Reflection on the teaching of angle bisector

Part 1: Reflection on the teaching of angle bisector

Let students grasp the nature theorem and the application of the inverse theorem of the bisector of the angle, and learn the following design of the two theorems: give the conditions and conclusions in the mathematical language, let the students familiar with the conditions and conclusions of the two theorems, and then Take some specific questions for students to apply these two theorems in context. The mathematical theorem is used to describe the property theorem of the angle bisector. Condition: Point P is a point on the angular AOB bisector, PD vertical OA, PE vertical OB. Conclusion: PD = PE. The inverse theorem of the property theorem of the angle bisector is described in mathematical language. Condition: Point P is a point on the corner AOB, PD = PE, PD vertical OA, PE vertical OB. Conclusion: Point P is on the bisector of the angular AOB. Specific topic design, page 22, 2, 3, page 26, question 5. Let the students see which topic to use after seeing the topic.
First, the success
1. It is easier for students to apply these two theorems through specific situations.
After many students learn a certain theorem, they often do not know which theorem to use when encountering corresponding themes. They give the conditions through some corresponding questions or in mathematical language, let the students draw conclusions and say which one is used. The theorem can strengthen students' ability to use theorem.
2, pay attention to the analysis of ideas, students learn to think about problems, pay attention to the writing format, let students learn to clearly express the process of thinking. On the topic of proof, pay attention to slowing down the slope and proceeding step by step. In the initial stage, the direction of certification is clear, the process is simple, and the writing is easy to standardize. At this stage, students are required to understand the proof of ideas and format of the questions, and then gradually increase the complexity of the questions, make small progress, and each step prepares for the next step. The next step is to pay attention to reviewing the content of the previous training. Slow down the slope of the student's geometric proof by proving the problem of the horn bisector.
Second, the inadequacies
1. Students lack the opportunity to explore the geometry independently, but only cultivate the geometric proof of the students.
2. There is no theory combined with real life. The textbook has the conclusion that by determining the location of the bazaar market, the conclusion that “the points on the two sides of the angle bisector are equal to each other on the bisector of the angle” makes the students see the theory from actual needs. But teaching is not reflected.

Part 2: Reflection on the teaching of angle bisector

The introduction of textbooks is a way to recall students' knowledge in a passive way. The introduction of the author allows students to take the initiative to recall the concept of the angle bisector and the drawing method, which is inspiring to the students' thinking. It also allows the students to understand the connection between the former and the knowledge, and to give the students the diagonal of thinking in the form of fill in the blanks. The bisector is the ray, the triangle bisector is the line segment has a full understanding and mastery. In this way, students learn about knowledge and realize the effect of knowing it.
1. This lesson is mainly to use analogy teaching methods - to express the hidden content of the book's knowledge, to give students a beautiful feeling; to write old knowledge and new knowledge in an effective language, in a proper way To create a good atmosphere for the exchange of teachers and students; so that students' learning is easy to achieve twice the result with half the effort. Through the solution of problems, students can learn to analyze problems and solve problems from different angles; let students learn to extend and change problems to cultivate students' creative ability to find problems and ask questions.
2. Emphasis on situational creation, let students experience the process of seeking knowledge. This lesson introduces the model of problem teaching. Its purpose is to guide students to actively participate in the classroom, actively participate in the exploration process of problem-solving ideas, guide students to participate deeply through cooperative learning, and advocate that students should learn to think with their brains and listen with their ears. Use the eyes to observe and use both hands to operate, so that students' speech and action gradually play a role of self-conscious regulation, promote the "internalization" of thinking, and thus develop students' independent thinking.
3. Inadequacies in the teaching process
In the specific teaching process, the entire classroom appeared to be in a hurry, leaving no sufficient time and space for the students to apply the theorem. Especially in the classroom summary, it is obviously not enough to sort out the knowledge. If you want to make a second design for this lesson, I would like to explore only the angular bisector nature theorem, and then add some examples to give students enough time for them to analyze and apply, to implement the exploration and clarity and rationality of the reasoning problem. The process of writing proofs effectively cultivates students' logical reasoning ability and the ability to use knowledge to solve problems flexibly. In addition, the teaching language is not refined, and some repetitions are repeated several times. Excessive dialing deprives students of opportunities for thinking participation; the quality of classroom questions is not high, especially the tempering of classroom language, not only clear expression, but also concise, Leave more time for students and let students have more time to think in class. It should also be noted that the student's subjectivity should not be kept on the verbal, but also in the actual operation, the teacher is the leader of the student's learning, and the student is the true master of learning.

Part 3: Reflection on the teaching of angle bisector

The growth of teachers is to constantly summarize the teaching experience and reflection on teaching. The following is my analysis of the gains and losses of this lesson:
First, the textbook analysis
This lesson is the first lesson of the nature of the nine-year compulsory education curriculum standard experimental textbook eighth grade book 11.3 angle bisector. The angle bisector is an important concept in the national number. It has a very important nature. Through the study of this section, students can enrich and deepen their understanding of the learned graphics, and lay a good foundation for learning other graphic knowledge.
Second, the student situation
Eighth grade students have a certain degree of self-study and exploration, and they have a strong desire for knowledge. With the advantage of the courseware, the brain and hands can be fully moved, the students explore each other, and the enthusiasm is fully mobilized. Teaching and law
Through the creation of situations and hands-on practice, students' interest in learning is stimulated, students are encouraged to think positively, and ways and means to solve problems are sought.
Under the guidance of teachers, students use their own hands-on learning methods to allow students to think about problems, acquire knowledge, and master methods, so as to cultivate students' ability to use their brains and mouths to make students truly become the main body of learning.
Third, the design of the teaching process First of all, this class I am based on students, highlighting the key intentions, combined with the courseware to make it fully explained. For example, in the summarization of the angle bisector, I asked the students to do their own work, and compare the principle of the instrument with the bisector, and leave enough time for the students to prove. In order to solve the difficulty of the nature of the angle bisector, I let students feel the coherence of knowledge through concrete practice, conjecture proof, and language conversion.
Secondly, in the process of explanation, I highlighted the knowledge of the senior high school entrance examination, and let the students feel the examples in life, embody the connection between mathematics and life; infiltrate the aesthetic value.
Again, from the teaching process: situation creation---practice operation---communication----practice and summary---expanding and improving, such teaching links stimulate students' interest in learning and will want to organically combine Get up, let students feel and experience in the way they want to do, and take the initiative to acquire mathematical knowledge. Like adopting this kind of easy-to-difficult approach, it conforms to the students' thinking development and breaks through the key points and difficulties of this lesson in one go.
Fourth, the lack of this lesson
This lesson begins with the lecture. I did not fully convey the modeling ideas of the angled learning tools to the students. It only used it to play a role in the introduction of the lesson, and did not divide the angles of the learning tools and corners after the ruler was drawn. The relationship of the bisector drawing is in contrast.
In the course of teaching, I have some underestimation of the students' ability. In the whole teaching process, I have always been overwhelming. I have not let go of the students to cooperate on their own. In the teaching, I always speak mainly and do not cultivate the students' ability.
The time spent on the class was not accurate enough. Because part of the time was wasted in the beginning of the ruler drawing, so that the exercises prepared in the back did not have time to practice, giving people the feeling that the lesson was not complete. Then there is too much content arranged in the class, which is also the reason for the problems mentioned above. This also makes me notice that the teaching content should not be rigid and dogmatic, but should be more rationally configured according to the content and student situation.
Through the reflection of this lesson, I deeply realized that I still have too many deficiencies in the teaching of the new curriculum reform. In the future, I must not only recognize the importance of the new curriculum reform, but also always implement the first in practical teaching. The mode of post-school education is to better cultivate students' cooperative spirit and inquiry ability.

Part 4: Reflection on the teaching of angle bisector

This lesson is about the nature and judgment of the angle bisector. The following is a reflection from the teaching design of this lesson, the classroom effects, and the inadequacies of this lesson.
I. Reflection on teaching design
When designing this lesson, I think that if you finish the nature and judgment in a class, you can only design this lesson as an inquiry lesson, but the application of nature and judgment can only be placed in the next lesson, so I This lesson is designed as an inquiry lesson, and the exploration of the nature of the diagonal bisector and the judgment theorem is the focus of this lesson. The teaching method of this lesson is inspirational. In order to increase the classroom density and teaching effect and to break through the teaching difficulties of this lesson, I used the geometric sketchpad and slides to create courseware to increase the understanding of any point on the student's diagonal bisector. In the nature and judgment of the student's exploration angle bisector, I created the situation separately, one is to build a platform for the students' inquiry and cultivate the students' hands-on ability. The second is to make students feel that mathematics knowledge comes from reality and is applied to reality. At the same time, it also reflects that the classroom under the new curriculum standards should reflect the subjectivity of students.
Second, re-recognition of the classroom
If the classroom design of a class is the foundation of a good class, then the way teachers are taught in the classroom is even more crucial. This includes the teacher's grasp of the classroom atmosphere and the students, whether the teacher's teaching style is decent, especially when there are many teachers to listen to the class, including whether the language is refined, whether the logical sense of knowledge is coherent, and whether the level is clear. First of all, I would like to say the classroom atmosphere of this lesson. I don’t know if it’s the first lesson or the students are a little nervous. The students who usually answer the questions don’t dare to speak, so I feel that the atmosphere in the classroom is still a bit dull. Of course, when mobilizing the enthusiasm of students, teachers should try to eliminate the tension of students and let students learn knowledge easily and happily in class. This is a test for any teacher. Secondly, by looking at his own video, the details that he usually did not care about, including his position and standing on the podium, his casual gestures and spoken words were exposed. I feel that my carefully honed language is still a bit confusing in the video. I always feel that I have so much regret when I go to class. Again, the time spent on the class is not accurate enough. Because part of the time was wasted in the beginning of the ruler drawing, of course, the waste of time and the way I teach the ruler is not reasonable enough, so that The exercises prepared in the back have no time to practice, giving people the feeling that this lesson is not complete. Then there is too much content arranged in the class, which is also the reason for the problems mentioned above. This also makes me notice that the teaching content should not be rigid and dogmatic, but should be more rationally configured according to the content and student situation.
Third, the reflection of the inadequacies
By looking at my own video lessons, I feel that there are still many places in my classroom teaching that need to be improved and improved. In particular, the tempering of the classroom language is not only clear, but also concise, leaving more time for the students, allowing students to have more time to think in the classroom. It should also be noted that the student's subjectivity should not be kept on the verbal, but also in the actual operation, the teacher is the leader of the student's learning, and the student is the true master of learning. It is also necessary to implement the mode of pre-learning and post-teaching in practical teaching to better cultivate the cooperative spirit and personal ability of students.

Pt 5: Reflection on the teaching of angle bisector

This lesson uses the process of “creating situation—independent inquiry-cooperation exchange-feedback test”
First, attach importance to situational creation, let students experience the process of seeking knowledge. This lesson introduces the model of problem teaching. Its purpose is to guide students to actively participate in the classroom, actively participate in the exploration process of problem-solving ideas, and guide students to participate deeply through cooperative learning.
Second, the effective use of multimedia-assisted teaching to increase classroom teaching efficiency. After the students use the hands-on practice, conjecture, generalization and other activities, use the geometric drawing board to demonstrate the point movement on the angle bisector, the change of the distance from the point to the angle, further understand the law of change and quickly feedback the corresponding conclusion. Lay the foundation for the induction, generalization and proof of the next proposition. The dynamic demonstration of courseware has better help for students with weak abstract thinking ability and effectively promotes the transition from intuitive thinking to abstract thinking.
Third, pay attention to the evaluation of the students' mathematics classroom learning process, and try to fully understand and respect the students' speeches. Give sincere affirmation to the correct statement, intentionally cold-process the wrong opinions, and create opportunities for students to argue. Students can dare to speak, dare to discuss, and dare to evaluate in the classroom. Insufficient is sometimes too impetuous, more time should be left to students, so that students have more time to think in class.