the position between one and ten with red chalk and added "1". Then he changed the "7" in the ten digits of the product to "8" and said, "This is cured." At this time, before I could speak, the following students had already said, "Yes, yes, that's the same as my opinion." Since all the students have expressed their opinions, and this "patient" has indeed cured the disease, I will take the opportunity to boast: "It seems that there are many doctors in our class who are as skilled as Dr. Zhang, thank you." Zhang is very happy to return to his seat. At this time, other students even called her "dr. zhang" one by one, which made Zhang look like a "hero who returned home in triumph". The atmosphere was warm and interesting.
On the second question, because the atmosphere created by the question just now still hangs over the students, the students raise their hands more actively. This time, I called a student with unsatisfactory academic performance: "Now please ask Guo Panda to open a doctor to see the second patient." Guo was obviously surprised that I would invite him up, but immediately cooperated with me and went to the stage happily to see a doctor. He carefully read the topic again and told me with certainty, "This patient is actually not sick." So, I pretended to be surprised and asked the students, "Is Dr. Guo's diagnosis correct?" The founder immediately stood up and said, "His diagnosis is right, and this question is indeed right." Other students also nodded in agreement. I am happy to say, "I think he should be relieved by the diagnosis of Dr. Fang, Dr. Guo and so many doctors." Thank you Dr. Guo. " The third question is the same as the first question, asking a student to "see a doctor and treat a disease".
Finally, at the conclusion, I said to my classmates, "In fact, when we apply new knowledge to solve problems, we will inevitably make mistakes. The key is whether we are qualified math doctors, find out the cause in time, and then prescribe the right medicine to prevent a minor illness from becoming a serious illness and avoid the recurrence of the same disease next time. Of course, whether problems can be found in time is related to our inspection habits. For those questions that have not been done wrong, just be a free physical examination! Students, I hope you can not only do well in other people's mathematics doctors, but also do well in your own doctors, ok? " The students said in unison, "Good!" The voice is very loud, but the firm and confident tone moves me even more.
In fact, I just set the wrong topic in the error correction situation of Mathematical Hospital. I didn't expect the children to show such high enthusiasm and such jumping thinking ability, which made me deeply surprised and moved. Yes, in mathematics learning, many exercises are boring and monotonous, and students often feel submerged in the sea of questions and are very passive. Even if you do it right, you won't feel much joy of success. At this time, teachers are required to pay more attention to the form of practice design. As long as the forms are diverse, interesting and close to students' lives, students will naturally be willing to do exercises, from which they will experience the fun of learning and their interest in learning will be greatly improved.
There are not enough grids. What should I do?
I remember that when I was studying statistics, the students were very interested and the children were very motivated. After the study, investigate the sports that the students in this class like and let the children complete the statistics in the book. Originally, I wanted to consolidate my new knowledge. Unexpectedly, students encountered new problems when completing the statistical chart-too many people like swimming (there are 25 people), and the statistical chart in the book shows that there are only 20 people in two units, so the children began to worry. "What should I do?" . The classroom suddenly became quiet. Suddenly, Fan Feng said proudly, "That's not easy. Add three squares and draw two and a half squares. " At this time, the monitor Lu Haolan raised an objection: "This method doesn't work, there is no place to add it." "Is there a better way?" I said to them. The children began to think ... "I see, since a grid can represent two units, I can also use a grid to represent three units." Zhang Ke stood up and said. A classmate then stood up and said, "I think one grid can also represent four." Fan Feng jumped up quickly: "No,no." "Why not?" I asked him. He said, "How can five people who like running draw it?" Too much trouble. "At this point, Wang Yasong stood up. He said slowly, "I think it's best to use a grid to represent five people, because these numbers are all five and five." For example, if there are five people who like running, that is a five; Those who like skipping rope have 10, which is two fives; There are 25 people who like swimming. This is five fives. It is simple and convenient to represent five with one grid. " The children all nodded in agreement. I affirmed their ideas, and then led them to say, "Please think about it, how to determine how many cells are represented in a grid when making statistical charts?" The children began to discuss, and soon, many children raised their hands.
"I think this is related to statistics. If not many, use the grid to represent one. "
"I want to observe the characteristics of statistics first, and then determine how much a grid represents."
"yes! I think we should also observe the maximum number and minimum number to determine the number of grids. "
"Yes, I think that to determine how many numbers a grid represents, we should first observe the characteristics of numbers and the number of statistics, and also consider how to draw them conveniently."
"That's very kind of you. Would you like to design a statistical chart yourself? Please choose one of the following statistics and design a statistical chart with your friends. " I took the opportunity to arrange the content of the next link.
I am also surprised and moved by the creativity and thinking ability of the children in this class. In mathematics learning, children will encounter all kinds of problems. Teachers should not remove all the "obstacles" in children's learning, but should let children learn to think and find their own solutions to problems. We should also provide more opportunities and create conditions for children in normal teaching. When children encounter difficulties, teachers should consciously talk less, leave time for children in class, let children talk more and think more, and let children solve math problems in life through their own efforts.
Narrative Case of Mathematics Education 4 Since one semester, I have been engaged in teaching with a serious and rigorous academic attitude and a diligent and persistent spirit.
Mathematics is inseparable from life, and life is inseparable from mathematics. For example, you need math to buy breakfast in the morning and math to cook for a day. How far is your home from school? ..... are inseparable from mathematics. I often say to students, "If you learn math and physics well, you are not afraid to travel all over the world." But I also stressed: "If you want to learn math well, you can't learn Chinese well. If you can't understand the conditions and requirements of a math problem, how to analyze and solve it? Therefore, we should also learn Chinese well, and everyone should work hard to learn every subject in the course. " By stimulating students' interest in learning, most students in this class have developed in a more all-round way. While learning knowledge, it is more important to learn to be a man.
The new curriculum advocates that students can initially learn to ask questions and understand problems from the perspective of mathematics, and can comprehensively use the knowledge and skills they have learned to solve problems and develop their application consciousness. In teaching, they can't turn a blind eye, regardless of practical application, which is probably out of date. The purpose of students' learning knowledge is to use knowledge, but the long-term exam-oriented education makes most students wonder why they study mathematics and what is the use of learning mathematics. Therefore, in teaching, I pay attention to students' age characteristics and psychological characteristics. Close contact with students' real life, carefully create situations, let students apply mathematics knowledge in real life, and effectively improve their potential to solve practical problems. Through regular training in this way, students can deeply realize how important mathematics is to our lives and how valuable it is to learn mathematics, thus stimulating their strong desire to learn mathematics well and changing "learning mathematics" into "using mathematics".
Mathematics curriculum standards point out that students are the masters of mathematics learning. Teachers should start from students' cognitive level and existing knowledge and experience, give students full opportunities to engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills and mathematical thinking methods in the process of independent inquiry and cooperative communication, so as to gain rich experience in mathematical activities. With the implementation and promotion of the new curriculum, some teaching methods that overemphasized teacher-centered in the past are being eliminated, which is followed by gratifying changes in mathematics curriculum.
In short, in the future teaching work, we should constantly sum up experience, seriously reflect on teaching, and strive to improve our teaching level; We must make more efforts to strengthen the counseling for individual poor students, and firmly believe that all problems will be solved, and I also firmly believe that efforts will always pay off!
Narrative Case 5 of Mathematics Education I believe that after you become a mathematics teacher, you will encounter many interesting or thought-provoking things. So what are the specific ones? Let's have a look.
I have been engaged in mathematics teaching for nearly 20 years, and I have been engaged in mathematics teaching since I stepped onto the podium. Students like my math class. Of course, many things have happened in teaching. Sometimes I am angry, but I like it and love it. Elementary school mathematics is simple and boring in the eyes of many people. But in my eyes, it has many attractions. Thanks to the school leaders for making me a math teacher, I am a happy teaching partner of math subjects every day. I can proudly say that I am a qualified math teacher and a math teacher deeply loved by students.
As a math teacher, we can use the teaching of math class to guide students to appreciate the overall beauty of math knowledge structure and the concise beauty of math generalization; Leading students to explore the mysteries of mathematics, wandering in the kingdom of mathematics, stimulated students' strong interest in mathematical knowledge.
Of course, there are many times when I feel helpless in my teaching life. For example, some students still don't understand a topic after several lectures. Seeing the busyness of students' faces, they also lack confidence in these students. After class, some students took the initiative to ask me to say it again, saying that they didn't understand. They also have their own basic problems, and some of them can't keep up with me because I speak too fast. At this time, I also reflected on myself and asked too much of them, which made them feel too much pressure to study. I remember once there was a comprehensive application problem, and the thinking method was already talked about in class. However, a student in Zhang Ning made a mistake in her class homework. When she was asked to correct it again, she burst into tears. Finally, she said that I spoke too fast in class and many students couldn't understand me. My homework was copied from other students. After listening to this, I deeply reflected on my teaching methods. Paying too much attention to top students and too little attention to poor students in class has caused this situation today. In the future teaching, I show more love for poor students. They found that the teacher ignored them, and their interest in mathematics gradually increased, and they could finish their homework by themselves. After class, I can also talk to my teacher about my study and ask more and more questions.
When we explore the wonderful world of mathematics kingdom with students in teaching, we will enjoy learning mathematics. At the same time, I also care about students, and I can treat every student equally. I remember when I was teaching in Grade Three, a classmate named Xin Li. His parents quarreled with the teacher at school because of homework problems. As a result, other students thought it was about this student and refused to talk to him. When I took over, I often found that she sometimes sat alone in her seat after class without communicating with other students, or walked around the classroom alone, looking so lonely. After that, I often ask him in class and explain to other students that it is not her reason. At the same time, I asked several classmates to play games with him, and Xin Li gradually integrated into the class group. Later, his parents talked with me for a long time, saying that the child told him at home how the teacher cared about her, and he was very grateful to me. He also said that what he had done before was wrong and had a great influence on children. At that time, it was just what I should do. I didn't expect my parents to be so grateful, which made me further realize the importance of teachers.
I remember on Teacher's Day, a student named Guo Lin called me aside and said to me, "Teacher, today is Teacher's Day. I can't buy you any presents. Can I give you a word? " The teacher wishes you a happy Teacher's Day. I will study hard in the future. "I said excitedly," son, the teacher doesn't want you to buy me any gifts. This is the best gift you can give your teacher. You should study hard in the future. "In fact, I didn't take special care of this classmate, but this classmate is fat. I stopped other students from joking in time and told them to respect others. I didn't expect him to take it to heart. After these two things, I feel deeply. What will happen if I ignore these two students? They also feel that teachers don't care about them, which will cause resistance, affect their grades and even affect their lives. .
Through many things, I feel that teachers have great responsibilities. As long as you undertake it, you will be loved by students and recognized by parents. At the same time, the profession of teacher has brought me endless happiness, so I said, "I am happy because I am a teacher."