A: Case clips: teaching clips of "similar items"
Teacher: When we visited the zoo, we found the tiger in one cage and the panda in another cage. Why not put the tiger and panda in the same cage?
Health 1: For the safety of pandas.
Health 2: For the convenience of administrators.
……
A stone stirred up a thousand waves, and students expressed their views one after another. )
Teacher: What everyone said is very reasonable. Indeed, in daily life, many things need to be classified. Can you give an example of this classification in life?
Health 3: recyclable garbage and non-recyclable garbage.
Student 4: I keep the study materials of different subjects in different categories.
……
Teacher: the classification habit that everyone has developed in life is great! There is also the problem of mathematical classification. (Large screen display, 10a and 20a, 2b2 and 6b2, -9xy and 5xy, 5a2b and-13a2b. ) They belong to the same category in pairs. What are the characteristics of the two categories?
Health: They contain the same letters and the same index.
Teacher: Good, but we don't classify 5a2b and-13ab2. You see, their letters and indexes are the same. You look again, the classification on the big screen, what are the same characteristics?
Health (immediate supplement): contains the same letters, and the index of the same letters is the same.
Teacher: Good! (big screen display: items with the same letters and the same letter index are called similar items. )
Teacher (pause, let the students recite it before adding it): I also want you to remember that all constant terms are similar.
Teacher: Please use your critical eyes (on the big screen) to judge whether each of the following formulas is similar? Why?
The principle of basic skills teaching is: (1) the principle of subjectivity. (2) the principle of appropriateness. (3) the principle of effectiveness. In this case, the teacher first designed a scene introduction to stimulate students' desire to explore from the classification of animals in the zoo, and paid attention to connecting with real life, so that students could accurately find the characteristics of similar items. It fully embodies the three basic principles of teaching.
2. Explain the main strategies of listening and dialogue teaching with math class? (Chapter 1 Section 2)
A: For example, the teaching clip of "Application of Binary Linear Equations"
Question: How many chickens and rabbits are there in a cage? They have 50 heads and 140 legs. How many chickens and rabbits are there in the cage?
Teacher: I ask my classmates to talk about the ideas and methods of solving problems.
Health 1: Let the number of chickens be X and the number of rabbits be Y. ..
The following equation can be drawn from the meaning of the question:
The main strategies of listening and dialogue teaching are: (1) the time, content and methods of listening. (2) Equal dialogue creates an effective learning environment. (3) The dialogue of life opens the door to spiritual interaction. (4) Seamless dialogue is the highest level of teaching.
3. Give an example to illustrate the basic principle of ppT mathematics courseware making? (Chapter II, Section III)
Answer: For example, when a teacher teaches algebra, he first presents several practical problems with PPT courseware, lists the slides of algebra according to the quantitative relationship in the practical problems, then shows the slides of algebra definition, and then shows the slides of examples and exercises. The teacher's courseware production follows the following principles:
(1) The principle of serving teaching. (2) The principle of moderate use. (3) the principle of reducibility.
④ Pay attention to the scientific principle of content. (5) the principle of improving artistic taste.
4. Illustrate the principle of feedback and adjustment in mathematics classroom teaching with examples? (Chapter III, Section IV)
For example, there is such an exercise in the exercise class of "Solving Binary Linear Equations".
The teacher asked a student to answer on the blackboard. The student transformed each equation in the equations into the standard form by removing the denominator and brackets, and then got the solution of the equations through calculation: x=3, y=2.
After the teacher affirmed the students' practices and answers, he found that several students next to him had an "argument"
Teacher: XXX, do you have any questions?
Student: Teacher, they say my method of this problem is wrong, but I think my method is better.
Teacher: Oh? Then let's all judge together, shall we?
Health: I think the two equations have the same denominator, so
The teacher was very happy after listening and motioned XX to sit down. She looked at her deskmate again and asked, why do you think her solution is wrong?
Student: Because the teacher's method is not like this, like the students on the blackboard, we should first turn the equations into a standard form and then solve them. She didn't follow the teacher's method.
Teacher: But her conclusion is the same as that of other students!
The student can't answer.
The teacher took the opportunity to praise XXX: XXX's solution is correct and innovative! She can explore a new way to solve the problem according to the characteristics of this topic, which is an innovative act. Students should think more, learn more from students and explore ways to solve problems from more aspects.
The feedback and adjustment principles of classroom teaching are: (1) the principle of timeliness. Teachers should adjust and evaluate students' feedback information in time. (2) the principle of accuracy. (3) the principle of comprehensiveness. Teachers should adopt scientific methods and try their best to feedback the knowledge level of each student in the class. (4) Incentive principle. Stimulate students' curiosity and self-motivation. (5) The principle of equality and respect. Respect students' personality differences and don't dampen them. (6) The principle of teaching balance. Make teachers, students and knowledge in a dynamic balance, and always keep the information flowing.
5. How to arouse students' problem consciousness? Try to explain it in detail with mathematical examples. (Chapter 4, section 1)
A: There are several basic ways to stimulate students' problem consciousness.
(1) Create a democratic atmosphere and encourage students to ask questions. Therefore, teachers should devote more attention to students' feelings, go deep into students to chat with them, and tell anecdotes in various fields of mathematics to help students solve some difficult problems in life; It is also necessary to create a relaxed, free and democratic teaching atmosphere, establish an equal and democratic relationship between teachers and students, encourage students to boldly associate, question and ask questions, and encourage students to innovate and explore their own value points. In this way, students will naturally like teachers, and then like this subject, and the problem consciousness will be aroused.
(2) Create question situations and guide students to ask questions. For example, when studying the power section of rational numbers, the teacher set such a question: There is a piece of paper with a thickness of 0.1mm. If it is folded in half at a time, what is the thickness? What is the thickness after folding twice? What about three times What about 20 times? When you fold in half, students will find many problems, and at the same time, they will find that the paper in their hands can't be folded in half for 20 times. At this time the teacher asked questions again. Guess if the paper is big enough, who is taller than Mount Everest after 20 folds? Students' interest was suddenly raised, and they naturally entered the teaching of "Power of Rational Numbers".
(3) Construct independent inquiry, train students to ask questions and be good at asking questions. Teachers should pay attention to teaching students some questioning skills in time to improve their thinking ability. First, let the students know the questions. Second, we should pay attention to timely guidance and teach students how to find problems. Third, students are required to firmly grasp the basic knowledge and understand the basic principles in textbooks, which is the basis for them to find problems. Fourthly, students are required to integrate theory with practice and try to analyze and explain these practical problems with some knowledge and principles learned in textbooks. Teachers can also guide students to consciously ask "what", "why" and "how to do it" according to the topics and important principles of textbooks, so as to promote the development of thinking and improve students' ability to find and ask questions.
6. Briefly describe the strategies to improve students' non-intelligence factors in combination with mathematics learning? (Chapter 4, Section 6)
A: (1) Cultivate students' good learning will. First, educate students with typical examples. This paper introduces the deeds and stories of famous mathematicians Hua, Chen Jingrun and Gauss. The purpose is to let junior high school students learn from these famous mathematicians, their perseverance in sleepless nights for science, educate students to learn the valuable qualities of scientists, cultivate their perseverance in overcoming difficulties, and make them study hard and tenaciously. Second, choose different teaching contents and set different teaching difficulties to cultivate students' brave and tenacious will. Students will encounter many difficulties in the process of learning mathematics. Teachers should find and give help in time in teaching, protect students' enthusiasm for learning mathematics, and consciously set learning difficulties of different difficulties to cultivate students' will to overcome them step by step. Enumerating equations to solve practical problems is a common headache for students, and many students choose to give up. If the equivalence relation in the question is given in words first, then the corresponding numerical value is substituted, and finally it is tested according to the actual life, most students can keep up with the teacher, feel happy after constantly overcoming difficulties and achieving success, and then overcome greater difficulties and achieve greater success, so that students can cultivate tenacious will quality in mathematics learning.
(2) Stimulate learning motivation. Good learning motivation occupies a core position among non-intellectual factors, and it is a psychological motivation that can directly promote students to engage in various mathematical inquiry activities in mathematics teaching. Through the study of mathematics, not only can the educated better master a powerful tool to understand nature and human society, but also can train people's thinking and cultivate and develop people's scientific thinking mode. Therefore, we must strengthen the purpose education in teaching, let students know the practical social significance of learning mathematics through examples, help students establish the lofty ideal of rejuvenating China, and correct their learning attitude.
(3) Cultivate students' interest in learning mathematics knowledge in many ways. Interest is the best teacher. A strong interest in learning can make the brain in the most active state and enhance people's observation, attention, memory and thinking ability.
First, study the textbook and explore the connotation of the textbook.
Second, innovate teaching methods according to the characteristics of teaching materials.
Third, create problem situations to stimulate students' interest in learning.
(4) Adopting different teaching methods and organizational forms to stimulate students' emotional motivation.
In short, improving students' non-intelligence factors requires teachers to study students' personality characteristics, change teaching methods and means in a targeted manner, start with studying students' learning motivation, pay attention to giving play to non-intelligence factors such as interest and will, and constantly stimulate and maintain students' learning motivation through various channels to achieve the best state of learning motivation. On the premise of maintaining the stability of students' learning motivation, we should effectively mobilize the positive role of their emotions, overcome the negative role, adhere to the people-oriented, give full play to students' autonomy, educate them with emotion, feedback their learning situation in time, and constantly adjust teaching strategies to ensure that students are in a relatively stable state.
7. The meaning of encouragement and punishment (Chapter 5, Section 3)
A: "Appreciate, encourage and love" can make students learn to respect and appreciate, and moderate punishment will make students have a sense of responsibility and mission. Therefore, scientific and appropriate punishment has become a highly targeted educational means and a necessary supplement to humanized educational means. Therefore, it is necessary to grasp the educational means of combining "encouragement" with "punishment", adopt appropriate educational means according to different educational objects, and pay attention to the effect of education, so that these two necessary educational means can play their due roles in education and teaching.
(1) Encourage and punish to guide students' healthy growth. The purpose of education is not only to improve people's morality, knowledge and ability, but also to standardize people's behavior according to the norms of communication between civilized society and people. Children are born with instinct, and all habits need to be cultivated. When a student needs motivation, teachers should seize the opportunity in time and give sincere praise and encouragement; When a student makes a mistake, the teacher should prepare him for punishment and teach him to take responsibility for his mistakes. What they understand in the process of accepting punishment will make them unforgettable all their lives. Scientific rewards and punishments are an important means to be responsible for students and fully embody the educational function of schools.
(2) Appropriate rewards and punishments are conducive to the cultivation of talents. Education focuses on praise and positive guidance, which conforms to the law of human growth. However, praise is not the only complete method. Education pays attention to the doctrine of the mean and should be appropriate. Too much is too late to achieve the expected results. We can see that criticism rather than praise and punishment rather than encouragement have special significance for everyone, especially the growing students. Punishment is punishment and vigilance, that is, to hold students accountable for the mistakes they made in the process of growing up, so that students can bear the consequences of their mistakes and grow up better. "Without rules, there would be no Fiona Fang." With rules, if you break them, you will be punished, and students will pay the price for breaking them. Because students are growing up and have strong plasticity, they must be made to understand that everyone's freedom should be relative. When you violate the freedom of others, you should take restricting your own freedom as a disciplinary condition, and everyone should be responsible for their own actions. Grasping the combination of "encouragement" and "punishment" can effectively play the role of education in awakening people and promoting their healthy growth.
8. Take a middle school mathematics classroom teaching fragment as an example, analyze the principles that should be followed in collecting classroom generative resources. (Chapter VI, Section III)
Answer: For example, the teacher (for example): The picture (omitted) shows the relationship between the distance S from home at any time after someone leaves home and the time T spent. Can you tell a story according to the picture?
Student 1: After school, Xiaoming goes to Liang Xiao's house to ask math questions. After leaving home 10 minutes, he arrived at Liang Xiao's home 500 meters away from his home. Liang Xiao spent 20 minutes explaining these problems to him. After 20 minutes, Xiao Ming went home.
Health 2: Grandpa went out for a walk after supper. I walked for 10 minutes and arrived at the newsstand 500 meters away from home. After reading the newspaper for 20 minutes, he went back and walked home for 20 minutes.
……
While enjoying the wonderful story, students should consider whether the plot conforms to the meaning of the question.
At this time, the teacher found that Xiaojie, the class representative who has always been active and enthusiastic in class, frowned slightly.
Teacher (kindly): It seems that there is something wrong with our class representative. Tell everyone what you're thinking.
Xiaojie: In the story, reading newspapers, studying, resting and eating are all in the middle. These are all motionless situations. Teacher, I wonder if this horizontal line segment can represent movement.
After listening to Xiaojie's words, everyone froze, and the heated discussion turned into quiet thinking. Miss Wang was even more surprised: the distance is constantly changing with the passage of time, of course it is static, isn't it? When preparing lessons, I only consider the static situation, and I don't consider whether I can exercise. But do you have any sports? After a series of questions, she couldn't think of the answer at the moment.
Teacher (sincerely): The teacher didn't expect it at the moment. Why don't we compare and see who thought of it first?
The teacher's modest words shortened the distance between teachers and students, and also stimulated students' curiosity. They thought to themselves, "Today's question stumped the teacher, too. I must compare with the teacher! " "Teacher Wang is still reading materials after class and thinking seriously.
Early the next morning, Xiaojie excitedly found Mr. Wang: "Teacher, I thought of it! Turn around, turn around. 10 minutes later, this person took home as the center and walked on the circular road with a radius of 500 meters for 20 minutes. " This coincides with Mr. Wang's idea after class.
In math class, the teacher praised Xiaojie's spirit of being brave in questioning and diligent in thinking, and shared it with his classmates: After dinner, Xiaojie set off from home 10 minute, walked along a circular road with a radius of 500 meters, and got home in 20 minutes. Because the distance from the point on the circumference to the center of the circle is equal everywhere, you can move or stand still along the circumference, move forward and walk back and forth, or return by the same way or change the way.
Principles to be followed in collecting classroom-generated resources
(1) the principle of subjectivity. Let all students become masters of learning, establish students' dominant position in learning activities, respect students' autonomy, respect students' unique way of thinking and activities, respect and ensure the independence and difference of learning activities, and truly let students become masters of their own learning and activities.
(2) the principle of participation. Generative teaching is based on students' subjective participation, and only through the active participation of learning subjects can we truly achieve the purpose of effective generation. Without participation, there is no dialogue, and without dialogue, there is no construction and generation of knowledge. To truly realize the development of students, students must fully, fully, actively and effectively participate in teaching.
(3) the principle of interactivity. The real classroom teaching process is the dynamic interaction between teachers and students and various factors. The motivation comes from the interaction between teachers and students and between students. Teaching is communication, and communication is the essential feature of the teaching process. The whole class is a dynamic communication process. The interaction of communication activities is reflected in the interaction, mutual transmission and mutual learning between teachers and students, and in the mutual teaching and learning between teachers and students, forming a real "learning body" with each other.
(4) The principle of dynamic generation. In the teaching process, because both sides of the activity are active people, there are many internal and external factors that affect and participate in educational activities, and there are many possibilities hidden in the development of the activity process, which will constantly produce and present new States, which is very dynamic. Only by accurately grasping the dynamic generation of the process and flexibly and tactfully adjusting the original plan and objectives according to the changes and development of activities can teachers make the teaching objectives flexible.
(5) the principle of openness. The teaching process is an open process. The open humanistic environment requires creating a democratic, creative and subjective teaching atmosphere accepted by students, so that students can form a free and fearless attitude of independent exploration and stimulate their enthusiasm for learning; The open space-time environment is not limited to a class and study time at school, but pays attention to the flexible arrangement and combination of classroom environment in space. At the same time, the classroom will be led to society and nature, and more extensive educational resources will be used to give students the widest attention and development.
9. Teaching Principles of Creative Use of Textbooks (Chapter 6, section 1)
A: (1) Abandon the old view of using textbooks. Zheng, the king of fairy tales, said: "It is simply a fairy tale to educate different children with the same textbook." Textbooks are the most important materials for teaching activities. In the new round of curriculum reform, although textbooks are becoming more and more scientific, some teachers often just follow the book, lacking creativity in teaching activities and unable to give full play to the role of textbooks. As a teacher, we must change the old concept of using textbooks, combine the actual situation of students, rely on textbooks to impart knowledge and exercise ability, and change from relying entirely on textbooks to using textbooks creatively, so as to create a good teaching situation for students to actively explore knowledge.
(2) Closely follow the curriculum standards. Teachers should study curriculum standards in depth, and then combine teaching practice to properly integrate teaching materials. Teaching materials are the support of classroom teaching and a highly scientific teaching carrier compiled by educational experts under the guidance of national curriculum standards. Don't deny them easily. Teachers' creative use of teaching materials must take curriculum standards as the starting point and the end result, strengthen in-depth study and correct grasp of teaching materials, be familiar with teaching objectives, clarify important and difficult points, clarify the context of knowledge, strive to be targeted, truly realize the innovation of teaching materials and serve students.
(3) Focus on students. All teaching activities must take students as the main body. Teachers' creative use of teaching materials must proceed from students' reality. Teachers are only the "directors" of the whole teaching work. Because every teacher has each teacher's specialty, different teachers will explore the connotation of teaching materials from different angles and use them creatively. Some teachers are good at using modern teaching methods and the teaching effect is good; Some teachers are good at organizing teaching with art, and the effect is good. For example, when teaching the positional relationship between a straight line and a circle, an ancient poem "The desert is lonely and the smoke is straight, and the long river sets the yen" is used to lead the class, so that students can think in images. Through this artistic conception, the mathematical model is abstracted, and the three positional relationships of straight line and circle are initially formed, which is an expansion of the teaching materials and the effect is very good.
(4) Flexible use of curriculum resources according to specific teaching situations. In the specific teaching situation, teachers should handle textbooks flexibly according to many unexpected problems, guide students to approach the intention of textbooks, and create a good learning situation for students. At the same time, the content of teaching materials should be determined according to the teaching environment. There are a wide range of curriculum resources, such as newspapers, television and daily life. Creative use of teaching materials requires flexible use of curriculum resources, thus broadening students' learning space and realizing an open teaching model.
10, the basic principles of teacher action research (Chapter 7, Section 4)
A: The basic principle of teacher action research is: (1) participatory principle. To be a researcher, teachers should study themselves and their own education and teaching. Teachers should love teaching, feel at ease in teaching, have a strong desire to improve teaching, and constantly achieve new teaching goals.
(2) Question principle. Action research is to solve problems, and there is no such thing as research. Teachers should grasp problems in fleeting phenomena, even find problems where there seems to be no problem, be good at thinking, be diligent in questioning and be brave in exploring.
(3) Systematic principle. Action research is very systematic. The so-called systematicness means that after we find a problem, we should systematically analyze, think about the methods and implementation plans to solve the problem, collect data, analyze the results, and then reflect.
(4) experimental principle. In teaching practice, implement the scheme, try to solve the problem, observe, analyze, reflect and evaluate the implementation effect.
(5) Principles of scientific research. Scientific research generally refers to a series of activities such as investigation, experiment and trial production by using scientific research means and equipment in order to understand the internal essence and motion law of objective things. The basic task of scientific research is to explore and understand the unknown. When conducting action research, teachers should master certain research methods and skills, learn to observe and collect data, and master analytical methods.
(6) the principle of cooperation. There is cooperation between teachers and students, and between teachers and researchers. In action research, teachers should actively reflect and participate in the research; Students should cooperate closely and actively participate; Researchers should go deep into reality and participate in practical work. People involved in the research are required to cooperate with each other and work together to achieve a win-win situation.