Reflection on the teaching of the angle

Part 1: Reflection on the teaching of the angle

Primary school students are mainly image thinking, but mathematics has a high degree of abstraction. Therefore, when they learn mathematics knowledge, they can only barely know it. It is difficult to know why it is wrong. In order to enable students to truly understand the abstract mathematical theory and enhance the teaching effect, we often use visual demonstrations, activity exploration and other methods. I used a very simple and very effective method in the "Awareness of the Corner" lesson - by reason.
Since the angles students see in life are all connected with each other, it is difficult to really understand that "the size of the corner has nothing to do with the length of the side", which makes many teachers feel very difficult. When teaching, I first let the students demonstrate through the demonstration of the activity corner that "the larger the angle between the two sides of the corner, the smaller the angle, the smaller the angle of the two sides"; then let the students compare The size of the two corners in the following three groups. When the students compared the size of the two corners in the third group, the opinions disagreed. Some students thought that it was the same size. Some students thought that it was the second corner. I did not judge and asked them to talk about it separately. Than. The classmates who held the second opinion thought that the two sides of the second corner were widened on both sides. I listened and nodded and said: It seems to make sense. Then I asked a classmate who was thinner in the class to stand up and let other students come to the arm of me and the classmate. Who is thick? After everyone agreed that my arm was thick, I said that the classmate's arm was thick and compared in public with his wrist and the student's upper arm to prove that my conclusion was correct. At this time all the students shouted: unfair, not the same. At this point, the teacher is on the way: when you compare the size of the two corners, is the size of the same fork? The students who hold the second opinion suddenly smiled embarrassed, then I will do it again. The two corners in the first group overlap, so that the students clearly see that the two corners are the same size, so that the size of the corner is irrelevant to the length of the edge.
By analogy and living things, activate the students' existing experiences and experiences, trigger the inspiration of ideas, and quickly understand the abstract mathematical theory with simple and familiar affair. Since the abstract logical thinking of primary school students is still directly related to the perceptual experience, it still has a large composition and specific image. Therefore, for some mathematical knowledge that is difficult to visually demonstrate or explore activities, we may wish to use For example, methods such as the use of life-related affair to explain the abstract mathematical theory will also achieve satisfactory results. Perhaps "lack of reasoning" lacks a high degree of rigor, but for elementary school students who are just beginning to learn mathematics, strict understanding is not as strict as understanding, because only the knowledge that is truly understood can be mastered and applied by students. _ Elf Children's Network

Chapter 2: Rethinking the Teaching of Angles

First, use mathematics in a living classroom
How can we make children feel that mathematics is a visible, tangible, and useful subject, and it is no longer a boring math game. It is the biggest problem I have considered in this lesson. The biggest feature of the new textbook is to start from the life scenes that students like to see, so that students can understand that mathematics is in our lives, and life is inseparable from mathematics. However, how to use these conditions to creatively exert the subjective initiative of teachers and make mathematics teaching closer to the reality of life is to ask our teachers to think further. One of the main objectives of this lesson is to guide students to gradually upgrade the "corner in life experience" to "mathematical angle." Therefore, on the basis of arousing the students' existing experience, these angles are abstracted through a dynamic process, and the students perceive the image of the mathematical "corner" through careful observation. These "mathematical horns" are somewhat different from the students' "angles in experience", and they also create a cognitive conflict in their psychology, and it is this kind of conflict that will inspire students to invest with higher enthusiasm. To compare and discover.
Second, do mathematics in the active classroom
Freudenthal once said: "The best way to learn an activity is to do it." Effective mathematics learning activities cannot rely solely on imitation and memory. Hands-on practice, independent exploration and cooperation and communication are important ways for students to learn mathematics. Therefore, we must attach great importance to the practical operation training for students in the teaching process, so that students can perceive in practice and solve problems and acquire knowledge through their own efforts. In actual teaching, teachers should adopt flexible and diverse forms according to the age characteristics and knowledge level of students, and stimulate students to participate voluntarily, and give full play to students' initiative, independence and creativity, so as to achieve twice the result with half the effort. The characteristics of primary school students are: "If you have heard it, you will forget it. If you have read it, you will remember it. If you have done it, you will really master it." In the teaching corner, the problem is mainly reflected in two aspects: First, draw a right angle, draw The right angle is more difficult than the general angle. The direction of the two sides cannot be fixed. The right angle can only be determined according to the right angle of the triangle. With certain restrictions, the method of drawing the right angle is more difficult than the method of drawing the general angle. Big, then I especially emphasize that the apex of the student's right angle must be pointed, the right angle also has two sides, can not be drawn into a triangle along the triangle, and emphasize that the right angle symbol must be square, do not draw an arc. Second, when judging whether a corner is a right angle, the student does not rotate the right angle on the triangle to verify. So I combine the demonstration on the blackboard with the visual and dynamic presentation method on the courseware, letting the students know how to judge whether an angle is a right angle, and also in the comparison, this angle is larger than the right angle or smaller than the right angle. However, I feel that if you want each student to learn how to judge and compare, you have to let the students personally operate and learn mathematics and master the methods. So I asked the students to demonstrate many times and deepen their understanding.
In short, this kind of "experience learning" is carried out in the teaching of mathematics in elementary schools. Give full play to the main role of students, let students be in a certain situation, call various senses to experience and feel; pay attention to practice, create more practical and specific image problems close to students' lives, in order to fill the gaps in student experience and promote Students feel in the experience.

Chapter 3: Rethinking the Teaching of Angles

The flat angle and the peripheral angle are two special angles. The students understand it more abstractly. This lesson takes full advantage of the learning tool "activity angle", allowing students to fix one side of the corner and the other side of the rotation angle to observe the formation during the rotation. Various corners allow students to establish the concept of a corner in the “play” tool. Understand the connection between acute angle, right angle, obtuse angle, flat angle, and circumferential angle.
The teaching design mainly reflects the following points:
1. The focus of this lesson is to recognize two special angles: the flat angle and the square angle. I remember an educator said: "Let the students forget to listen, let the students read it and remember it, let the students do it." In order to let the students experience the process of understanding, I use the activity. Angles, respectively, show sharp angles, right angles, obtuse angles, and then guide students to find the common points of the angles: the angle is a figure composed of two rays from a vertex, in order to make it understand the special angle, paving the way. The angle of the movement I made, the two sides of the corner are made of materials of different colors, and the two sides are not the same length, plus a striking apex. The teaching aids produced in this way play an important role in understanding the special angles of the students.
2, the teaching of this lesson, starting from the living environment of the excavator work, find the mathematics problem in life---angle, so as to review the knowledge of the corner, further study the relevant knowledge of the corner, let the students feel the mathematics knowledge and life close Connected to develop the habit of paying attention to the exploration of mathematical phenomena in life. In the study and study, the understanding of the flat angle and the perimeter angle makes full use of the knowledge transfer. It is necessary to use the operation of the moving angle to feel the formation of various angles, and then form a new angle to discuss the characteristics, to understand the flat angle, the circumference angle, and master the Features. I feel that the formation process of knowledge is more natural for students, and it becomes abstract and concrete, which is conducive to the students' good grasp.
3, multimedia intuitive teaching, the effect of doing more with less, especially on the drawing and representation of the flat and the corner, making the abstract concept more visual and concrete. In addition, when using the display function of the booth to understand the flat angle and the angle of the week, the effect is clear and clear, which is convenient for the students' overall cognitive learning.
4, difficult breakthrough
Follow the students' cognitive rules, based on the students' understanding of the diagonal, start with the most familiar right angle, sharp angle, and obtuse angle, and finally understand the flat angle and the square angle. The understanding of the flat angle and the angle of the week is difficult in this lesson. Although the students have already recognized the right angle, the acute angle and the obtuse angle, the appearance of the flat angle and the angle of the corner still conflicts with the cognitive experience of the students. In order to break through the difficulties, I seize this cognitive conflict. Two debates have been carefully designed to try to make students' thinking collide with each other in the process of debate, making the whole process of debate become a process of students' serious speculation, active exploration and self-construction. It also tries to teach students to analyze problems from the definition. Methods.
5, from life, to life
Mathematics comes from life. I have always believed that daily life should be a big classroom for students to learn mathematics, and students should be trained to observe the habits of life from a mathematical perspective. Therefore, this lesson has made some efforts in this area: from the busy construction site, the various angles formed by the bucket arm when the excavator works, let the students find the various types of corners around the end of the class, and finally demonstrate various life. The example of the corner can certainly stimulate the desire of students to find their horns in life and the enthusiasm of observing life with a mathematical perspective.

Chapter 4: Reflections on the Teaching of Angles

In mathematics teaching, I always adhere to the teacher's leading line, taking students' inquiry as the core, developing students' thinking as the purpose, and cultivating students' mathematical emotions as an opportunity to let students do mathematics in middle school mathematics. Use mathematics in mathematics and mathematics in mathematics.
My whole teaching activity is interesting: because the second-grade children are not very interested in pure knowledge, so I put the story through the whole teaching process, so that students can learn in a pleasant atmosphere, which also reflects " In the middle school of happy middle school mathematics, learning happy mathematics. Such a design is bound to arouse students' interest in learning and let students learn new things in a pleasant atmosphere.
Mathematical “experience” teaching refers to students actively participating in mathematics activities under the guidance of teachers, personal experience, and gaining rational understanding and emotional experience of mathematical facts and experiences. It allows students to participate in a rich and lively activity as a cognitive subject, fully participate in the learning process, and truly become the protagonist of the classroom, thus learning mathematics in experience and creation.
First, contact the reality, let students experience life mathematics
The “experience” in the pedagogical sense is both an activity process and the result of activities. Many concepts, rules and algorithms in the mathematics of the country can find their life background by searching for the source. Therefore, the teaching content should be optimized in the context of "life" as the background, life materials, life experience and life situation. As an important resource, introduce and provide to students to understand and experience. Therefore, in the teaching of this lesson, I started with the sensible object, abstracted the angle of the figure, revealed the characteristics of the corner, and then let the students find the corners in the things around them, make the corners, and finally explore the size of the comparison angle independently. The method guides students to gradually deepen their understanding of the diagonal.
Second, practical operation, let students experience the process of knowledge generation
Through practical operation, students are open to the whole brain, guiding them to participate in various senses such as eyes, hands, brains, and mouths, so that students can experience the dynamic generation of knowledge and help students understand concepts. Corner is more abstract for second-year students, and student acceptance is more difficult. Therefore, in order to help students better understand the angle, I will observe, operate, demonstrate, experiment, and cooperate in the whole course in the whole course. The basis for guiding the student experience. The concept of cognition, by looking for, looking at, touching, folding, doing, doing, comparing, thinking, speaking, drawing, painting, and living in a happy and personal way, Personally experience the different educational scenarios created by teachers according to the teaching content, and experience the process of knowledge formation in a large number of practical activities. Let students analyze and observe in the hands of observation. Therefore, the students' interest in learning is further mobilized, and the best combination of teaching methods and learning methods is made, so that all students can participate in the process of exploring new knowledge. Taste the autonomy. Collaborate to explore the success and joy of learning. Self-confidence and a sense of accomplishment have also increased.
Third, return to life, let students experience the process of applying knowledge
Students should be allowed to learn mathematics and develop mathematics in their activities and in real life. It is necessary to solve the practical problems encountered, cultivate students' initial logical thinking ability, use mathematical thinking and methods to further analyze the ability to solve problems; in the process of applying mathematics, cultivate students' sense of innovation; let mathematics return to life and obtain learning A positive emotional experience that is useful.
In the lesson of "Awareness of the Corner", if you cut two corners, will you get a few corners? "The guidance of this experience process leaves the blanks to the students, so that their thinking has more space, and the different ways of thinking are compared. In this process, not only the students' sense of numbers, space, etc. Cultivation is achieved through experience; and the correct way of thinking is tempered in a violent collision.
In short, this kind of "experience learning" is carried out in the teaching of mathematics in elementary schools. Give full play to the main role of students, let students be in a certain situation, call various senses to experience and feel; pay attention to practice, create more practical and specific image problems close to students' lives, in order to fill the gaps in student experience and promote Students feel in the experience: mathematics in life is everywhere, everywhere. This kind of psychological experience will make students have a stronger interest in knowledge, and also make students more willing to participate in classroom learning activities. Let students gradually learn to use mathematical eyes to examine practical problems, to conceive social reality, and to profoundly understand the enormous value and infinite power of mathematics. Students are deeply aware of how important mathematics is to our lives, thus stimulating their strong desire to learn mathematics, from "learning mathematics" to "doing mathematics" and then to "using mathematics."

Chapter 5: Rethinking the Teaching of Angles

"Angle" is more abstract for second-year students. It is not easy for students to establish correct appearances. It is also difficult for students to accept them. Therefore, the teaching of this lesson focuses on the correct appearance of the students to form the corners. The difficulty of each part of the name is to let students know what the size of the corner is related to. Therefore, throughout the class, I will observe, operate, demonstrate, verify, communicate and other methods organically throughout the teaching process, guiding students to abstractly summarize on the basis of perception, fully following the perception - the representation - to the concept The cognitive law adopts teaching methods such as finding, seeing, folding, taking a ride, comparing, and speaking, so that students can feel in a large number of practical activities and experience the "corner". Understand the relationship between the size of the corner and the relationship between the two sides.
When the size of the breakthrough angle is related to the difficulty of opening the two sides of the corner, the activity of the inquiry is carried out by the operation, so that the students realize that the two sides of the corner are opened and closed, and the size of the corner changes, so that the student experiences the angle. The size and what is relevant. For how to compare the size of the corners, the students realize that by comparing the size of the comparison angle, they should stack the vertices of the two active angles, align one of the sides, and then look at the other side. Whose mouth is big? The angle is large, which effectively strengthens the teaching focus, breaks through the teaching difficulties, and the effect is good. However, because of the limited time in teaching, I can only let students understand the sentiments through display reports, without special emphasis and summary, so some of the contents of this part of the students do not understand very thoroughly.
In organizing teaching activities, it is not so easy for teachers to be a good guide and organizer. First of all, in the organization of teaching activities must be able to flexibly regulate and control, grasp the essentials of mathematics to communicate; secondly, in the activities, teachers must guide students to carry out purposeful activities, and at the same time ensure the participation of students. To be broad, let the whole class be able to really move, teachers should also interact effectively with the students; finally, let the students truly become the main body of learning, through some creative activities, exploratory activities continue to train students Self-exploration ability, language expression ability, and innovation ability.
Teaching and then knowing the insufficiency, if the teaching concept can be more open, increase the mathematical activities of rich diagonal sensibility and rational understanding, let the students participate, can face the whole, improve the effectiveness of learning, this class I think will be better .