First, the meaning of teaching reflection
What is reflection? The concept of reflection appeared as early as in ancient China. What "self-seeking", "self-examination", "self-examination", "thinking behind closed doors" and "I live in three provinces" all witnessed the ancient people's reflection. Modern Chinese Dictionary explains: "Think about the past and think about the future, and learn from it." Teaching reflection is a process in which teachers consciously take their own classroom teaching practice as the object of thinking, and examine and analyze the teaching activities that have happened or are happening and the theories and assumptions behind the teaching activities. Its purpose is to make teaching activities enter a more optimized state, make students get more full development, and make teachers grow faster and more professionally. Friedenthal, a famous mathematics educator, once asserted: "Reflection is an important manifestation of creative thinking in mathematics. It is a high-level mathematical innovation activity and the driving force of mathematical activities. Students must be educated to think and confirm their own judgments and activities, so that they can learn to reflect. " Professor Friedenthal, a world-famous Dutch mathematician, once brilliantly pointed out: "Reflection is the core and motive force of mathematical thinking activities. Only through reflection can students' real world be mathematicized. Without reflection, students' understanding cannot be sublimated from one level to a higher level. "
Second, the content of teaching reflection
(A) Reflection on the concept of education
Concept is the soul of behavior, the internal motivation of educational practice, and directly guides teachers' teaching behavior. The traditional teaching view regards students as containers to receive knowledge, and pays attention to mastering knowledge, training skills and improving grades. Little attention is paid to experiencing the value, spirit, beauty and communication of mathematics. The students trained under the guidance of this traditional teaching concept can only get "more points" with high scores and low skills, which can not adapt to the development of society and stand the test of the times. The new curriculum calls for talents with innovative consciousness and spirit. Based on "students' all-round, sustained and harmonious development", we strive to provide "realistic, meaningful and challenging" learning content, advocate "hands-on practice, independent exploration and cooperative communication" as an important learning method, pay attention to "students' different cultural environment, family background and their own way of thinking", and guide students into a "lively, proactive and personalized" learning process. This requires teachers to be people-oriented, treat students with a developmental perspective, and gradually unify their educational concepts in the direction of the new curriculum.
(B) Reflection on the teaching process
Teachers should reflect on the teaching process, sum up the success or failure of teaching, and form the habit of reviewing, analyzing and examining the teaching process, so as to improve the ability of self-reflection, self-monitoring and self-development, and then improve the teaching art.
First, teachers should reflect when preparing lessons. The ancients said, "No matter how clever a person is, no matter how long he thinks, he will lose." . As a teacher, we should reflect on our past experience, new educational ideas, students' actual situation, current teaching conditions and teaching methods, so that the new teaching design can be based on the reflection on past experience, lessons, current educational ideas and teaching conditions. Especially when designing lesson plans, we should ask ourselves: "What life experience and knowledge reserves do students have", "What abilities do students have" and "What mistakes do students easily make when accepting new knowledge". , to save for a rainy day, don't fight unprepared.
Second, we should pay attention to reflection in the teaching process. The teaching process is a process of communication, positive interaction and common development between teachers and students. In actual teaching, students often encounter some unexpected situations through teacher-student interaction. If students can't answer, the answers are varied, unexpected, disputes between teachers and students, and the "group talk" with flamboyant personality makes the situation out of control, and the teaching task can't be completed ... Teachers should reflect on "why such problems occur, how to adjust the teaching plan and how to take effective strategies and measures" to ensure that the teaching process runs along the best track.
Third, we should pay attention to reflection after teaching. "It is difficult to know after teaching." After class, teachers should reflect on whether the teaching content has been fully displayed and what needs to be supplemented; Reflect on whether the knowledge preparation and pre-class teaching design scheme are reasonable and whether the students really master it; Reflect on the success, failure and improvement of this lesson; Whether the teaching evaluation has been encouraged and cared about; Whether the courseware is high, new and strange, and whether the thinking is clear; Whether the key points are prominent, whether the primary and secondary roles are clear, whether the "three main roles" are well played, and whether the purpose is achieved ... Write a diary of harvest or teaching after class, sort out the gains and losses, correct the problems, and urge yourself to ask the teacher for advice and treasure in the sea of books. Constantly explore new ways to express the content of teaching materials, and build a teacher-student interaction mechanism and new ways for students to learn.
(C) Reflection on teaching behavior
The new curriculum standard requires teachers to establish new consciousness and change their roles. Their identity is not only the imparting of knowledge, but also the organizer, guide and collaborator of students' learning activities.
First, strengthen collective lesson preparation and reduce the burden on teachers and students. Teachers in the same subject in the whole grade should strengthen collective lesson preparation, * * * study key and difficult points, carefully analyze hot test sites, broaden knowledge points and ability points, unify data, progress, monitoring, assessment and analysis, realize teachers' complementary advantages and resource sharing, and strive to reduce the burden on teachers and students. Strive to change the bad situation of going its own way, fighting alone and marking time.
The second is to tap educational materials and strengthen knowledge clearance. There are many materials in junior high school mathematics textbooks that are worth digging, summarizing, analyzing and summarizing, and there is room for us to use. At the same time, teachers should fully grasp the knowledge points of mathematics, make clear the requirements of teaching contents and objectives, list them emphatically, classify all knowledge points according to the six-level objectives of "memory, understanding, application, analysis, synthesis and evaluation", digest and absorb them step by step, and "prevent students from eating uncooked rice".
Third, correct the position of teachers and establish a good image. In teaching, teachers should and can only be the organizers of students' learning activities, not the masters of students' learning activities. Students are the masters of learning, and teachers should provide students with time and space for communication, create a relaxed and harmonious learning environment, and let students experience the joy of success; Teachers should and can only be the guides of students' learning activities, not the dominators of knowledge transfer. In class, we should fully mobilize students' enthusiasm and creativity, and take the initiative to explore and explore independently. Teachers can only guide students in thinking and methods, fully tap their potential, inspire and inspire students, point out the direction, melt the ice and overcome difficulties; Teachers should and can only be collaborators in students' learning activities, not "teachers with dignity". To shorten the distance between teachers and students, we should exchange our hearts, talk to each other, join the students, make ourselves a member of the students, discuss the problems in learning with the students, exchange ideas and experiences with the students in a tone of communication, cooperation and discussion, and let the students kiss and trust the teachers.
Third, the way of teaching reflection.
First, grasp the law of solving mathematical problems. Method is a shortcut to learning, and there are rules to follow in solving problems. In teaching, it is necessary to guide students to reflect on the law of solving problems, see through the clouds, break through difficulties, cultivate the habit of in-depth study and improve students' problem-solving ability. For the same type of problem, the method of solving problems often has its regularity. Therefore, when solving problems, we should seize the opportunity to guide students to reflect on the methods of solving problems, sum up the laws and characteristics of solving problems, discover new universally applicable things, and then gain experience in solving problems, which is conducive to solving problems in the future.
Second, follow up the problem-solving process. It is an effective way to improve the learning effect and cultivate students' ability to form the habit of checking and reflecting in the process of solving problems. Reflecting on the structural characteristics of the topic can cultivate the profundity of thinking; Reflection on solving problems can cultivate the flexibility of thinking; Reflection on problem-solving methods can cultivate the rigor of thinking; Reflection on problem-solving methods can cultivate the creativity of thinking; Reflection on the conclusion of solving problems can cultivate the criticism of thinking; Reflecting on the formed knowledge module can improve the thoroughness of thinking; Reflecting on the interrelation of knowledge points can improve the breadth of thinking; Reflecting on the transformation of question conditions can improve the agility of thinking ... In short, we should "squeeze out" as many questions as possible in students' minds, observe, associate and reflect from multiple angles and in all directions, so that students can be cultivated and developed in the training process.
Third, the pursuit of problem-solving methods. Being good at reflecting after solving problems, classifying methods, summing up laws, and trying to figure out skills, further making a question changeable, asking more questions and solving more problems, mastering everything, excavating the depth and breadth of examples, and expanding the radiation surface of examples will undoubtedly be of great benefit to the improvement of students' ability and the development of thinking.
Fourth, focus on the students' wrong questions. Students' careless study of basic knowledge, content with a little knowledge, and neglect to think carefully about the conclusion often lead to unrealistic, wrong data, irrelevant answers, incoherent preface and other phenomena, especially some "hidden mistakes" frequently occur. Therefore, teachers should pay close attention to students' mistakes, carefully design teaching situations, guide students to analyze the causes of errors, give students a chance to re-understand, and enable students to master, understand and use errors in the process of error correction. Students should collect mistakes, extract them into the error correction book, establish their own mathematical error question bank, obtain the information of the object of reflection, and make up for the lack of knowledge and thinking in reflection. Help students analyze the root cause, whether the old knowledge interferes or the new knowledge is not mastered; Is knowledge itself difficult or careless? Whether there is no deep understanding or no serious thinking; Is it an experience mistake or a hands-on mistake? Is it a common mistake or a specific mistake ... suit the remedy to the case, improve it in time, put an end to this kind of situation from happening again, and optimize students' thinking quality.
Fourthly, the strategy of teaching reflection.
(A) improve the understanding of teaching reflection
To a certain extent, reflection means "looking back", that is, "exposing one's weaknesses" and "self-criticism", which is a very difficult behavior. A teacher who loves education, students, noble morality and dedication is often strict with himself, strives for perfection in his business and is not satisfied with his immediate achievements. Their desire for success and self-realization will be the source of their continuous teaching reflection. Through practice, they constantly learn, accumulate and reflect from experience, constantly increase their knowledge and enrich themselves, and treat mathematics practice with a "scientific attitude", so as to cope with teaching freely and grow into thoughtful and creative mathematics teachers.
(B) improve teachers' teaching reflection ability
Teachers should constantly plan, check, evaluate, feedback, control and adjust themselves and their teaching, so as to improve their teaching reflection ability. Therefore, teachers should first strengthen the study of mathematical theory. A wise man corrects his own mistakes through the mistakes of others. We should be good at learning from others, peers and famous teachers, and learn from each other's strengths. By studying the teaching ideas and methods of excellent teachers and special-grade teachers, we can find out the differences in ideas and analyze the differences in means and methods, so as to improve ourselves. We should learn to actively explore the mysteries of teaching, find the laws of mathematics education, deeply understand and appreciate the advantages of new curriculum reform, fundamentally overcome the disadvantages of traditional education, actively and effectively carry out education and teaching reform, and often reflect on teaching practice with a critical attitude and make continuous progress. Secondly, actively participate in educational research, explore the law of junior high school mathematics education and teaching, deeply understand the true meaning of junior high school mathematics teaching, adapt to the development of the times, and gradually become a "reflective" teacher.
(C) flexible use of reflective methods
Solving problems is the only way for students to learn mathematics well. To improve students' learning effect, teachers should master the skills of reflection, flexibly use reflection methods, strategize and integrate, and students' learning effect will be immediate.
1. "Looking at the side of the ridge is the peak"-make good use of "empathy". There is a saying that "it doesn't hurt to look at others" and "I don't know if I am hungry when I am hungry". Due to the differences in people's understanding and experience, it is inevitable that their understanding will be biased, and sometimes they can't even see the problem. From the teacher's point of view, put yourself in the other's shoes: "What if I were a student union?" "Why does this student have such an idea?" "At this age, how can we learn to be effective?" Frequent reflection on empathy is of great benefit to the formation of a harmonious, harmonious and equal learning atmosphere and a unique teaching style.
2. "Sima Guang smashed the jar"-it might as well be "retroreflection". Reverse thinking is an important thinking ability and an important thinking form. When solving problems, people are used to thinking according to the familiar conventional thinking path. But in practice, it is difficult to find correct answers to some questions with positive thinking, and once you use reverse thinking, you will often get unexpected results. This shows that reverse thinking is a creative way of thinking that gets rid of the shackles of conventional thinking. In history, Sima Guang could not solve the problem by climbing into the jar to save people, but transformed it into a broken jar to save people, successfully solved the problem and was passed down as a much-told story. Luban accidentally cut his hand by weeds when he went up the mountain. He thought backwards, "since the fine teeth of grass can cut my hand, if there are many small teeth on the iron bar, you should be able to saw the tree down!" " In this way, the first saw in the world was born. There are countless examples of this "thinking in the opposite direction". Use reverse thinking to "surprise". The result was unexpected, unexpected, and there was no other gain.
3. "Cao Chong is an elephant"-skillfully using "transforming ideas". Transforming ideas means choosing appropriate methods through observation, analysis, association and analogy to transform unknown solutions or difficult problems into mathematical ideas that have been solved or are easy to solve within the known knowledge. Professor C.A. Yatekaya, a famous mathematician of Moscow University, once said in a speech entitled "What is problem solving" to the contestants of the Mathematical Olympiad: "To solve a problem is to turn the problem to be solved into a solved problem". There are many transformations in mathematics, such as elimination method, method of substitution, the combination of numbers and shapes, and the problem of evaluation domain, all of which embody the idea of equivalent transformation. We often carry out equivalent transformations among functions, equations and inequalities, such as from unknown to known, from number to shape, from space to plane, from high dimension to low dimension, from multivariate to unary, from high order to low order and so on. These all reflect the idea of transformation. Taking "Cao Chong as an image" as a typical example to solve mathematical problems, pushing the boat with the current and often infiltrating the idea of equivalent transformation can improve the level and ability of solving problems.
4. "The wine in Zhumen stinks, and there are frozen bones on the road"-using contrast reflection. Only comparison can distinguish, and people often find the essential attributes of things by finding the negative characteristics of things. In mathematics teaching, we will compare relevant knowledge, find out similarities and differences, and improve ourselves by studying and comparing, thinking and reflecting, so as to reach the realm of "reaching the peak, knowing at a glance that other mountains are dwarfed". .
5. "Sticky mud painting"-do not avoid "questioning and reflection". Only by seeking questions from questions can we form reasoning thinking, and asking questions is the beginning of human thinking. Only by constantly questioning can teachers improve, make new discoveries and gain something. The teaching of every knowledge point, the formation of every decision, every class, every set of questions and so on. We must question and reflect: "Is this ok?" "Is this a reasonable arrangement?" "Is this the best solution?" Only when there is doubt can there be discovery, only when there is discovery can there be efforts, only when there is efforts can there be gains, and only when there is gains can there be development.
Because mathematical thinking itself is a kind of reflective thinking, in essence, mathematics is the queen of science, mathematics is the foundation of all sciences, and mathematics is a kind of spirit, that is, rational spirit. Only through teaching reflection can teachers improve their teaching level, incorporate teachers' subconscious activities into teachers' conscious activities, improve teachers' educational and scientific research ability, and make mathematics teaching level move towards a higher and more effective realm.