First, what is "reflection"?

Locke: "Perception of the inner activities of the mind" is called "reflection".

Dewey: Reflective thinking is a form of thinking, and it is an individual's repeated, serious and continuous meditation on the problems in his mind.

Teaching reflection: it refers to the process that teachers analyze and correct their own behavior and its basis in the process of education and teaching practice, and then continuously improve their own education and teaching efficiency and literacy.

Simply put, teaching reflection is to study how to teach and how to learn. Teach middle school and learn to teach.

Second, why should we reflect on teaching?

(A) from a practical perspective

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(2), from the theoretical level.

1. Teaching reflection is an effective way and core factor for teachers' growth.

Teaching reflection is a ladder to promote teachers' growth. American Posner put forward the formula of teacher growth in 1989: experience+reflection. Generally speaking, old teachers have more practical knowledge than young teachers, but not every old teacher has better practical knowledge than young teachers. Mainly to see if they can reflect in time after class. Therefore, someone once said, "If a teacher is only satisfied with gaining experience and doesn't think deeply, even if he has 20 years of teaching experience, he may only repeat his work 20 times a year. Unless he is good at learning from experience, there will be no improvement and he will always stay at the level of a novice teacher. " "Experience without reflection is narrow experience, which can only become superficial knowledge at most."

It can be seen that only reflection can lead to breakthrough and development.

Lin Chongde, a famous psychologist in China, also put forward the growth model of "excellent teacher = teaching process+reflection". Professor Ye Lan said: It is difficult for a teacher to become a famous teacher by writing a lesson plan for a lifetime, but it may become a famous teacher after three years of reflection.

Professor Liu Jiaxia of Beijing Institute of Education put forward that experience+reflection+action = teacher growth. She said that if reflection only stays at the level of "thinking", it will not be effective if it is not put into action. It can be understood from the words of these experts and professors that teaching reflection is the only way for teachers to grow up.

2. Teaching reflection meets the needs of curriculum reform.

Four relations in the new curriculum: 1. Emphasize respect and appreciation when dealing with the relationship between teachers and students. When dealing with the relationship between teaching and learning, we emphasize help and guidance. 3. Emphasize self-reflection. 4. Emphasize cooperation with other educators. Therefore, reflection is the need of new curriculum reform.

Case 1: A teaching clip of Hesheng mL

After the teaching activities, in the last part of the class, the teacher should ask questions: "Do you have any questions?" At this moment, a student asked such a question: How many grams is 1 ml? Then the teacher hesitated. The teacher handled it this way and said, "Let me give you an example. How many meters is 1 hour? " The students at the bottom all laughed.

3. Teaching reflection is a bridge between teachers' own experience and teaching behavior.

Teachers transform teaching experience into teaching theory through reflection, from spontaneous to conscious, from random to intentional. The experience without reflection is an experience that cannot be improved, a narrow experience, and can only be said to be the repetition of work.

Third, what does teaching reflect on?

Simply put, teaching reflection is to study how to teach and learn; How others teach and learn; How to teach and learn in middle schools? There are many contents of teachers' reflection. We can simply divide the scope and contents of teachers' reflection into two aspects: teachers' ideas (or knowledge) and behaviors (or operations). Among them, the concept field focuses on education and teaching ideas, while the latter focuses on teaching practice. It includes reflection on teaching ideas, teaching objectives and means, teaching behaviors and strategies, teaching and learning methods and teaching situation design.

(1) Rethink the concept of education and teaching.

Case 2: Calculation of Square Area

In the teaching of square area, the area derivation begins with several squares, and teachers should spend a lot of time on this link, instead of just replacing students' operation exercises with calculus or multimedia demonstrations, and only hand over the derived conclusion-the formula of "square area = side length × side length" to students. Students seem to have mastered this knowledge point through a lot of calculus, but the result is not the case. We can distinguish different teaching levels through a practical problem: how to quickly calculate the area of 80×80 cm floor tiles in a hall? Students with operational experience immediately think of the method of counting floor tiles, while students who ignore operational teaching only think of measuring the length and width to calculate its area.

Reflection:

Because a large number of topic calculus can not replace children's "personal experience", multimedia can not replace students' operation exercises. In order to effectively improve students' quality and implement the requirement of "students' all-round, sustained and harmonious development", in mathematics teaching, we should completely change our educational concept, not let students only solve mathematical problems, but more importantly, let students experience the role of mathematics and cultivate and improve their mathematical literacy.

(B) Reflection on teaching practice

Case 3: How to evaluate students?

A teacher teaches 37+5. In the lively classroom atmosphere, the students talked about many calculation methods, and the teacher's face was full of excitement and pride. At this moment, another student raised his hand and the teacher hesitated. Finally, he stood up and answered. The student said, "Teacher, 37+5 = 42 on the blackboard, and you wrote 43." The teacher's face turned black at once, and with a sound of "Oh", he turned around and changed the topic on the blackboard. Suddenly the teacher remembered something and said, "XX is not very active in class at ordinary times, but he is very serious today. We praise him. " The students listened to the teacher's password and mechanically "snapped", and several applause rang out. XX sat down, wondering what the expression was on her face.

Reflection:

Teachers have realized the importance of incentive evaluation, but only regard it as an ornament to realize the new curriculum, rather than sincere admiration. While the teacher is praising, there is a kind of "high above" judgment: you don't study hard and are not excellent at ordinary times. How do the students feel after listening? Therefore, to give students an encouraging evaluation, we can't just stay in words, or it is a decoration formed when we need to do it. It needs to penetrate into teachers' educational thoughts from time to time and be implemented in teachers' daily teaching behavior. However, some teachers treat students with appreciation when dealing with this kind of classroom embarrassment. Students dare to find fault with teachers and challenge authority, which is very attractive in itself and often can firmly grasp students' attention. Isn't that what each of our teachers prayed for?

(3) Reflecting on the classroom teaching situation.

Case 4: Teaching clip with division of remainder

The teacher created such a situation: a fruit tree forest full of peaches makes people drool. In a burst of "tut tut", the teacher said vividly, "Do the students want to play in this Taoyuan?" Students should all say "think". The teacher turned to Gao Feng and said, "Well, as long as everyone listens carefully and speaks actively in this class, we will take everyone on a spring outing." Then, the teacher first took out six fresh peaches and divided them into three plates, two for each plate. The formula is 6÷3=2. Then take out seven fresh peaches and divide them into three plates, two for each plate, leaving 1. The formula is 7 ÷ 3 = 2... 1.

Reflection:

The creation of this situation looks "beautiful", but there is little internal connection between the situation and the teaching content, which can not stimulate students' desire to learn, make mathematics learning more lively and lose its due value.

Case 5: Fragment Teaching of Prime Numbers and Composite Numbers

Design a rectangular or square contest in class. Boys and girls put the cards around them into rectangles or squares. Whoever has multiple squares is the winner. Scene 1: 4 square cards for girls and 5 for boys; Scene 2: There are 4 girls and 7 boys; Scene 3: There are four girls, 1 1 boys. At this time, the question was raised: "Why do girls always win and boys always lose after three games?" "What are the types of graphics related to?"

Reflection:

A stone stirs up a thousand waves, and the problem arouses students' strong desire to explore. Students speculate that at first, some students thought it was related to the parity of the number of cards. Later, some students quoted "9" as an odd number through analysis, but there were also two squares, which were overturned by counterexamples. Finally, some students found that it was related to the number of factors in these cards. Everyone actively verifies, actively discovers and acquires new knowledge.

Fourth, how to reflect on teaching?

(A) choose the right object of reflection

The main objects of "teaching reflection" are: reviewing and reflecting, recording and improving one's own teaching behavior and ideas; Observe and reflect on colleagues' teaching behaviors and ideas, participate in collective exchanges and discussions, diagnose their own or colleagues' teaching problems, and propose solutions; Analyze and reflect on the intentions and ideas of publicly published classroom records (lesson examples), compare and reflect on your own classroom teaching, and find out what others can learn from.

(B) familiar with the process of reflection

The basic process of reflection generally includes: self-reflection-finding the reason-finding the theoretical destination of the reason-how to improve it. In this process, teachers' reflective ability is improved, thus improving teachers' teaching ability.

(C) master the method of reflection

1, case reflection method

2. Process reflection method

3. Action research methods

4. Observation and analysis methods

5. Brief recording method

Five, how to write a good teaching reflection?

(1) From the perspective of stylistic structure, we believe that "teaching reflection" should be a unique style of teachers with a very close combination of theory and practice. Its writing structure can be summarized as "teaching examples-gain and loss (success or failure) analysis-rational thinking", the first and second parts are "opposition" and the third part is "thinking". The third part is the key point, which should be written in detail and try to write a profound and feasible scheme strategy.

(B) From the writing content, we can choose a topic to write "Teaching Reflection" in mathematics from the following five aspects:

1, written successfully. For example, in the teaching process, the pre-designed teaching purpose is achieved, which causes the teaching vibration effect; Appropriate temporary measures in classroom teaching; Clear and organized blackboard writing; The infiltration and application process of some teaching ideas and methods; Reform and innovation of teaching methods. And on this basis, continuous improvement, perfection and innovation.

2. Write down the shortcomings. Even if it is a successful classroom teaching, there will inevitably be omissions and mistakes. We should systematically review and sort it out, and deeply reflect, explore and analyze it as a reference for re-teaching in the future.

3. Write teaching wit. In classroom teaching, with the development of teaching content, the harmonious thinking development and emotional communication between teachers and students will often be inspired by some accidental events. These "sparks of wisdom" often suddenly appear involuntarily. If we don't catch them through after-class reflection in time, they will disappear with time, which is regrettable.

4. Write about students' innovation. In the process of classroom teaching, students are the masters of learning, and there will always be "sparks of innovation" flashing. Teachers should fully affirm some unique opinions put forward by students in class, which will not only promote students' good methods and ideas, but also be an appreciation and encouragement to students.

Case 6: What is the teaching fragment and reflection of area?

After making students feel what area is, I designed a link to let them experience the diversity of strategies to compare the size of the area. In this session, I provided students with various learning tools, such as cubes, nickels, scissors, rulers, mimeographs and so on. Organize students to work in groups and compare the areas of rectangles and squares by hand. The teaching situation is as follows:

A minute later, a student stood up and said loudly, "I can see that the square is very big."

Teacher: Oh, can you show us your method?

Health 1: Of course. (Health presentation method)

Health 1: I used the method of pressing my fingerprints. You see, I pressed the 10 fingerprint on the rectangle and the 12 fingerprint on the square, so the square is larger than the rectangle.

(Students point leisurely and count proudly. )

Teacher: Children, do you have anything to say about this method?

Student 2: (unconvinced at all, with a sarcastic tone) Haha, how can it be so comparable? It's messy and wrong. I don't know.

Health 3: I think I still have a clue about his comparison, but I just didn't do it well. But we can't laugh at others like this.

Health 4: Yes, I find it interesting, too. It seems that I didn't follow certain rules and standards when I pressed my fingerprints.

Teacher: Well, that's right. Then how can we achieve regularity and standards by fingerprinting? Tell you what, sit at the same table and discuss with each other.

Health 5: I think you should press your handprints line by line, and the interval between every two handprints is almost the same, so that it doesn't look messy and it's easier to count.

Health 6: I think it is very important to use one finger from beginning to end when fingerprinting.

Teacher: You are all so talented, and the teacher agrees. (The teacher approaches Sheng 1 and caresses his head. )

Teacher: Your "fingerprint method" is very creative and remarkable. Although there are some problems with your handprints, it is because of your problems that we have a lot of inspiration and thinking. Do you accept these suggestions from your classmates?

Student 1: Admission, teacher. Can I press it again now?

Teacher: Sure, class, do you want to press it?

Health (excitedly): Yes.

(All students compare the areas of rectangles and squares according to their handprints. )

……

Try other methods to compare the areas of rectangles and squares.

With the support of fingerprint method, students can easily find ways to put coins, put squares and draw squares.

Reflection:

The new curriculum standard points out that "doing mathematics" is not only a simple mathematical operation activity, but also a dynamic process of self-exploration, self-construction, self-discovery and self-creation of learners. In the classroom, if students have unique ideas and practices, the "spark of innovation" is flashing. Our teachers should affirm and appreciate it in time to stimulate everyone's enthusiasm for participation. In the process of exploring and comparing the two graphic areas in this clip teaching, the teacher did not presuppose that the children would have such a wonderful class because of the mathematical activities of pressing handprints: while other students were still trying to explore the comparison method, a student quickly and casually pressed handprints, which triggered the children's confrontation and judgment again and again. After this interactive discussion, the rest was the harvest again and again. This kind of confrontation and evaluation, harvest and summary is not only a wonderful interpretation of children's thinking development, but also a way for children to explore, build, discover and innovate themselves, so as to obtain solutions to problems and truly let children "know why, know why".

5. Writing and teaching design. After a class, I meditate: What teaching rules have been explored in this class? What are the innovations in teaching methods? What are the new discoveries in knowledge points? What are the new tricks for organizing teaching? Whether there is a breakthrough in solving many misunderstandings of the problem; Whether the enlightenment is proper and the training is in place. Write down these gains and losses in time, make necessary classification and balance, consider what to do when re-lecturing this part of the content, and write the design of re-lecturing, so as to foster strengths and avoid weaknesses, strive for perfection, and raise their teaching level to a new level and height.

In a word, it is very important to write teaching reflection in time and persistently. Write it down as soon as you get something. Something is long. If you have nothing, it's short. Write to promote thinking and think to promote teaching. Long-term accumulation, there will be a harvest of "collecting arms and making a mickle, gathering sand and making a tower".

Sixth, the teaching reflection of typical cases

Case 7: After-class reflection of the observed object

"Class is finally over", which is my first feeling after class. Throughout the class, the students are busy observing and moving. Every step I take is carefully led, for fear that students will take detours and delay time. As a result, a class was silent for 50 minutes, and every activity didn't seem to be completely completed. Everyone is in a hurry. In short, one word-tired.

Why? I asked myself, is my teaching design imperfect? Isn't every step a solid step with students? The best way to solve this problem is to ask students. So, I interviewed several students, and the students' words made me suddenly enlightened: "Teacher, sometimes we all know what the cup looks like without looking, and you let us look at it, which makes me feel boring." Sometimes I don't know what you are showing us, so give me an answer. Yes, how high is the observation ability of students? The teacher doesn't even know this, how can he design a scientific and reasonable teaching plan? Teaching was conducted without any pre-class investigation, and as a result, a lot of useless work was done.

Pre-class research activities:

Activity 1: Divide the class of 32 people into 8 groups, with 4 people in each group, standing in four directions of the table. Who's on your left? Who is on the right? Switch seats clockwise. Who is on your left? Who is on your right? (Change seats four times in turn and repeat the question just now)

Survey results: 30 people judged correctly, accounting for 93.8%; Two people were confused and misjudged, accounting for 6.2%.

Activity 2: Observe the kettle from different directions. Number of people surveyed: 8 people were randomly selected.

(1) (Students look at the kettle from the front) What do you see about the kettle? Choose the right picture.

(2) (The teacher looks at the kettle from the side) Guess what the teacher will see in the kettle. Please help the teacher choose the right picture.

Survey results: 1 The question was completed well, and 7 people were able to select the correct picture at one time, accounting for 87.5% of the total number of people surveyed. 1 People can choose the correct picture under the guidance of the teacher. The quality of 2 questions is not high, and 6 people made mistakes, accounting for 75% of the total number of people surveyed; They made the right choice, accounting for only 25% of the surveyed population.

The first reflection: reflection = teaching link+theoretical "hat"

1. Observe whether there is a purposeful, planned and active psychological participation process.

2. Under the guidance of this theory, the teachers of this class have made a careful observation plan for the students.

3. The new curriculum standard (hereinafter referred to as the standard) points out that mathematics teaching is the teaching of mathematics activities, so teachers have designed a variety of activities, students' observation activities are orderly, and independent exploration and cooperation are organically combined.

The second reflection: put the "breakthrough" on understanding students' learning.

"Teacher, in fact, sometimes we all know what a glass looks like without looking. I'm tired of you showing us. The children's words helped me find the reason. I think children should be given some independent space, give full play to their existing observation ability and stimulate their enthusiasm for participation. After all, children are the masters of the classroom.

The third reflection: re-design the teaching according to the students' investigation.

After the investigation, combined with the survey results, I analyzed the students' understanding level. Through the analysis, I found that although students didn't systematically learn the method of observing objects, their life experiences have enabled them to have preliminary observation ability. Although this ability is not high, it can help them to complete some simple observation requirements well.

I designed re-education like this:

1, get to know the students before class and avoid the blindness of observation.

One of the design of re-education is to pay attention to the guidance of students' observation methods.

2. Put forward observation requirements step by step to avoid the rapid evolution of observation.

Re-education design 2: design layered group observation activities.

3. Adopt various evaluation methods to avoid the formalization of observation.

Finally, I ended the topic with a poem with a smile, "A thinking reed/trembling in the wind/no less than a symphony/flowing from the fingertips to the stomach of the city." Let's be a reed of happy thinking and grow up in teaching reflection.