Reflections on the teaching of factors and multiples
? Factor and multiple is a mathematical concept course, and the new textbook of People
Reflections on the teaching of factors and multiples
? Factor and multiple is a mathematical concept course, and the new textbook of People's Education Press is different from the previous textbooks in introducing the concepts of factor and multiple. This lesson is the focus of this unit. In order to make students feel the meaning of factors and multiples well, and skillfully find out the factors and multiples of a number, the textbook is flexibly handled and divided into two classes. In the first class, students only know the meaning of factors and multiples and the method of finding a number factor, and the effect is good.
First, design the situation, causing thinking.
Change the situation diagram of the textbook and introduce the topic that students are interested in: there are 12 small squares, which are required to be put into a cuboid. How do you want to put them? Arouse students' thinking. Students think there are three arrangements. How to find out how many squares there are in each arrangement in a * * *? Due to the diversity of methods, it provides space for the display of different thinking. So as to solve the meaning of factor and multiple.
Second, guide students to explore ways to find factors, so that exploration has a direction.
How to find the factor of a number is the focus of this lesson. First, let the students find a factor of 24. Due to the differences in personal experience and thinking, different methods and answers have emerged. In the process of exploring these methods and answers, students understand how to find a factor of a number, thus mastering the knowledge points.
According to students' learning characteristics, we should use teaching materials flexibly, make them serve teaching, and carry out teaching effectively to achieve teaching objectives.
Teaching reflection on factors and multiples of 1 (Ⅱ)
The factors, multiples, prime numbers and composite numbers involved in this unit, as well as the greatest common factor and the smallest common multiple in the fourth unit, all belong to the basic content of elementary number theory. After more than four years of mathematics study, students have mastered a lot of integer knowledge, including the understanding of integers and the four operations of integers, and further explored the properties of integers.
In teaching, by teaching students to know "factors and multiples", we can master their characteristics: factors and multiples cannot exist independently. By observing and comparing the factors (or multiples) of several numbers, we know that the factors (or multiples) shared by several numbers are called their common factors (or multiples), and we can find out their common factors (or multiples) from the factors (or multiples) of several numbers.
Next, learn the characteristics of multiples of 2, 5 and 3. The law and characteristics of finding multiples of 2, 5 and 3. Before that, students should be taught what is odd and what is even. Only by mastering odd and even numbers, it will be much easier to learn the characteristics of "multiples of 2 and 5" The characteristic of "multiple of 3" is to guide students to add up the numbers on each number. If this number is a multiple of 3, it means that this number is a multiple of 3.
In order to consolidate prime numbers and composite numbers, let students find all prime numbers within 1~ 100: first, cross out all multiples of 2 except 2, then cross out multiples of 3, cross out multiples of 5, and finally cross out multiples of 7. The rest are prime numbers, and let students count them. Remember that there are 25 within 100. You can also use the same method to judge whether numbers other than 100 are prime numbers or composite numbers.
Finally, students explain and introduce "prime factor decomposition" and know how to decompose prime factors by short division. Then sort out and classify the knowledge learned in the whole unit, so that students can remember some special laws and figures, do more exercises and strengthen the attention and guidance to underachievers.
Factor and multiplication 1 the third part of teaching thinking
There are complex relationships in simple content. Because the new textbook removes the concept of "divisibility" and does not mention who can be divisible by whom, it is easier to directly introduce the concepts of factor and multiple with the help of the divisibility mode Na = B. When students learn factors, the minimum factor for finding and understanding a number is 1, and the maximum factor is themselves and a number. When learning multiples, it is considered easy and simple to find and understand multiples of a number, but many students are hesitant and confused about the comprehensive practice of factors and multiples. For example, judging the number of factors of a number is infinite, and many students judge it as right. In the exercise: 18 is a multiple, and individual students choose 18, 36, 54 ... In view of this situation, I adjusted my exercises and organized students to study the following questions:
1, write the factor and multiple of 12, and write the factor and multiple of 16.
2. Observation and comparison will dispel the problem of the list: the relationship between the factor of a number and itself,
3. Why is the number of factors of a number limited? The minimum value is 1, and the maximum value is itself, that is, an integer between 1 and itself. Why is the multiple of a number infinite? The smallest is yourself, and there is no biggest.
Through the discussion of these problems, most students can distinguish the factors and multiples of a number well.
Factor and Multiplication 1 Part IV Teaching Thinking
The content of this lesson is to further understand the properties of integers on the basis of students' learning some integer knowledge (including the knowledge of integers, four operations of integers and their applications). The factors and multiples involved in this unit are the basic knowledge of elementary number theory.
Success:
1. Understand the classification criteria and clarify the meaning of factors and multiples. In the teaching of example 1, students are first classified according to different division formulas, and at the same time, what is the standard basis? Through independent thinking and group communication, students draw the following conclusions: the first one is divided into two categories: one is that the quotient is an integer, the other is that the quotient is a decimal; The second is divided into three categories: one is integer, the other is decimal, and the other is cyclic decimal. How to classify students in order to reach an agreement in argument and communication? There are two answers. Then according to the first case, the meaning of multiple and factor is obtained. Emphasizing the meaning of factor and multiple must meet two conditions: one is that it must be divisible by integer, and the other is that quotient must be an integer without remainder. With these two conditions, it can be said that the dividend is a multiple of the divisor and the divisor is a factor of the dividend.
2. Clarify the concepts of multiples and multiples, and emphasize the interdependence between multiples and factors. In teaching, students can be told directly that neither factor nor multiple can exist separately, 2 is a factor and 12 is a multiple, but who is a factor and who is a multiple. For the difference between multiples and multiples: multiples must be studied in integer division, while multiples can be studied in both integer and decimal ranges, and their research scope is greater than multiples.
Disadvantages:
1. The capacity of practice design is less, resulting in the remaining time of class.
2. The meanings of factors and multiples should also be summarized and raised to letters.
Re-instructional design:
1. Make corresponding supplements according to the exercises in the textbook.
2. The meanings of factors and multiples are summarized as a÷b=c(a, B and C are all non-zero natural numbers), A is a multiple of B and C, and B and C are factors of A. ..
Factor and Multiplication 1 Part V Teaching Thinking
1. The combination of numbers and shapes reduces the difficulty.
? Factors and multiples are students' first contact. In the lead-in, I create an effective mathematics learning situation, combine numbers and shapes, and turn abstraction into intuition. Ask the students to put 12 small squares into different rectangles and express their thoughts with different multiplication formulas. With the help of multiplication formula, the meaning of factor and multiple is deduced. Due to the diversity of methods, it provides a space for different thinking and activates students' thinking in images. Through the potential relationship between "shape" and "number" in mathematics, we can lay a good foundation for the subsequent study of the concept of "factor and multiple", from image thinking to abstract thinking, and effectively realize the connection between the original knowledge and the new knowledge. On the basis of students' existing knowledge, let students intuitively feel the combination of numbers and shapes, and then form the meaning of factors and multiples, so that students can initially establish the concept of "factors and multiples". In this way, students' existing mathematical knowledge leads to new knowledge, which reduces the difficulty and has a good effect.
2. Independent inquiry and cooperative learning
Let each student find all the factors of 36. Students revolve around the teacher's question "How can I find all the factors of 36?" To solve this problem, we should find out all the factors of 36. Because of different personal experiences and thinking, there are different answers, but these different answers have become resources to explore new knowledge, and the thinking method of finding a factor of a number is summarized by comparing different answers. It not only leaves enough space for independent inquiry, but also guides the methods and avoids students' blind guess. By showing and comparing different answers, we found a good way to search one by one in order, which highlighted the importance of orderly thinking and effectively broke through the teaching.
Difficulties. By observing the factors of 12, 36, 30, 18 and the multiples of 2, 4, 5, 7, let the students tell themselves what they have found. Because it provides rich observation objects and ensures the purpose of observation. Induce students' desire to explore and learn, thus activating students' thinking. Let students find the same through cooperation and communication among many differences.
3. Experience the joy of learning in the game.
In the last link, I designed the game "Finding Friends". The grade is to find factor friends first, then find multiple friends, and finally find two friends with the same number. This design from the shallow to the deep conforms to the students' psychology of picking fruits in one jump, and also allows students to experience the characteristics of factors and multiples again in the game. For example, when looking for a factor friend, it is pointed out that the number of factors of a number is limited, and when looking for a multiple friend, many students get up and let the students experience the infinite number of multiples of a number again. Finding like-minded friends is a sublimation process of thinking, which can effectively activate students' thinking and think effectively under the control of curiosity. This link makes the classroom atmosphere more enthusiastic, and also allows students to experience the joy of learning in a relaxed atmosphere.
I still have many shortcomings in this class, and my teaching philosophy is very clear. In class, students are the main teachers and the only collaborators. But in the teaching process, many places still talk too much involuntarily, leaving too little room for students to explore independently. For example, in the process of finding the factor of 36 in teaching, children are worried that it is the first time to contact the factor, and they don't know enough about the concept of the factor, so they make mistakes of one kind or another, so they guide too much and explain too carefully, so the space for them to explore independently is too small to reflect the students' subjectivity well. Although it is a new concept.
But it follows the old model, and I will continue to improve my teaching methods in the future so that students can become the real masters of the classroom.
Personally, my language in this course is too casual, mathematics is rigorous, and casual language will have a certain impact on students' learning and understanding. Due to my long-term teaching habits and my own personality characteristics, my language is not rigorous at some times. I know this very well, and I am constantly correcting it in my daily teaching, but I still haven't noticed some places in this class. Therefore, in the future teaching, I will actively learn from other teachers, walk into the class of excellent teachers, learn more and ask more questions. Grasp all kinds of learning opportunities, keep learning through various channels, and improve your quality. Reflect more, carefully analyze the problems in teaching, and improve your professional level through continuous reflection.
Thank you teachers for giving me such precious learning opportunities and giving me guidance and help in this process. In the future, I will take this class as an opportunity to constantly improve teaching, sum up experience and lessons, be strict with myself in all aspects, and do better in my future work!
Factor and Multiplication 1 Part VI Teaching Thinking
? Multiplication and factor is a lesson learned in our studio in April. Let's draw lots for 20 minutes of classroom teaching first, and then discuss. We studied the treatment methods of each part. At the same time, in order to make our class more coherent and natural, we also studied the transition links between examples, trying to find a more suitable treatment method. After that study, every member of our studio revised the lesson plan according to his own ideas. A few days ago, our studio took this course in the activity again. This time, it was me. Due to insufficient preparation in advance, many problems were found in the class, including the problems that needed to be improved in the last discussion and the new problems that appeared in this class. After class, the members of the studio gave me a lot of good advice. I revised my teaching design according to good suggestions. Let me elaborate on it.
1, situation import. The content of this lesson is multiples and factors. In order to make students feel the interdependence of multiples and factors more clearly, I used the examples of big-headed son and small-headed father in class, and also used the example that I am a teacher and they are students. However, these two examples may not be of great significance to the teaching of this course. Students can't seem to clearly feel the dependence of multiple factors. We can get rid of this part and go directly to the classroom for students to operate.
2. The meaning of multiples and factors. The purpose of this lesson is to make the same square as 12 into a rectangle, so that students can feel the relationship between multiples and factors in activities, and then explain the meaning of multiples and factors to students with specific examples. In class, I let the students operate directly, in pairs, and try to put it on the table to see if there are any different ways. When communicating, let the students talk about their own arrangement, how to arrange a few in each row, how to express them by multiplication formula, and then let the students say it in an orderly way to pave the way for finding a number factor later. There is also a specific formula to illustrate the meaning of multiples and factors. Ask the students to talk about the other two multiplication formulas by multiplying the multiplier by the multiplier equal to the product. After the lecture, give the students a hint and ask them to say who is a multiple of who and who is a factor of who according to the formula shown. Finally, let the students write a formula and say it.
3. Find the multiple of a number. This should be the key and difficult content of this class. In teaching, students must pay attention to the method of multiple, and I can see that a large number of students have not mastered the method of multiple through this important part in class. So I'm thinking about how to break through this difficulty. Should students be allowed to think independently, talk more and give them enough time to talk about their methods of finding multiples, so that after various methods come out, we can optimize the methods and choose the fast and simple methods. In teaching, at the same time, pay attention to cultivate students' awareness of orderly writing multiples, pay attention to the format of multiple writing, let students find in order and disorder, and let students feel the benefits of order. After students have the basic method of orderly search, they will also choose the method just optimized to practice.
4. The characteristics of multiple. After finding the multiple of a number, you can directly show what the multiples of 3, 2 and 5 are, let the students observe the three multiples, and then talk about their findings. Let the students find it. Maybe students can find out quickly, but if specific questions are given, some students' thinking may be limited. If students don't find the characteristics we want to summarize in their observation, we can give them appropriate hints to let them observe the minimum multiple, the maximum multiple and the number of multiples. Give students enough time to find it by themselves, and we should believe that they can do it by themselves.
5, the problem of classroom routine. Before class, I should first make sure the specific distribution of the group, so as to prevent students from finding partners in group activities. If the group is divided in detail before class, the efficiency of group discussion will be much higher. In class, I should talk less, leave more opportunities for students to express their ideas and trust students at the same time. Don't be afraid that students don't know, but give many rules and regulations, which limit the development of students' thinking.
Factor and Multiplication 1 Part VII Teaching Thinking
? The main content of this section is to let students explore and summarize the methods of finding multiples and factors of a number on the basis of existing knowledge and experience; Study the characteristics of multiples of a number and factors of a number by "enumeration method". This part of the content is difficult for students to master for the first time. First of all, the names are abstract, and they are not often contacted in real life. For such concept teaching, students need a long-term process of digestion and understanding if they really want to understand, master and judge. In this class, I fully embodied the student-centered teaching, which provided enough time and space and appropriate guidance for students' exploration and discovery. At the same time, in order to improve the effectiveness of classroom teaching, I have embodied autonomy, initiative, cooperation and emotion in the teaching of this class, and specifically achieved the following points:
(a) Business practices, such as internalization, understanding multiples and factors.
I create an effective mathematics learning situation, combine numbers and shapes, and turn abstraction into intuition. First, let the students put the small square of 12 into different rectangles, then let the students write different multiplication formulas, and draw the meaning of factors and multiples with the help of multiplication formulas. In this way, on the basis of students' existing knowledge, from hands-on operation and intuitive perception, concept revelation has broken through from abstraction to abstraction, from mathematics to mathematics, allowing students to experience the combination of numbers and shapes independently, thus forming the meaning of factors and multiples, enabling students to initially establish the concept of "factors and multiples" and organically combine numbers and shapes. In this way, we can fully study, use and dig textbooks, and introduce new knowledge by using students' existing mathematical knowledge, which reduces the difficulty and has a good effect.
(B) independent exploration, intended to build and find multiples and factors.
It is not difficult to accept the characteristics of multiples and factors of a number by memory alone. In order to prevent students from "mechanical learning", I put forward "What are the characteristics of any factor that is not zero in natural numbers?" Let the students observe the factors of12,20,16,36 and think: Is the number of factors of a number limited or infinite? What is the biggest factor? What about the youngest? Let students' thinking have a clear direction. In the whole teaching process, students are the main body of learning, and teachers are only the organizers, directors and participants of teaching activities. In the whole class, teachers always create a relaxed learning atmosphere for students, so that students can explore independently, learn to understand the meaning of multiples and factors, explore and master the methods of finding multiples and factors of a number, and guide students to acquire knowledge independently in full oral, hands-on and brain.
(3) Grasp the "zone of recent development" of students' thinking, and let students learn to think in an orderly way in the process of "independent thinking-collective communication-mutual discussion", thus forming basic skills and methods, paying attention to both process and result.
Finding a factor of numbers is the difficulty of this course. In the teaching process, students are allowed to explore independently. In the subsequent tour, I found that many students were not very good at it. I decided to communicate first and then let the students find it, so I spent a lot of time and didn't have much time to practice at last. I think that although it took too much time, I think students have explored more fully and gained something. It is very difficult for students who just have a perceptual knowledge of multiples to find out the factor of 36 without repetition or omission. Here, we can give full play to the advantages of group learning Let the students find the factor of 36 independently first. I interviewed a third of the students and thought methodically. Most students don't write formulas in a certain order. Then let the students discuss two problems in groups: how to find the factor of 36, and how to find it without repetition or omission. In the process of group communication, students reflect on their own methods, absorb the good methods of their peers, and then the teacher gives effective guidance and summary.
(D) Variant expansion, practical application-promoting intellectual internalization
The design of exercises not only focuses on the key points of teaching, but also pays attention to the hierarchy and interest of exercises. In the game, the interaction between teachers and students activates students' emotions, and students' thinking is constantly active. Students not only have a high participation rate, but also can consolidate new knowledge. In the classroom, I can pay attention to the cultivation of students' learning interest, enthusiasm and self-confidence from beginning to end, so that students can feel the joy of learning success, enjoy mathematics and feel the cultural charm in time.
(5) Pay attention to the infiltration and expansion of the meaning of mathematics, strive to attract students with the essence of mathematics, and establish the consciousness of serving students' continuous learning and lifelong development. In the design of this class, I paid attention to the students' learning stamina. Such as the introduction of enumeration method, orderly thinking strategy to solve problems and so on.
Because this class is a concept class, a lot of things are said by the teacher, but it does not mean that students passively accept it. Before teaching, I knew that the time of this class would be tight, so when preparing lessons, I carefully studied the teaching materials and carefully analyzed the lesson plans to see where I could arrange less time, so I asked students to preview the advanced nature and made some preparations. In the first part, I think it is ideal to shorten the presentation time and present it directly in the link of knowing factors and multiples. In the classroom, we should also use multimedia to present the factors that students are looking for in time and guide students to sum up their findings: the smallest factor is 1, and the biggest factor is themselves. Teachers should keep up with personalized language evaluation in time, activate students' emotions and keep students' thinking active.
Factor and Multiplication 1 Part VIII Teaching Thinking
I found that most students have a good grasp of the basic knowledge and concepts of this unit, and quite a few students are flexible in the application of multiples and factors. Judging from the students' answers, there are also many questions. Throughout the teaching of this unit, we get some thoughts from it:
1, creating a familiar life situation for students.
Both the teaching of new courses and the practical application of knowledge are based on students' existing life experience, which stimulates students' interest in active learning and participation, and guides students to realize that there is mathematics everywhere in life, and the multiples and factors in mathematics are around them, so as to learn mathematics and apply mathematics problems from life.
2. Adopt the mode of group cooperative learning.
In the new curriculum teaching, let students discover the characteristics and applications of numbers and related multiples and factors in real life through observation, and then discuss in groups on the basis of students' independent attempts to solve problems: how to reasonably classify the characteristics of multiples of 2, 3 and 5, how to find factors and prime numbers, etc. Group discussion is the starting point for exploring new knowledge, and independent activity space and communication platform are built for students in group cooperative learning.
3. It fully embodies the guiding ideology of taking students as the main body.
In the classroom, strive to create a relaxed and happy learning environment and guide students to actively participate in the learning process. Pay attention to let each student express his ideas in the group. The establishment of each knowledge point and the formation of new knowledge try to let students discuss and seek from what they already know, and at the same time listen to their peers' views and learn from each other. Reflect the new concept of "people-oriented development", respect students, trust students, and dare to let students learn by themselves. In the whole teaching process, students experience the process of knowledge discovery and inquiry through operation, discussion and induction, starting from the actual state of existing knowledge and experience, and realize the joy or failure of solving problems.
4. Pay attention to the application of new knowledge.
Every time you learn a new knowledge point, you should let students use what they have learned to solve practical problems in time, so that students can feel that mathematics is in life and use new knowledge flexibly to solve problems.
5. disadvantages
(1), there are still a few students who are not actively involved in learning. How to make all students participate in mathematics research needs to be further strengthened.
(2) In the application part of this unit, students are required to explain the reasons for solving problems, and students also lose serious points, indicating that students have weak knowledge in this area and should strengthen breakthroughs in future teaching.
(3) There are many teaching puzzles, such as knowing that a small number of students have defects in some knowledge points in teaching, but it is difficult to take the time to make up and follow up.