How to effectively open up in mathematics teaching and comprehensively improve students' learning efficiency? Through this study and the experience gained in teaching, I would like to talk about some experiences.

Chapter 1: The new curriculum reform of mathematical research journals calls for the reform of teaching methods, which requires teachers to change the traditional closed teaching methods and implement open teaching. The so-called open teaching refers to a teaching practice with students as the main body, starting from cultivating students' attitude, thinking and ability in learning and practice, activating students to actively discover, imagine and explore, and forming scientific quality, innovative consciousness and practical ability. On the basis of giving full play to students' main role, we should change "learning knowledge" into "knowing learning".

First of all, open the relationship between teachers and students and democratize the teaching atmosphere.

The basic principles of open teacher-student relationship are democracy and equality, respect for students' personality and rights, and liberation of students' subjectivity and creativity. This open teacher-student relationship mainly includes two meanings. One is based on "teacher-student dialogue", which aims to show that teachers and students are not simply giving, and teachers are no longer the authority to give orders to students, but an equal and democratic communication relationship and a "partner" relationship of mutual respect, mutual influence and mutual promotion. Second, the relationship between teachers and students is "consultant" and "master". That is, teachers actively participate in and guide students' learning activities, point out the direction for students' learning activities and development activities, and play a leading role and a "consultant" role; Students can actively generate and construct themselves, knowledge system and ability system through autonomous learning activities, and become the masters of learning in the process of interacting with the outside world.

Second, open the teaching process, so that students have their own income

In the specific operation process of learning, we should pay attention to creating a democratic and harmonious psychological environment and a teaching situation of independent participation. According to different classes, there should be no fixed procedure in this operation process, and the specific teaching measures should be decided according to the teacher's personality, students' situation and other factors.

First, pay attention to guiding students to think for themselves.

"self-study" means that students read books and understand textbooks by themselves, and teachers guide their study; Find out the key points and mark the problems when you find them. As the ancients said, learning begins with thinking, and thinking begins with doubt. Let students read and think, which not only gives students time and space to think, but also lays a good foundation for the next step of teaching, and enables students to develop a good study habit of being diligent and eager to learn.

Second, pay attention to let students explore mathematics and develop their thinking ability in "doing mathematics"

For example, when teaching geometry "the positional relationship between circles" in the third grade, it can be so attractive: we live in a rich graphic world, and the graphics composed of circles are the most common pictures in our lives. Can you give two examples of circles? By giving students examples, students' perception of the different positions of two circles in the objective world is enriched, which makes it possible for students to explore independently. Design problem: Because of the similarities and differences between circles, colorful pictures are formed. Do you know how many different positional relationships there are between these two circles? Please draw a picture. Here, five positional relationships of two circles are not directly given. Let students draw a picture first, which is beneficial for students to actively participate in teaching activities, so as to obtain different "knowledge" with personality. Draw two circles separately and gradually enlarge the radius of one circle. What will happen at this time? Is there a connection between these phenomena? Through the exploration of this problem, students can further perceive the interdependence between "positional relationship" and "quantitative relationship" of graphics, understand that "quantitative relationship" is a concise symbolic language to describe "positional relationship", and get the judgment of five positional relationships of two circles. Through experiments, production, measurement and other activities, we can guide students to practice, experience, try and make mistakes and succeed, deepen their understanding and application of knowledge, thus cultivating students' practical operation ability and developing their personality.

Third, create teaching questions to stimulate students' discussion and debate.

① Pay attention to guiding students to communicate, ask questions and solve doubts in groups. On the basis of students' self-study, exchange key points in the group, question each other, and write down the unsolved problems. In this process, because everyone has to explain their own views and opinions, we can fully mobilize and give full play to the enthusiasm and initiative of students to participate in teaching, drive students with learning difficulties, play a complementary role in communication, and stimulate people's intention to study in depth. At the same time, it can cultivate students' spirit of unity and cooperation.

② Actively ask questions between groups. First of all, students write the unsolved problems in the group on the blackboard, and students number them according to the content of the textbook. Psychological research shows that students have a strong desire to express themselves. The problem of letting students write on the blackboard on the stage gives them the opportunity to show their talents; The serial number is compiled by students according to the content of the textbook, which deepens the understanding of the textbook knowledge system. Secondly, the teacher organizes the whole class to solve the problems on the blackboard and form a group to solve them. During this period, the whole class can express their views on every issue, illustrate their views with examples, and even debate. Students ask questions mainly by solving doubts, and teachers organize, participate, guide and learn in the teaching process. For problems that students can't solve, teachers may study with students, or guide and guide them in time, but they can't think for students.

Third, open teaching evaluation to stimulate students' enthusiasm for innovation

The implementation evaluation should pay attention to:

First, highlight the subjectivity of evaluation. The evaluation of mathematics open teaching should not only evaluate "teaching", but also evaluate "learning", that is, the evaluation of mathematics open teaching should highlight students as the evaluation subject. The purpose of evaluating "learning" is to promote the main body to actively participate in the process of mathematics learning, constantly adjust themselves, step by step towards the learning goal, promote the development of students' personality and develop their creative potential.

Second, pay attention to the integrity of evaluation. The evaluation of mathematics open teaching should master the unified evaluation standard, pay attention to the overall evaluation of a class, and pay attention to the evaluation of the improvement of students' comprehensive quality. We should not only pay attention to the evaluation of the relationship between mathematics knowledge and teaching in different fields, but also pay attention to the relationship between mathematics and other disciplines, and pay more attention to the evaluation of students' learning interests, emotional attitudes, mathematical views and values formation process.

Third, pay attention to the dynamic nature of evaluation. The purpose of teaching evaluation should not only use summative evaluation to judge open teaching or give a grade, but also closely combine the evaluation of mathematics teaching with the improvement of mathematics classroom teaching and mathematics teaching quality, focusing on teaching.

Fourth, open the exploration space, so that students can form the ability to analyze and solve problems in the process of exploration.

Open teaching cannot be confined to classroom teaching. It is also necessary to open up learning space, so that students can go out of the classroom and go out to the society, participate in colorful extracurricular activities and practical activities, broaden their horizons, and discover, think and explore according to existing mathematical knowledge in the process of feeling new knowledge, so as to solve problems. First, attach importance to developing math activity classes. According to students' hobbies, various forms of math activity classes can be set up, so that students can find math problems from life and labor, bring them to the activity classes, design and solve them themselves, learn from each other, inspire each other and communicate with each other. For example, hold math competitions, math games, math study seminars and exchanges, and hold math lectures and exhibitions. Second, encourage students to use mathematics knowledge flexibly in social practice, let students connect with life and labor, and find mathematical problems in the process of activities. For example, in the teaching practice homework class "Measuring Inclination", my classmates and I made a measuring tool to measure the heights of flagpoles, teaching buildings and ancient trees on campus. These practical activities can cultivate students' ability to observe, apply, analyze and solve problems, activate students' creative potential, and finally enable students to reach the realm of flexible creation.

In a word, the implementation of open teaching has given full play to students' learning initiative, met each student's learning psychological needs, fully developed students' good personality and effectively cultivated students' ability.

Chapter II: Junior high school mathematics training log In the teaching process, many teachers think that they are methodical in class, thorough in knowledge analysis and clear in calculus, but as a result, many students can't draw inferences, which leads to difficulties in mathematics learning. Most teachers attribute this phenomenon to factors other than teachers, such as poor students' quality and poor family education environment, and rarely find that it is caused by their own teaching ability and literacy.

Classroom teaching is a bilateral activity between teachers and students. The essence of classroom teaching is the process of information exchange between teachers and students and the same school. When the teacher learned that students had difficulties in learning mathematics, did he think that it might be because the teacher didn't understand the textbook enough, didn't accurately grasp the key points and difficulties of the textbook, didn't make clear the content level of the textbook, and the teaching method didn't adapt? Under the guidance of mathematics curriculum standards, the purpose of our mathematics teaching is to let students go from "listening" to "understanding", to "meeting" and finally to "meeting". Therefore, teachers must deeply reflect on their own educational and teaching behavior and critically examine the performance and basis of self-subjective behavior. Through observation, review, diagnosis and self-monitoring, we can combine "learning to teach" with "learning to learn" by affirming, supporting, strengthening or denying, thinking and revising, so as to improve the rationality of teaching practice, improve classroom teaching efficiency and achieve the purpose of improving teaching quality. Now I will talk about my views on the following aspects.

First of all, teachers should reflect on educational concepts.

The new curriculum standard requires teachers to change the concept of subject education, always embody the scientific concept of "students are the main body of teaching activities", pay attention to students' lifelong development, and pay attention to cultivating students' strong interest in learning and correct study habits. Mathematics attaches great importance to the close connection between teaching content and real life. However, in teaching activities, many teachers are accustomed to the traditional teaching mode, pay attention to imparting knowledge and emphasize receptive learning, which makes many students lose interest in learning mathematics. In teaching, teachers should seize the opportunity, constantly guide students to create cognitive "conflicts" in the process of setting doubts, questioning and solving doubts, stimulate students' continuous interest in learning and desire for knowledge, successfully establish mathematical concepts, and master mathematical definitions, theorems and laws.

Teachers should base themselves on and cultivate students' independence and autonomy in inquiry teaching, guide students to question, investigate and explore, learn to learn by practice, and gradually form their own learning strategies in cooperative middle schools. For example, when learning the properties of an isosceles triangle with three lines in one, three students can cooperate to draw the bisector of the top angle, the height on the bottom edge and the center line on the bottom edge respectively. This is why students will find that three lines are one line. There are many ways to prove the congruence of triangles. Why can't "corner edge" determine the congruence of two triangles? When learning mosaic, you can ask such questions. Why can regular triangles, squares and rectangles be regular hexagons, but regular pentagons are not? Wait a minute.

In this way, teachers' constant questioning and questioning can guide students to think positively, stimulate students' strong interest in learning and desire for knowledge, and urge students to discover and summarize all kinds of mathematical laws in life, thus laying a solid foundation for the next step of learning mathematical knowledge. Therefore, we teachers must reflect on our educational ideas, firmly grasp the relationship between dominance and subjectivity, and solve the problem of students' learning enthusiasm.

Secondly, teachers should reflect on teaching design.

Teaching design is the blueprint of classroom teaching, the overall planning and presupposition of classroom teaching, and outlines the interest orientation of classroom teaching activities. When designing teaching plans, teachers should pay attention to the current teaching content and its status (deconstruction of concepts, separation of thinking methods, contact methods of related knowledge, etc.). ), students' existing knowledge and experience, teaching purpose, key points and difficulties, how to design teaching process according to students' existing cognitive level and logical flow of knowledge, how to highlight key points and break through difficulties, what may happen when students understand concepts and thinking methods, how to deal with these situations, and what exercises to design to consolidate new knowledge. The reflection of instructional design is whether these ideas and presuppositions have been taken into account. After the teaching, we should reflect on the actual process and students' acceptance, find out the successes and shortcomings and their reasons, so as to effectively improve the teaching.

Thirdly, teachers should reflect on teaching methods.

Teachers teach well, and students learn well in essence. In the actual teaching process, do our teaching methods conform to the students' reality? In class, marking papers and answering questions, some teachers think it has been made clear, and students have been inspired to some extent. However, after reflection, it was found that the teacher's explanation did not start from the students' original knowledge base and fundamentally solved the problem of students' cognitive gap. Some teachers just blindly imagine solving a certain kind of problem according to their own fixed procedures. Maybe the students understood it at that time, but it was often specious and didn't really understand the essence of the problem.

In junior high school mathematics teaching, example practice teaching is an important part of mathematics teaching and an extension and development of concept teaching. The example exercises in the textbook are carefully arranged by the editor, which are typical and enlightening. They are not only the consolidation of basic knowledge, but also of great significance for cultivating students' intelligence, mastering mathematical ideas and methods, cultivating students' awareness and ability of applying mathematics and improving students' mathematical literacy.

Fourth, teachers should reflect on students' learning methods.

"Mathematics Curriculum Standards" points out that effective mathematics learning activities can not only rely on imitation and memory, but also practice, independent exploration and cooperative communication are important ways for students to learn mathematics. Therefore, changing mathematics learning methods and advocating meaningful learning methods are the core tasks of curriculum reform. Junior high school students are generally between the ages of 12 and 16. They are in the period of growth and development. They are immature in thought, unstable in behavior, emotional in handling affairs, fond of showing off, impulsive, shy in meeting teachers, and have the habit that newborn calves are not afraid of tigers. In mathematics learning, students' interests, emotions and personalities are more prominent, and many students also have certain problems in their learning methods. At the same time, it is often difficult for them to find that their learning methods are inappropriate. Therefore, teachers should reflect on students' learning methods, find out their existing problems, and help them try to change inappropriate methods to make students meet the requirements of the new curriculum standards.

In short, to learn, we must take thinking as the basis, thinking can get it, and thinking can't. Teaching is also this law. If you don't think about it, you will become a teacher who teaches dead books, and students will not get good benefits. If you want to be an excellent teacher, only by summing up while teaching and reflecting while teaching can you achieve your goal.

Chapter III: Primary School Mathematics Training Log Through participating in distance education and training, during this period, I made full use of the time of training activities to study, which was both hard and rewarding. There is both pay and new income. Although we have never met, distance learning has brought us closer. I have improved my basic quality and comprehensive business ability in an all-round way, which has played a positive role in promoting my future development. I think in my future work, I should do the following:

First, change ideas and update them.

I actively participated in the online training, and I should have achieved three "consciousnesses": consciously participating in online learning and training, consciously participating in discussions, and consciously handing in homework. Through research, I have made clear the essence of modern education and what kind of quality requirements the curriculum reform puts forward for teachers. Through in-depth study, I made it clear that as a teacher, I must constantly improve myself, enrich myself, have rich knowledge and solid teaching basic skills, otherwise I will be eliminated by the times, enhance my sense of urgency, crisis and responsibility in learning, establish the educational thought of "student-oriented development", constantly update my teaching concept, and fundamentally change my teaching behavior and students' learning methods.

Second, actively study and deeply understand.

Through the study, I learned a lot of knowledge, created a broad learning world for me, and made me master advanced educational concepts and methods. I think there has been great progress in the formation of theory.

Third, reflect on teaching work and keep making progress.

In teaching, we should constantly think about the shortcomings in our work and strive to improve our professional level, constantly learn from outstanding backbone teachers and consult thoughtful teachers.

Fourth, based on the classroom, enhance their own value in practice.

Classroom is the main position for teachers to reflect their own values. In line with the concept of "all for students, all for students", I devote my love to students wholeheartedly. In the future teaching, I will try my best to apply the new curriculum ideas I have learned to classroom teaching practice, based on "using new and old textbooks and practicing new ideas." Strive to make my mathematics teaching more distinctive, form a unique teaching mode, better reflect the requirements of quality education and improve the quality of mathematics teaching. I deeply understand that teachers' words and deeds affect students and will set an example for them. Ideological education should always be unremitting, focusing on cultivating students' good moral quality, study habits, labor habits and civilized behavior habits.

Through this national training study, I am deeply touched. Really realize that "it's never too old to learn, but not too much to learn", in short, people should learn all the time throughout their lives. As teachers through the ages, all these require teachers to keep learning and improving, and to be innovative teachers, research teachers and guiding teachers. If teachers don't realize the necessity and importance of their own study, and use the knowledge and concepts your teacher taught you decades ago to educate students now, isn't that wearing new shoes and taking the old road? I think teachers nowadays should have dual identities: both teachers and students. Teachers study to "educate people". As teachers, our study is not ordinary study, but based on the study of an educator. Our ultimate pursuit is to educate good people, and learning for "educating people" is the bounden duty of teachers. We should actively participate in all kinds of training and continuing education organized by higher authorities, constantly learn new teaching methods and new teaching concepts, make ourselves a "source of living water" and better nourish students' thirst for knowledge. In the future study process, I should actively study, increase my knowledge, make full use of this knowledge and apply it to the classroom to improve the teaching quality.

Chapter four: Mathematics classroom teaching in senior high school is the center of school teaching and the main channel to implement quality education; Using mathematics teaching language is the most important means for mathematics teachers to carry out teaching work. Therefore, accelerating the reform of mathematics curriculum, making it more open, comprehensive and practical, and constantly improving the application level of mathematics teaching language are important topics that every mathematics teacher must explore.

First, thinking about the phenomenon of "group cooperation" in the current classroom.

In this study, the popular group cooperative learning is deeply discussed and analyzed. From "cooperation" to "cooperation", from creating "hegemony" to "superficiality" to solving problems, the problems that should be paid attention to in organizing this activity in the future are pointed out.

Second, listen, think, discuss, say and discuss.

On the basis of this study, I fully exchanged and discussed my thoughts and opinions, and put forward my own confusion and solutions. The content of the seminar was fed back and summarized. It can be said that through this study, I have a deeper understanding and understanding of math class. Really achieved the purpose of organizing this study.

Third, the sense of crisis in learning.

In this study, there are both old math teachers and young college students who have taught me this way for several years. To tell the truth, I always feel that they are still young and despise them. However, through this study, we feel the power of youth. They are not only young, but also have some unique ideas and opinions. "Teachers can't be referees and athletes at the same time" is their view, which is a bit extreme, but it may also show their thinking about the current classroom teaching. Not blindly following experts, not superstitious; I think, in a few years, if they can keep this skeptical spirit, they will certainly grow up quickly. If we don't strengthen our study from now on, in a few years, perhaps, we will be left far behind.

Fourth, strengthen self-study.

In this study, I reflected a lot. I don't have time, and my working hours are very tight-I gave myself several reasons, but in the end, I found that all the reasons were not reasons, because I still had a lot of time. Why? I was thinking. You are lazy and play whenever you have time, for no reason. It was I who relaxed my demands on myself and muddled along-"caused the present situation." I made up my mind in my mind, "from now on, I won't find any reason for everything." I will go my own way step by step, so that people who care about me will no longer be disappointed. "