Rethinking the teaching of countdown

Part 1: Rethinking the teaching of countdown

The countdown is a conceptual teaching class. It is based on the calculation of fractional multiplication. By observing the characteristics of the number of groups with a product of 1, the students are guided to recognize the reciprocal, mainly for the preparation of the learning division later. In the middle, we must lay a solid foundation to clear the obstacles and improve the learning efficiency in the future.
In this lesson, I mainly focus on the links of “introduction, inquiry, discussion, practice, and summary”.
Through the introduction of a couplet in a small story, the connection between the language subject and the mathematics learning is taken as the entry point, and the law of the composition of the characters stimulates the curiosity of the students and causes interest in learning. Let students initially feel the meaning of "down". This makes it easier for students to understand the “reciprocal countdown” that they are immediately exposed to. After the student knows what is called the countdown, let the students use the example of the student to further understand the phrase "the two numbers of the product are reciprocal of each other" according to the example of the countdown. At the same time, let the students say that you think that the two numbers in the product are reciprocal. Then, according to the student's answer, understand: "mutually", "product is 1", "two numbers". An in-depth analysis of the definition of the reciprocal.
Finally, through proper practice, the students can sum up their own scores, and the reciprocal of the decimals is generally deformed first and then changed. And let the students summarize some of the small rules found in the process of reciprocal. In the discussion, let the students study according to their own ideas: the reciprocal of 1 is 1, 0 has no reciprocal.
Looking at the whole lesson, I feel that the whole lesson is taught more solidly. When the teaching is done, the appropriate teaching is carried out, and the practice has a sense of hierarchy. For the two special cases "1" and "0", the teaching is not specifically proposed by the teacher. It is derived from the students' in-depth thinking, which is the result of student learning. Self-feeling is better handled.
The enthusiasm of the students was fully realized in the parents' lectures. The children who did not speak loudly dared to raise their hands and raised their hands on the same day, fully mobilizing the children's desire to answer questions.
In the design, the design of the practice is still lack of difficulty, lack of flexibility, and the application of the "countdown" is not rich enough.

Chapter 2: Rethinking the Teaching of Countdown

After the recognition of the countdown to this year, I have a lot of feelings. In the past, this part of the teaching, I directly asked the students to write the formula whose result is 1, and then put the formula board with the product of 1 on the blackboard from the formula that the students said, and then let the students observe the characteristics of the calculation, and then let the students Understand the meaning of each other, and finally summarize the meaning of the reciprocal. Now think of it, there is a feeling of holding the student's nose. I redesigned the lesson plan by reading magazines and other teaching publications. I think this kind of design is to let the students themselves summarize the meaning of the countdown by observing, comparing and summarizing. It is the students who have real gains after participating in the whole learning process. In particular, through the form of competition to stimulate students' interest in learning, the students discovered the characteristics of the formula, and let the students find out that the formula with such characteristics can not be written. Then let the students follow the teacher's look, say the meaning of the countdown by example, and emphasize the countdown keyword words. This is very necessary for students to master the concept. When students are happy to think that they have mastered the method of finding the countdown of a number, I have designed obstacles for students: how to find the reciprocal with fractions, decimals and integers. Although the new content of the textbook does not have this knowledge, it appeared in the later exercises. I mentioned it to the front and everyone studied it together. I think it is necessary. In this way, the student is prevented from taking the reciprocal of the score with the method of reversing the position of the numerator and the denominator. This will not mislead students' perceptions. After the students know the method of reciprocal scores, scores, integers, and decimals, I ask whether all the numbers have countdowns. Make students think of the countdown problem of 0. I used to ask students directly "0" is there a countdown? It seems that the student "0" has no countdown. Changed to ask today, students think through their own, get two answers, "0" has a countdown, and the other is "0" has no countdown. With disagreements, students were once again brought into the problem kingdom. Students express their opinions separately.
Finally, everyone agreed that "0" has no countdown. Because "0" can't be divisible, that is, 0 can't be used as denominator. I think that the teaching of this lesson has changed in essence from the previous teaching, which is to play the main role of the students.

Chapter 3: Rethinking the Teaching of Countdown

The Understanding of Countdown is based on the fact that students master the fractional multiplication. In this lesson, I have grasped two main contents to start teaching: 1. Learn to understand the meaning of the countdown. 2. Learn how to find the reciprocal of a number. I use text games to introduce new lessons to attract students' attention, and at the same time instill in students the idea of ​​"down" and integrate the phenomenon of the game into mathematics. In understanding the meaning of the reciprocal, let the students grasp the key words "product, mutual" to understand, and emphasize that the reciprocal is not isolated, but for two numbers. With the introduction of the word game, the students observed that the positions of the two numbers and denominators that are reciprocal are reversed, and the reciprocal of the scores of truth and false scores are easy to grasp, so the atmosphere of the classroom is very strong, and the answer is positive and active. There are a lot of students in the problem. But for the reciprocal of the natural number and the reciprocal of the decimal and the score, most students' thinking can't turn around anymore, and only a very small number of students can tell the method. For the special numbers 1 and 0, students are basically able to know their reciprocal.
The improvement in this lesson is that there is another way to find the reciprocal of a number. One method is to multiply one number by another. The product is 1, and the other number is the reciprocal of the number. For example, 5×=1, the number in parentheses is the reciprocal of 5. In this lesson, I didn't explicitly emphasize this method. I still can't let students really understand the meaning of countdown. Therefore, the goal of knowledge and skills cannot be achieved.

Part 4: Rethinking the Teaching of Countdown

“Reciprocal recognition” is a conceptual teaching class, which is based on the learning of fractional multiplication. To understand the meaning of the reciprocal, the reciprocal of a number is the premise of the student's learning score division. Students only have to learn this part of the knowledge to better understand the calculation and application of the subsequent fractional division.
First, thinking and presupencing before class
For the content of this lesson, it seems to be simple, the characteristics of the essence is very rich, combined with the current situation of the weak foundation of most students in this class. Seriously thought about the teaching objectives and the difficulties and difficulties in this lesson. Strive to make students listen clearly, lively and learn easily. Therefore, we should start from the following aspects when thinking before class.
1. Knowledge points of this lesson
The content of this lesson is “recognition of countdown”, which is the recognition and recognition of countdown. How can students clearly understand the meaning of countdown? And how to find the reciprocal of a number?
2, the key points of this lesson
The "New Curriculum Standards for Elementary Mathematics" points out that it is necessary to pay attention to the learning outcomes of students as well as the learning process of students. The teaching of the meaning of the reciprocal is carefully analyzed, and the meaning is divided into several parts: "The product is 1", "two numbers", "reciprocal to each other", which looks simple, but each part After careful scrutiny, I found out "How can I get 1; how many numbers are, what kind of numbers are there? How do you understand each other?" Is there something similar in life that can be moved? These aspects are for students. It is very important to understand the meaning of the reciprocal.
3. The focus of this lesson
Based on careful consideration of key points, it is difficult to understand that the word “mutually” is more difficult to understand than the other two key points. Therefore, it is necessary to work hard and work hard in this aspect, because understanding this key point is a sign that students have the countdown meaning, and it is also one of the ways to help students recognize the concept of “countdown”.
4, the deepening point of this lesson
Based on the consideration of the meaning of the reciprocal, it is found that the key point of the "two numbers" in the definition is very rich, what are the two numbers? Can they be integers? Can all be scores? Can all be decimals? ... Is there a special number? For example, do integers have countdowns? Do the decimals count down? Are the scores countdown? Because there are special numbers such as 0 and 1 in the integer, there are also negative integers. There are finite decimals, infinite decimals, and infinite non-cyclical decimals in decimals. Do they have these questions in the classroom? How did it happen? If not, how to deal with it.
Second, the implementation and experience of the classroom
1. Create a scenario to introduce a new lesson
In the introduction part of the lesson, some interesting words lead to the problems to be explored in this lesson----reciprocal, from the visually intuitive feeling of reversing position, not only stimulates students' interest in inquiry, but also prepares students for new knowledge. To pave the way for students to better understand the meaning of the countdown.
2. Cooperative inquiry learning
The teaching of the variation is a self-study textbook for students, find the meaning of the countdown, and analyze it with the students, find the method of finding the countdown of a number, and then check the student's mastery by example, the group cooperation discussion: the reciprocal problem of 0 and 1, and then Summarize the method of finding the reciprocal of a number.
3, practice forms are diverse
While making full use of the practice of the textbook, I also supplemented the content of the exercise appropriately so that the students can consolidate in the exercise and improve in the practice. For example, the design of “everyone has the same problem at the same table”, so that students can not only learn in the classroom, but also use it in the classroom to achieve true mastery.
Third, after class thinking and feelings
Through teaching, I feel that teachers should believe in the ability of students in teaching, and actively become the partners, helpers and promoters of student learning, and deal with the relationship between support and release.
1. Give students time to think independently; believe that students can have the ability to think independently. Every question in the teaching should be made so that students do not wait to listen to others, but can develop the habit of thinking positively.
2. Give students the opportunity to cooperate and learn; when students are confused, teachers can give full play to the collective wisdom of students, guide students to cooperate, learn from each other, communicate with each other, communicate in cooperation, improve in cooperation, and solve confusion in cooperation.
In teaching, I explore the "0 and 1 countdown" links, give full play to the role of cooperation and exchanges, and work together to solve problems. For an in-depth understanding of "mutually", I give examples of "mutually the same table" and "mutually be friends", so that students feel that "mutually" is around, and can resonate with understanding key points.
In the practice, three judgment exercises were designed around the key points, so that the students can understand the conditions for the countdown in the exercises, which are indispensable.
3. Confusion and deficiency
Through the teaching of this lesson, I found that most students can understand the meaning of the reciprocal and master the method of reciprocal of a number, but a few students have an understanding of the reciprocal, just staying on the surface form of whether the numerator or the denominator is reversed. On the above, the essential condition that the product of two numbers is 1 is ignored, so they mistakenly believe that the decimal and the score are not reciprocal. Later, although most of the students discussed the decimals and the scores by simple communication, there are countdowns when they find the countdown. However, when the countdown is found, the reciprocal of 0.5 is 5.0, and the reciprocal of 1 is 1 error.
In the face of such a situation, I feel a bit confused. Why does the teaching material only count down in the range of integers and true and false scores? The calculation of the subsequent fractional division also involves the decimal number and the reciprocal problem with the score. Do we need to fill in the relevant content in the actual teaching?

Chapter 5: Rethinking the Teaching of Countdown

This part of the countdown is taught on the basis of fractional multiplication. The learning reciprocal is mainly prepared for the later learning score division. Because a number divided by a fraction is calculated by multiplying the reciprocal of this score. So learning this part of the content is crucial to the subsequent learning score division. Since I am the first-level teacher of the sixth-grade math group, this class is my unit class. So before the class, I read a lot of teaching designs about this class. I think it is varied and has its own strengths. The learning situation of the class students, the design of the teaching program, and achieved a good teaching effect, mainly in the following points:
First, the introduction of features, straight to the theme.
In the introduction of this lesson, I let the students understand the contrasting antonyms and position exchanges through the conversation, and then let the male and female students calculate the two sets of multiplication formulas of the small blackboard, observe the characteristics of the product and the characteristics of the two factors in the formula, directly A preliminary understanding of the reciprocal is made, and it is better understood that a new score will be obtained by simply changing the position of the numerator and the denominator. Then let the students name the two scores with such characteristics, and the students call them countdown. In order to give students a deeper understanding of the meaning of the reciprocal, I guide students to give a large number of examples, and through observation, calculation and other methods to make students clear that "the product of the two numbers reciprocal is 1", "the two numbers of the reciprocal are only The exchange of the position of the numerator and the denominator, and what makes me happy is that students can notice that "the countdown is interdependent." Grasping the student's discovery, I led them to quickly sum up the concept of countdown—the two numbers whose product is 1 are called reciprocal. When emphasizing the emphasis, the students found that there are still cases like the reciprocal in mathematics, such as the divisor and the multiple, and the reciprocal is also interdependent.
Second, let students experience the joy of success in the collision.
The famous educator Suhomlinski said: "In the depths of people, there is a deep-rooted need, that is, I hope that I am a discoverer and explorer." In the children's psychology, this demand is special. Don't be strong. In order to meet the psychological characteristics of the students, I asked the students to ask for the number of countdowns. In my encouragement, the students began to propose integers, true scores, and false scores. When I think of taking scores and decimals, I think of two special cases 1 and 0. When faced with the special numbers 0 and 1, the students have a small "dispute". Some people think: "0 and 1 have countdowns." Some people think: "0 and 1 have no countdown." I did not directly intervene in the students' "disputes," but guided them to talk about each other's reasons. In their communication, The students reached a consensus: 0 has no countdown, and the countdown of 1 is itself. And when explaining the reasons, the students also believe that "0 can not be used as the denominator, so 0 does not count down", "0 multiply any number is 0, impossible to get 1" two reasons, expand the knowledge content that I provide to students Students draw conclusions in in-depth thinking, which is the result of student learning. I feel that this not only adds to the vitality of the classroom, but also allows students to experience the process of exploration, solve the confusion of students, and let students experience the joy of success.
My biggest achievement in this lesson is that the students have had a full debate and I am very happy. I feel that this is the biggest gain of the lesson. In the debate of the students, even I am full of passion. I think that I need to be fully presupposed in the teaching, let go of my hands and feet, so that my classroom will be wonderful.