Reflections on the teaching of drawing circles: 5 articles

Reflections on the teaching of drawing a circle 1

A class is over. Although Director Ding, Director Shi and the little teacher on

Reflections on the teaching of drawing circles: 5 articles

Reflections on the teaching of drawing a circle 1

A class is over. Although Director Ding, Director Shi and the little teacher only politely pointed out a few places, I know that the biggest problem in class is "classroom control ability".

I have been worried before class: I am afraid that there will be problems in class that I have no preset, which will affect the teaching content later. Therefore, I am particularly nervous. There are several inappropriate things in class.

First, when revealing the concept of perimeter, students should point out where the perimeter is for the objects in their hands, and make it clear that the perimeter is the length of the curve that forms a circle. Moreover, the method of asking students to point to the perimeter of two circles in my hand is not standardized.

Second, when students were asked to guess the relationship between the circumference and diameter of a circle, they were originally arranged to say why after guessing, but because they were worried about such problems, students were afraid to say why later, so they had to wait at least a few minutes. So it was deleted when designing the lesson plan.

Third, let the students talk about the method of measuring the diameter and circumference of a circle. I've been thinking about how to comment on a method after students say it before class, but I forget that there are various methods, but I don't give students more time to generate more methods. I remember listening to teacher Chen Jian's Discovery Law in primary school. Students come up with more and more ways, and he also shows them one by one in the courseware. Ni Dongyan, who went with me at that time, was very surprised. "Is this courseware made by him now?" The director of Nantong teaching and research section, who was sitting in front of us, turned his head and said to us, "He has made a preset before class, and students should think of their teachers." What I'm showing now is that I'm worried that students will come up with more and more methods that take up a lot of time in this session, so I didn't think much about more methods for measuring diameter and circumference before class.

4. After revealing that some students have made mistakes in the communication of pi, and this experiment sheet has been presented on the big screen, I should ask this group of students to take out this circle in time for the whole class to measure, otherwise many students will still think about what happened to this circle just now even if they know the conclusion. Maybe it's time again.

5. Back to the competition route between the king and the two generations at the beginning of the class, the first purpose is to test the use of pi formula in time, and the second purpose is to infiltrate the idea of estimation. However, the achievement rate of the second goal in the class may not be ideal, probably because of my introduction and comments.

Although I have written so much, and the advice they gave me is very pertinent. For example, Director Wei Shi suggested that the exercises should be close to life, and the exercises in the book were not used well. Director Ding suggested that the circle prepared by students should be made of cardboard, which is beneficial to the experimental operation. But I know what I lack most is the basic skills of mathematics teaching. Just when they commented that Mr. Ma Lihua's class was "very mathematical", what was missing from my class? Lack of confidence in mathematics teaching.

The class is over, but the pace of really reflecting on your classroom has just begun. In the morning, I specially called my former colleague Yao Xinfu. He said, "In math class, we must position our own language well, especially the revelation of some concepts and the elaboration of thinking methods." There are other people's teaching plans in class. If you don't fully understand them, how can you carry them out in class? You can't look at the basic teaching skills, but practice them. You try to record the words in your class after class, and you will find out how many languages are actually needless to say, and how many words are actually expressed more accurately in another way ... "

"Having a case in mind but no case in action" is my constant pursuit of teaching art, and effective classroom teaching is also the most basic duty of teachers' teaching work.

Reflections on the teaching of drawing circles II.

The focus of this lesson is to understand the meaning of the circle and the derivation process of the calculation formula. The difficulty lies in understanding and mastering the circumference formula and pi of a circle. According to these goals and my research topic-the design of the junction of old and new knowledge, in the teaching process, before each new knowledge point comes into being, I have carefully designed the problems of stimulating thinking, enlightening thinking and expanding thinking. In-depth and step by step. The classroom effect is quite good.

Before teaching, in order to enable students to use the law of knowledge transfer to summarize the concept of circumference, before exploring new knowledge, design review questions: what is the circumference of a rectangle and what is the circumference of a square? Then ask: what is a circle? At this time, students can use the concept of the perimeter of a square and a rectangle to summarize the meaning of the perimeter of a circle: that is, the length of the curve that encloses a circle. Then I designed the question: How to measure the circumference of a circle? There are several ways. I broke the traditional practice of teaching whatever the textbook is, and let students explore and create freely. The students think and do with the questions raised by the teacher. Give students the initiative to learn, so that students have enough time to think, free space for activities, opportunities for self-expression and more confidence in creation. The students are all in high spirits and eager to try. Through hands-on operation and bold practice, I explored three methods to measure the circumference, which promoted the development of its creative thinking. I affirmed their method. When students taste the joy of success, I lead out the game of throwing small balls and let students observe the virtual circle formed. Can you measure the circumference of the virtual circle with the method just now? This problem breaks the students' cognitive balance and makes them deep in thought. There are many circles in daily life that cannot be measured at all. At this time, I am here to guide students to guess and observe the game of throwing the ball, and finally make students realize that the circumference of a circle is related to its radius or diameter. Why is the circumference of a circle only related to its radius or diameter? There is no relevant content in the textbook of this question. If the teacher doesn't design this question, students often don't know why, so in this link, I designed balls with different rope lengths for students to observe and guess. Let students know why and why. It is very important to understand new knowledge, so that students' learning process can become a process of re-creation and re-discovery. This process highlights students' self-exploration of knowledge, how to generate "conclusions", and the training and cultivation of thinking modes and habits. When verifying the conclusion, I let the students choose the verification method independently, giving them the initiative in learning, which shows that students are the main body of the learning process and teachers play a leading role. Students are very interested in choosing their favorite learning style, and they quickly come to a conclusion. Because new knowledge is guessed by students themselves and verified by their favorite methods, students have a good understanding of new knowledge and have received good results in the application process. I realized that teachers teach to not teach and learn to learn the true meaning.

Through this study, I further feel the importance of questioning in classroom teaching, and understand that digging deep into the connotation of teaching materials is the premise of designing good questions. According to the connotation of teaching materials, cleverly setting questions can improve classroom efficiency. If we can fully mobilize students' learning motivation, explore students' internal positive factors and become a bridge and ladder for students to step into the knowledge hall, then our classroom questioning is effective. In the future, I will not only skillfully design the junction of old and new knowledge, but also carefully design ingenious, novel and easy-to-stimulate students' thinking in all aspects. Make my class more exciting and efficient.

Reflections on the teaching of drawing circles 3

A few days ago, I was lucky enough to listen to the lesson of "circumference" and I was deeply touched. "People-oriented, student development as the center" is the most urgent requirement for comprehensively promoting the implementation of quality education. In particular, classroom teaching, as the main position of implementing quality education, should adhere to the idea of "people-oriented, student-centered development", strive to create a good learning environment for students to be brave in asking questions, exploring, arguing, discussing, learning from each other and encouraging each other, and help students establish the idea of "not only books, but also teachers". "

First, release freedom and experience learning experience.

In the pre-class dialogue of this lesson, tell a story, then let the students review the knowledge of the circumference of a square, and then guide the students to touch and find the circumference of a circular object around them, thus revealing the concept of the circumference of a circle and guiding the students to find that the circumference of a circle is related to its diameter. On this basis, the question is raised: What is the relationship between the circumference and diameter of a circle? When asking students to summarize the methods of measuring the circumference, they came up with many methods: rope measurement, rolling method, soft skin measurement, classification method and the method of turning curves into straight lines.

After communication, students find that these methods can't be used to measure the circumference of any circle, which stimulates students' desire to learn and understands that only through practical operation and personal experience can we find a simpler method. In the whole process, students' thinking is open and free. They actively participate in learning and experience the learning process, while teachers only play the role of organization and guidance.

Second, hands-on operation, pay attention to learning methods.

"Listening will forget, watching will remember and doing." This course gives students plenty of opportunities and time to operate. When revealing the concept of "circumference of a circle", let students point to each other with circular pieces of paper prepared before class, then point to the circle on the blackboard with their names, and finally demonstrate the circumference of the circle dynamically through courseware, so that students can establish the representation and form the concept.

It is more willing to spend time when students explore the relationship between the circumference and diameter of a circle, so that students can choose the appropriate method to measure and calculate. In order to make students' operation process scientific and reasonable, let students communicate the matters needing attention in operation before starting operation. For example, when winding, pay attention to pinch the line, when rolling, aim at the 0 scale at one end of the diameter, and no sliding is allowed when rolling. Good methods achieve good results. When students master the correct method, it is easy to draw the correct conclusion: the circumference of a circle is always more than three times its diameter. After the students finished the operation, the teacher asked again: Some vendors on the screen made some mistakes. What could be the reason? Let the students reflect on the operation process just now, find out the cause of the mistake and feel the rationality of the conclusion.

Third, with questions, it is conducive to active exploration.

How to measure the circumference of a circle? How many ways are there? In the classroom, the teacher broke the traditional practice of teaching what must be taught in the textbook, allowing students to explore and create freely. Students take the questions raised by the teacher, think while doing, and give students the initiative to learn. In this way, students have enough time to think, free space for activities, opportunities for self-expression, and more confidence in creation. The students are full of enthusiasm and eager to try, and the classroom atmosphere is extremely active. Through hands-on operation and bold practice, this paper explores various methods of measuring the circumference, such as "winding", "rolling" and "cutting", and summarizes their common point: the measurement method of "turning curves into straight lines" This process has changed the passive measurement method of telling students how to do it first, and then asking them to do it as required. Instead, the method of giving students "materials" first is adopted, so that students can find laws and draw conclusions in operation and observation, so that students can consciously seek strategies to solve problems and promote the development of students' creative thinking.

When the students tasted the joy of success, the teacher introduced the game of throwing small balls to let the students observe the "virtual circle" formed. Can these methods measure the circumference of the "imaginary circle" just now? This problem breaks the students' cognitive balance and makes them deep in thought. Measuring various forms of circles in daily life is not only troublesome and inaccurate, but also impossible to measure.

Just when the students can't think hard, the teacher guides the students from association to conjecture, and then observes the game of throwing the ball again, and finally makes the students realize that the circumference of a circle is related to its radius or diameter. Why the circumference of a circle is only related to its radius or diameter. This question is not presented in the textbook, and many teachers don't explain it when teaching, so students often don't know why. Teachers dig deep into the connotation of teaching materials, adopt the method of "inducing students to go deep and press hard step by step", and make students' learning process become a process of re-creation and re-discovery through logical teaching activities such as association, conjecture and observation of pitching games. This process highlights how students explore knowledge, generate "conclusions", train and cultivate thinking modes and habits, and acquire ways and methods to solve problems, which embodies the quality education thought of "teaching is for not teaching, and learning is for learning".

At the beginning of this class, the teacher asked the students to compare the circumference of a circle with the circumference of a square when creating a situation, and found that the circumference of the circle could not be found and the problem could not be solved, and then introduced a new lesson. After learning the formula of pi, she immediately asked the students to go back and understand the calculation of pi in the "tortoise-rabbit race", so that students could discover the importance of pi formula and learn to solve life problems.

For another example, when students find some methods (rolling method, rope method, etc. ) When measuring the circumference of a circle, guide them to think: Can the circumference of all circles be measured in this way? The teacher shows the ball-throwing game and lets the students observe the "virtual circle" formed. Can these methods measure the circumference of the "imaginary circle" just now? So as to guide students to find simple and applicable methods, stimulate students' desire for learning and conduct further research. When the students understood the formula of the circumference of the circle, the teacher immediately turned around and asked the students to solve the circumference of the circle formed by the rotation of the "ball" with the simple method they had learned, thus highlighting the importance of knowledge application.

Generally speaking, this class is vivid, solid and effective.

Reflections on the Teaching of Drawing Circle (Ⅳ)

? The National Mathematics Curriculum Standard clearly points out that the content of mathematics learning should be "conducive to students' active observation, experiment, guess, verification, reasoning and communication", "Hands-on practice, independent inquiry and cooperative communication are important ways for students to learn mathematics, and mathematics learning activities should be a lively, active and personalized process", "Students are the masters of learning, and teachers are the organizers, guides and collaborators of learning"

First, attach importance to practical operation and highlight openness and exploration.

The content of this lesson is "Circle". With the help of students' existing learning experience, we can understand the meaning of "circumference" and base ourselves on students' personal experience and free expression. The construction of "pi formula" starts with the method of measuring the circumference of a circle by students, and then explores the relationship between circumference and diameter. The whole process is open and exploratory, giving full play to students' main role and allowing students to participate in all aspects from beginning to end. Through students' bold guessing, hands-on operation, independent exploration, discussion and communication, and statistical analysis, on the basis of full perception, the relationship between the circumference and diameter of a circle is discovered, the meaning of pi is understood, and the formula for calculating the circumference of a circle is obtained. The whole inquiry process gives full play to students' subjectivity and enthusiasm, cultivates students' ability to think independently and acquire knowledge, makes students gain a sense of accomplishment in learning, and establishes self-confidence in learning mathematics.

Second, carefully design the lead to build a communication platform for students.

In class, lively and interesting practical activities can create a good exploration platform for students; A relaxed and vivid teacher's classroom language can create an open and relaxed classroom environment for students and give them sufficient free space; Appropriate encouragement language can grasp students' hearts and make them find and solve problems step by step; The ideological confrontation of expressing their opinions can build a platform for students to communicate on an equal footing; Strict mathematical reasoning can cultivate students' rigorous humanistic spirit. "Classmate, did you have a good time yesterday autumn? Now the teacher continues to take you to a beautiful place. What is the circumference of a circle? Who can try to say it in their own words? " "In this lesson, we will learn the circumference together." In "Please guess boldly, what is the circumference of a circle related to?" "Is the circumference of a circle always greater than three times the diameter? Next, let's study this problem. " "Requirements, as long as you know what is ok? Please give examples to prove your idea, carefully design the lead between each link, and introduce each part by asking questions.

Third, it needs improvement.

Recall the teaching process of this class, the creation of scenarios, the introduction of questions, the discussion of activities, the verification, consolidation and application of guesses, the summary and evaluation, the embodiment of students' cooperative learning, the display of students' ideas and the feedback of final knowledge. Throughout the class, students study independently, and teachers and students study together, and * * * study together and experience the fun of acquiring knowledge together. Of course, there are still many imperfections in this class, such as the introduction of questions is too long and the teacher is too dead; The link of conjecture verification can be more compact, and each group can study one thing. 12 group has 12 examples; In this way, the final practice time will be more abundant, and you can practice the following problem-solving exercises; The derivation of pi formula shows that the circumference of a circle is always more than three times the diameter through cooperative learning, which is why teachers should use this conclusion of students to ask: Is it true? Then demonstrate it on the courseware. The class time is tight, and the preparation process is forgotten. I think this class is a bit flawed.

Reflections on the teaching of drawing circles 5

The "round understanding" I teach is the content of the eleventh volume of the mathematics textbook for six-year compulsory education primary schools. It is taught on the basis of a preliminary understanding of the circle in the lower grades. Although the circle has been preliminarily known before, it is still difficult to establish a correct concept of the circle and master its characteristics. It is another leap in cognitive development from straight line graphics on cognitive plane to curved graphics on cognitive plane. Therefore, I try to embody the following three ideas in my teaching:

1, which embodies the unity of subject and protagonist.

? Curriculum standards point out that students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning.

In the teaching of this lesson, after the students fully observed the circle and folded it, the teacher asked: Please look at the circle in your hand carefully. What did you find? Guide students to try to discover by themselves first, and teachers interact with students to fully understand the relationship between radius and diameter, instead of teachers blindly teaching and students personally operating perception, instead of teachers demonstrating and students observing. The interaction between teachers and students fully embodies the dominant position of students and teachers.

2. Create problem situations with the help of activities to improve students' independent inquiry ability.

Constructivism holds that the knowledge, ideas and methods of mathematics should not be acquired through teachers' teaching, but should be acquired by students through their own meaningful learning activities under certain circumstances with the help of teachers' guidance. So, in this class, I asked the students to create a circle by themselves. Through group cooperation, they use their original life knowledge and experience and various tools to create circles, which greatly mobilize the enthusiasm, initiative and creativity of students and make them participate in the activities of exploring new knowledge to the maximum extent. Through students' practical activities such as hands-on, oral and brain-thinking, external learning activities are gradually internalized into their own internal intellectual activities. Through all-round learning activities,

3. Reflect the connection between mathematics and life.

? Curriculum standard points out: "Mathematics curriculum should fully reflect the connection between human life and mathematics", and the same connection should also be fully reflected in mathematics teaching. This lesson focuses on two teaching links: the first is "Let students create circles in different ways". Because students have a lot of life experience about the circle before they know it, let them think of various ways to get it, which can make them feel that the circle is actually very close to our life, and it is around us; The second embodiment is that at the end of the teaching, after learning the relevant knowledge of circles, let the students talk about why the wheels are designed as circles. The purpose of this link is to let students use mathematics knowledge as much as possible to explain these life phenomena when they see the circle in life. This deepens the understanding of the circle and cultivates students' consciousness of applying mathematics.