Reflection on vertical and parallel teaching

Part 1: Reflection on Vertical and Parallel Teaching

"Vertical and Parallel" is taught on the basis of students' understanding of straight lines and angles, and is the basis for understanding parallelograms and trapezoids. Vertical and parallel are two special positional relationships of two straight lines in the same plane. In order to let students find the positional relationship of two straight lines in the same plane and draw conclusions. I strive to reflect in the design and implementation of classroom teaching: 1. Pay attention to creating a living situation, so that mathematics learning is closer to the students; 2. Let students complete the construction of knowledge through hands-on practice, independent exploration and cooperation and communication; 3 Efforts will be made to create a new type of teacher-student relationship, so that the classroom will rejuvenate; 4, pay attention to the stimulating role of evaluation and enrich the emotional experience of students. For this lesson, I mainly grasp the following points:
1. Accurately grasp the starting point of teaching and strive to return a “real” math class to students.
This lesson starts from the students' actual situation, pays attention to the students' life experience and knowledge base, starts from reviewing the "straight line" knowledge, arouses the students' memories, and makes a good street preparation for the new knowledge inquiry learning. At the same time, gradually cultivate students' interest in mathematics research, and use the charm of mathematics to attract and infect students.
2. The methods, methods, and teaching methods of classroom teaching are unpretentious.
In the teaching, I firmly grasped the "in the main line of classification" to carry out the inquiry activity, and proposed "Drawing the two straight lines that the students imagined on the infinite plane?" "Can you carry out these kinds of situations?" Sub-category?" This has the problem of thinking value. Students can observe and think through various activities such as drawing a picture, drawing a point, saying something, and gradually realize that the positional relationship of two lines in the same plane There are only two cases of intersection and disjoint, and there are two cases of right angle and no right angle in the intersection. This kind of teaching not only conforms to the students' cognitive rules, but also through classification and hierarchical understanding, which not only conforms to the students' cognitive rules, but also helps to improve the students' life reality, allowing students to discover mathematics knowledge from their own side and further develop students' ability to observe. Found vertical and parallel phenomena. When dealing with teaching difficulties "in the same plane", I use the courseware to produce a rectangular parallelepiped, draw two disjoint straight lines on different faces of the cuboid, ask students whether they are parallel, and help students understand the vertical and parallel relationship "must be in the same plane" Inside, intuitively in place.
3. The training points and expansion points of the new knowledge are solid and effective.
In addition to finding vertical and parallel phenomena from the theme map, looking from life, looking from the side, let the students put aside, fight, draw a picture... Through these exercises, let students further deepen the concept of parallel and vertical The understanding further expands the knowledge and enables students to overcome the boring feeling of learning mathematics. Let students really participate in the learning process and improve their abilities during the learning process.
There are also many shortcomings in the teaching of this lesson. In short, in the face of the success and failure of the new curriculum classroom teaching, I have taken it frankly, and will continue to re-learn and re-implement the "new concept" in the continuous self-reflection. I believe that I can grow up in constant self-reflection. Constantly develop in self-practice and innovate in constant self-growth.

Part 2: Reflection on Vertical and Parallel Teaching

"Vertical and Parallel" is the teaching content of the first class of the fourth unit of the fourth grade of the new curriculum standard. This part of the textbook is based on the knowledge of students learning straight lines and angles. It is also the understanding of parallelograms and trapezoids. The basics. Since vertical and parallel are two special positional relations of two straight lines in the same plane, and they are widely used in life, whether you are walking on a wide street or sitting in a bright and spacious classroom, you should look around. There is no shortage of vertical and parallel phenomena. For the children of the fourth grade, they should have the experience: which lines are crossed and which lines are not crossed. So what we have to do in class is to let the students experience in the same plane. The two lines that do not intersect are called parallel lines. There is a special kind of vertical in the cross, which makes the students' understanding rise to the level of thinking. In view of this, at the beginning of the lesson, students are allowed to draw two lines in different positions on a white paper, and then select representative paintings from the students' works to classify them, thus leading to the concept of parallel and vertical. Then let the students find a way to talk about the parallel and perpendicular phenomena in life, and deepen the students' understanding of vertical and parallel. Finally, through the search, pendulum and other links, while students further understand vertical and parallel, feel that mathematics is around us; feel the meaning of mathematics by appreciating the vertical and parallel in life.
1. At the beginning of the lesson, ask the students to draw the position of the two straight lines. Now I want to let the children close their eyes and imagine: a straight line appears on a large plane, and then another one appears. Straight line, then what is the positional relationship between the two lines? Ask the classmates to open their eyes and draw the position of the line you imagined. In this way, using space imagination as an entry point, let the students close their eyes and imagine that two lines appear in an infinite plane, and ask the students to draw the two lines that they imagined, and directly enter the atmosphere of pure mathematics research, creating such a The problem situation of pure mathematics research uses the charm of mathematics to infect and attract students, and is conducive to students to carry out research, especially to lay a solid foundation for deeper research and exploration, to make a good transition, and gradually cultivate students' interest in mathematics research. .
2. Let the child feel the knowledge in the experience. In the concept of parallelism, "the two lines that do not intersect in the same plane are parallel to each other", I immediately asked one question: Why do you want to add the words "mutually"? When the problem was thrown, I regretted it, because the children just had a general idea of ​​"parallel" and immediately asked them to say "why". As you can imagine, the students were confused by me, only very few. Several students can say a few words according to their own understanding. Later, in the course of the evaluation, many teachers shared the same feeling. As a relatively abstract conceptual knowledge, students must be sensible in their operations and experiences. If they use verbal explanations, they will only get half the effort. In fact, this issue is very important, but it should be considered and considered at the timing of the emergence. Teacher Lu suggested that this problem is actually better after letting students say the relationship between two parallel lines.
3, time is not good enough. Strictly speaking, there is still a link that has not been completed, although it does not affect the integrity of the entire class, but at least the latter part of the link does not appear to be a pity for yourself.

Part 3: Reflection on Vertical and Parallel Teaching

The content of this lesson is taught on the basis of students' understanding of straight lines and angles. It is the basis for understanding parallelograms and trapezoids. Vertical and parallel are two special positional relations of two straight lines in the same plane, which have a wide range of applications in life. How to abstract the life experience of students into mathematics? Using mathematical eyes to perceive vertical and parallel phenomena in life? How to further develop students' spatial imagination ability, let students find the positional relationship of two straight lines in the same plane and draw conclusions? Focusing on these goals and combining with our mathematics group's topic "Development and Research of the National Primary Mathematics Reading Teaching School", I have tried to embody the following characteristics when designing the lesson plans.
1. Use a little time before class to try out a small story with certain mathematics problems in the multimedia, let the students read and think while preparing for the class, to improve the students' reading ability and thinking ability, and the effect is still Yes, there were students who painted their own results on paper. After class, students came to me to exchange results. Adding such a small story and interesting questions to each lesson is good.
2. Create a pre-study situation and feel the positional relationship between two lines
In the course of design introduction, I prepared two small sticks to ask the students. If the stick is thrown on the ground, how can these two sticks be placed? Have students use a straight line instead of a small stick on paper to draw a picture of where it may be placed and display it. There are two reasons for this design: one is to reflect the idea that mathematics knowledge comes from life, and the other is to let students develop good habits. In the media, I will show the possible placements and number them in order to improve the operability of students in classification. After the students have determined their ideas, they will communicate in the group. Then I let the students imagine what happens if the stick becomes two straight lines and extends infinitely at both ends. Here, we make full use of the students' own learning ability, organize them in the group, and divide the possible situations into two categories. That is, intersecting and disjoint straight lines are displayed on the rear projection, where the thoughts of the limit and the thought of the collection are infiltrated.
3. With the classification as the main line, through the students' independent learning, collaborative exploration, and experience the positional relationship between the two lines in the same plane.
In the participation and active discussion between students and teachers, the consensus of classification is reached, that is, one type of intersection and one type of disjoint. This naturally leads to the fact that the two lines that do not intersect in the same plane are called parallel lines, and they can be said to be parallel to each other. From the perspective of the formation after the intersection, the students find a special case "+", which leads to the concept of mutual vertical. Guide students to use tools to verify the phenomenon of intersecting at right angles. Develop students' scientific and rigorous learning attitudes.
Make mathematics live and discover mathematics from the students. Find vertical and parallel phenomena. Develop students' ability to observe and further find vertical and parallel in life.
Aspects worth reflecting
1. It is a bit difficult to deal with the difficulty. The slow progress of this class is more, and some slow-moving students do not understand the position. Especially, the students in the same plane do not understand well. If they do not directly give In the same plane, I want to show the words "in the same plane" after I show two lines that are neither parallel nor intersect. I think the effect will be better.
2. This class will let students go home in advance one day in advance, because vertical and parallel are very professional, students have hardly heard of it, but often see such examples in life. Let students pre-read, so that these two concepts enter the student's impression in advance, at least the students have a general, preliminary understanding, we will explain through the norms in the classroom, the effect is better. Otherwise, it is difficult to talk to the examples in life in a timely and direct manner in the class. It is difficult to relate to the examples in life, not to mention the concept of verbatim. The impression is not deep and the understanding is not profound. However, from today's teaching, there are very few students preparing for the study. Although the concept of the accident is slow, and each concept has been read by the students several times, I will explain the places that I don’t understand, and there are still some students behind. I know that I can’t tell.
Of course, students must have a process to accept new mathematical concepts. The first is to accept the name of the concept. It is called Shunkou to understand it further. If you understand it, you can contact other knowledge. Otherwise, the student has not remembered the name of the concept. Teacher I went to explain it blindly. It is estimated that the students are really confused. I don’t know who the teacher is telling.

Part 4: Reflection on Vertical and Parallel Teaching

American linguist Bronfeld said: "Mathematics is just the highest level that language can achieve." Neglecting the teaching of mathematical language is tantamount to buying a bead. If mathematics is a ship carrying knowledge, then the mathematical language is water. The deeper the water, the bigger the boat is lifted. We all know that "people who want to be clear will be able to make it clear, and those who can speak clearly must be clear." Developing students' expressive ability is an important teaching goal of our mathematics class. In today's "Vertical Parallelism" lesson, there is a lot of conceptual knowledge that requires students to narrate in a concise, accurate, complete, and organized language that enhances students' deeper understanding of these abstract concepts. I will reflect on this lesson:
First, thinking
1. In this lesson, each concept is made by the students themselves. I use the tips, help, supplements, and the teacher's exemplary language to let the students sum up the complete concept and improve the students' accurate mathematics. At the same time, the language expression also makes the students deepen their understanding of these abstract concepts.
2, how to understand the concept of each other is the focus of this lesson, I let students use different methods to describe the relationship between the two lines, so that students deepen their understanding and mastery of knowledge. At the same time, in this class, I arranged some group cooperation content, paying attention to giving more students the opportunity to “speak” and let every student have an opportunity to express.
3. After the main content of this lesson, after learning, our group designed a link to “combine life reality” and let the students “speak” again, which not only exercises the expressive ability, but also has a total for this lesson. Review. So I think that the students' understanding of the knowledge points of this lesson has achieved the expected teaching goals.
Second, miss
1. Because my guidance is not in place, some students are not accurate enough in language expression. For example, when classifying several relationships of two lines, the students narrate Luo Wei and cannot say the key points, so the time is delayed. It affects the following teaching links and does not complete every link in the instructional design. In the enumeration of students, there are still parallel and vertical phenomena in the life, the language is not standardized, and my guidance has not been able to keep up.
2, because the usual training is not enough, so some children are still afraid to speak, so many students in this class have fewer opportunities to speak, or even do not speak in public, then their learning effect is questionable.
3. In the expression of the teacher's exemplary language, I have not done enough, and the research on teaching materials and teachings is not deep enough, and business learning needs to be strengthened. The writing of the blackboard needs to be strengthened.
Third, think
From the overall teaching, I basically completed the teaching objectives of this lesson. However, due to the personal language, I did not promptly and effectively guide students to express in a concise and accurate language, so the difficulty of teaching is not prominent. Most of the students are not actively involved in the initiative, and the learning efficiency is not high. The cooperation and communication of the group is only in the superficial form. Whether each student has the expression and expression is correct or not.
Fourth, thinking
In the future teaching, I must constantly strengthen the communication between teachers and students. It is necessary to evaluate the correctness of the students' responses. It is necessary to grasp the bright points in the students' thinking process to affirm. For those who are not good at words, give more enthusiasm and encouragement. Gradually let them say that they can speak, speak well, and be eloquent, so as to achieve the purpose of promoting the development of thinking. Students who are able to speak through thinking can make the students speak for themselves and let the students narrate in a clear mathematical language. In the future teaching, we must also pay attention to the hands-on operation of students. When guiding students to do hands-on operation, it is necessary to pay attention to let students use mathematical language to systematically describe the operation process, express the thinking process of acquiring knowledge, and combine hands-on operation, brain-brain understanding and dynamic expression to promote the effective transformation of perception. For the purpose of internal intellectual activities, deepen the understanding of knowledge. The summary is an important part of classroom instruction. Through the summary, students can improve their comprehensive generalization ability and clearly recall the main points of this lesson. The classroom section is one of my major weaknesses. In the future, I will often carry out purposeful classroom summaries in the classroom to improve the students' analytical ability, generalization, classification and other logical thinking skills, and improve the language expression ability.
Below, I would like to ask all leaders and teachers to provide valuable opinions to jointly promote our teaching and research capabilities.

Part 5: Reflection on Vertical and Parallel Teaching

Starting from the goal of this lesson, here are a few highlights of my class:
1. Start the course and solve one of the difficulties in this lesson: the perception and understanding of “plane and in the same plane”.
2. With the classification as the main line, through the students' independent exploration, experience the positional relationship between the two lines in the same plane.
Through imagining, hands-on line drawing, graphic feedback, classification, observation, analysis, discussion, verification, induction and other activities, students can gradually realize from these complex and diverse situations that the positional relationship of two straight lines in the same plane only intersects and In the two cases of disjoint, “disjoint” leads to parallel with each other, and at the same time deepens the understanding of “mutually”. Later, it demonstrates that there are two cases of right angle and no right angle in the intersection, and the concept of “mutually perpendicular” is obtained. Through two classifications and hierarchical understanding, I think it is possible to improve students' spatial imagination and to develop students' initial problem research awareness.
3. Develop students' spatial imagination in operation and imagination.
Mainly in the following aspects: 1 imagine the blackboard as a plane and the imagination of the two linear positions in the same plane, and then draw on paper. Imagine that when two lines appear on the plane, it is not for students to directly imagine two lines, but to appear one by one, which is conducive to students to imagine more positional relationship between the two lines, and to cultivate students' spatial imagination. 2 pairs of seemingly two lines do not intersect but the actual intersects the situation first let the students imagine, in the drawing verification; 3 for the teacher's example of the imagination and operation verification; 4 expansion exercises in the small stick operation and there are countless An idea of ​​a line parallel or perpendicular to a known line. When guiding students to do this set of questions, take a layered approach. It is for students to place two yellow sticks parallel or perpendicular to the known red sticks, and then imagine that the second and third sticks are parallel or perpendicular to the known sticks. Finally, observe the positional relationship of these small sticks, and imagine the positional relationship of other small sticks. This will help students to draw rules and further develop students' spatial imagination.
4. Closely integrated with life
Looking for the imagination of each other in the classroom parallel and perpendicular to each other, pay attention to the conditions, I will break through the difficulty of "in the same plane", when the students said that the two lamps on the ceiling are parallel, but When the two lamps are not in the same plane, I will promptly indicate to the students that they must be parallel to each other in the same plane. In the design exercise, look for parallel and vertical phenomena in letters or in your own name.
In this lesson, there are still some shortcomings: in the first link, the knowledge of the same plane is too much and general, so that students think that they are the same side before and after. I want to tell students directly mathematics. Book, it has six planes, we now touch the front plane, its left side is another plane, the front and back are not the same plane, showing a blank sheet of paper in the plane in front of the white paper, then later What happened to it? Forgetting that the time on the board is not well mastered is not enough.