Reflection on the teaching of multiplication and law

Part 1: Teaching Reflection on the Law of Multiplication and Combination

The traditional classroom teaching is the teacher's lecture, the student's listening, according to the examples given by the teaching materials, through observation, discovery of the law, and then imitating practice, the classroom is dull and boring, and this lesson I changed the traditional classroom teaching.
In the design of this section, in the introduction stage of the new lesson, the life situation is created. Starting from the students' existing life experience and knowledge, by asking the students to help the teacher build the building desk, how many bricks are needed to find the problem and propose conjecture. As a section The regularity class of mathematics should not only satisfy the students' understanding and mastering the law of multiplication and combination, but also use the law of multiplication and combination to carry out some simple calculations. It is important to let students experience a process of mathematics learning. This is a The focus of teaching is also difficult. Different students in the classroom have developed differently. When students explored the law of multiplication, they experienced the scientific exploration process of discovering laws, proposing hypotheses, verifying hypotheses, and inducting laws. When summing up the law of multiplication and law, students who are particularly active in thinking have exerted their ingenuity and have been further improved.
There are still some areas for improvement in the classroom teaching, especially in the evaluation, paying attention to increasing the evaluation between me and the students, as well as between the students and the students, especially the evaluation between the students, which can stimulate the students' emotions.

Part 2: Reflection on the Teaching of the Law of Multiplication and Combination and the Law of Exchange

First, the experience of using the theme map
The subject map provided by the textbook is to calculate the number of cubes. In the calculation, there are diversification of the problem-solving strategies to produce the materials we need. After teaching, it is found that the algorithms that students can present are basically limited to: 3×4×5, 3×5×4, 4×5×3. It is difficult to actively reproduce the 3×-like formulas we need to explore. . Therefore, in teaching, it is very unnatural and somewhat imposed by the deliberate "guide" of man-made. Perhaps it would be better to present it directly to students. However, it is contradictory to the knowledge that was learned before. For example, ×5, should not be bracketed.
Second, the experience of teaching content
In the teaching, it is found that students are difficult to distinguish between multiplication law and multiplication law in specific application. For example: 25 × 125 × 8 × 4, the first step of student processing is: 25 × 4 × 125 × 8, the second step is: ×. In general, students believe that the first step is based on the law of multiplication, and the second step is the law of multiplication. Obviously such an understanding is not comprehensive.
I think that some of the knowledge in the national stage can be blurred.
First of all, at the national stage, it is very difficult to find out some issues. For the multiplication law and the exchange law, there is no text definition in the textbook of Beijing Normal University. There is only a letter model. Referring to the PEP version, it defines the multiplication law and the exchange law: first multiply the first two numbers, or first The two numbers are multiplied and the product is constant; the two multipliers are swapped and the product is constant. This is called the multiplication commutative law. Compared with the original Zhejiang education version, the premise of multiplying three numbers and multiplying two numbers, combined with its teacher's book, we can easily find that the information it tells everyone is: editors helpless, primary school students' cognitive level is low. Scientifically analyzing the laws according to the calculation process is too cumbersome and difficult for them to understand, and only the combination of the law or the exchange law.
Second, there is no such necessity. In the small country stage, there is no need to clearly distinguish the multiplication law and the exchange law. We only need to let students understand that the law of multiplication is a mathematical law, the meaning is to change the order of operations, the product is invariant; the law of multiplication is also a mathematical law, changing the multiplier Position, the product does not change. As for the discussion of the three numbers multiplied and the two numbers multiplied, the student can't see the model of three numbers and two numbers in the simple calculation. It is hard to think of the law of the basis. Only know what is changed. Therefore, understanding the law in terms of meaning is more acceptable to the students, and then let the students experience that the law of change can express the most concise and essential of this change law.
Third, on the relationship between the law of multiplication and the simple operation
After learning the law of multiplication, will students simply calculate? There is an interesting phenomenon that teachers should have experience. Many students have already made simple calculations before learning the law of multiplication and exchange. I think there are three reasons: First, the textbook itself and the teacher have more or less infiltration before; the second is the student's extracurricular learning; the third is the student's own computing experience. Based on their own experience, they vaguely know that in the multiplication formula, changing the position of the multiplier and changing the order of operations, the result is constant, and sometimes the equations are converted as needed. They obviously do not pass the multiplication commutative law. Combination law. It seems that students will be the existing fuzzy understanding of the meaning of the law, and then we will refine them to an essential, concise model, and the role of this model is to find a mathematical basis for his previous simple algorithm.
Is the function of multiplication law only for simple calculations? When students think of the law of multiplication, they want to be simple, including examples of verification. In fact, the law of multiplication is a mathematical operation law. In all the multiplication equations, it is the most essential and concise model of the changeable law in this multiplication operation. The changeable laws represented by these models can sometimes make some calculations simple. But it is not because of simple calculations, it is not only for simple calculations. This opportunity can be experienced by students.
From the operating law to the simple calculation, is it a class time? I think it is unreasonable. It is suggested that in the teaching of arithmetic law, after focusing on establishing the model and understanding the meaning, the practice class of arranging a certain arithmetic law is not to strengthen the understanding of the operation law model, but the experience and significance of the operation law. At the same time, students' norms of expressing simple and simple computing processes are cultivated. When students encounter some special calculations, they can consciously convert according to the law to the direction that is convenient for us to calculate, that is, the consciousness of simple calculation.

Part Three: Reflection on the Teaching of Multiplication and Combination Law and Exchange Law

According to the students' cognitive rules, I insist on the concept of "student as the main body" in teaching, and strive to highlight the education thought based on student development. Therefore, the whole teaching process is based on students' independent learning and independent exploration. Mathematical learning forms such as verification, induction, and application allow students to experience the exploratory and challenging nature of mathematical problems.
Through reflection, I think there are several highlights in the teaching of this lesson:
1. In the course of the course, add the review calculation, through the calculation of 5×2, 25×4, and 125×8, make the students clear that the product of the three groups is a special whole ten, one hundred, one thousand, and will be given to the students. The calculations are a great help, paving the way for later teaching.
2, through the game calculation × 4 and 15 × who's calculation speed is fast, so that students themselves realize that the use of multiplication law can make the calculation simple. The purpose of learning the law of multiplication is to make the calculation simple, but I think if you tell the students directly, the students may not have a deep experience, so I used the game of calculating the competition between male and female students, that is, the calculation class is dull. The atmosphere of the classroom makes the students have a deep experience and feel the necessity of learning the law of multiplication.
3. There is a process for exploring the laws of mathematics. The understanding of this process is not taught by the teachers, but the students experience the feelings themselves. The timely summarization of the students' existing experiences and feelings is an important part of improving the exploration ability. In this lesson, I strive to highlight the development of student-oriented teaching. The whole teaching process is based on students' independent exploration and cooperation. Through the observation and verification of students, students can feel through a large number of emotional materials, and then pass the students. The bold communication naturally summarizes the content of the multiplication law, and better cultivates the students' abstract thinking ability.
However, there are still many shortcomings in the teaching of this lesson.
1. There is no specific situational teaching, and the enthusiasm of some students is not fully mobilized. Creating specific problem situations allows students to experience the close connection between mathematics and life. In the process of solving the problem, the problem is found, the problem is solved, the example is verified, and the law is summarized. Let students learn the law in the process of solving problems, and combine the exploration and learning of the law with the problem.
2. After all, this is a calculation class. In the teaching design of the whole class, the practice density is too small, which has a certain impact on the students' timely consolidation of the knowledge they have learned. There is also the level of practice is not very obvious, in the practice can be interspersed with variant exercises, such as: 25 × 16, so that all students can gain something. In order to enable students to flexibly use the multiplication law to prevent students' mindset, they can also design a multiplication method that cannot be simplified in practice, so that students can judge whether they can be simplified, and thus cultivate students' specific analysis of specific problems.
3, in the teaching, a little biased attention to some students, pay attention to communication with all students, so that everyone can actively participate in the study, and in the usual teaching, pay more attention to the students' development education, teach students to "listen" ".
In the teaching of this section, I tried the way of presenting mathematics by simply using a few calculations to teach students to directly perceive new knowledge. Although it does not make students clearly aware that it is mathematics in life, it can make students feel simple math lessons and simply learn mathematics.

Part 4: Reflection on the Teaching of Multiplication and Combination Law and Exchange Law

The course "Multiplication Law and Exchange Law" is further developed on the basis of learning the two-digit multi-digit multiplication and the first experience of interesting equations. It is different from the previous textbook arrangement in that the combination of knowledge and multiplication is placed in the students' independent exploration. Through the creation of situational activities, students are gradually found to find special phenomena in the multiplication calculation. The learning objectives of this lesson are: experiencing the exploration process, discovering the law of multiplication and exchanging, and expressing it by letters. On the basis of understanding the law of multiplication and the law of exchange, some calculations are easily calculated.
Looking back at the whole class, I feel deeply. I can make good use of the teaching and learning model, the classroom atmosphere is more active, and can better accomplish the learning goals. Reflections on this lesson are as follows:
1, the introduction is more exciting. As the saying goes: A good start is half the battle. When I started the class, I said, "Would we have a teacher and a student to play a game?" I heard that the students all said "good" in unison. The classroom atmosphere was mobilized, and the students stared at the big screen. I immediately showed a few questions, and I quickly said that I was counted. The students were so surprised and surprised to see the teacher. When the students are surprised, I showed the subject and told the students to study through this lesson. You will count as fast as the teacher. Then it is natural to derive the learning objectives of this lesson. This introduction of the teacher-student competition attracted the attention of the students, mobilized the students' interest and stimulated the students' desire to learn.
2. The group study is in place. The mode of guiding and learning is focused on group learning. In the classroom, I give full play to the group's cooperative learning and complete the learning goals. First of all, I used multimedia to show a rectangular parallelepiped: "This is a rectangular box that the teacher has built under the class. Do you know that the teacher used this cuboid to use several small cubes?" Then he showed the self-study tips and asked the students to use different methods to calculate one. Count, intra-group communication algorithm, the first self-study group. By observing these different formulas, what have you discovered and conducted a second group study. I take x4=3× as an example. What is the difference between the two sides of the equation, I let the group observe the research: In the example verification, I asked everyone to give an example, the group exchanged to see what was discovered. Through several group studies, the enthusiasm of the students who are mobilized makes everyone participate in the learning of the classroom, giving full play to the role of the teacher's leading and student subjects, so that the students become the masters of the classroom.
3. Give the blackboard to the students. The blackboard is not only the stage of the teacher, but also the stage for the students to show themselves. Return the class to the students and hand over the blackboard to the students. During the exchange show, I asked the representatives of each group to say the idea, while the board algorithm, students are very willing to show themselves, show their group's learning results, fluent in language, and the book is neat. On the student's face, there is a sense of happiness and accomplishment in learning.
This class is based on the fact that students have already mastered the calculation method of multiplication. Through learning, it is a good foundation for students to use simple rules in the future to improve the calculation speed. During the teaching, I gave full play to the group cooperative learning, so that the students can discuss each other and learn and communicate in a way that reflects the idea of ​​“student as the main body”.
4. Focus on infiltrating a scientific learning method. It is better to teach people to fish than to teach people to fish. Mathematical thinking is more important than mathematical knowledge itself. For the teaching of the combination law, we should not only be satisfied with the students' understanding and mastering the law of multiplication and combination. We will use the law of multiplication and combination to carry out some simple calculations. It is important to let students experience a process of mathematics learning, and receive scientific methods and scientific attitudes in their studies. Enlightenment education. In the teaching process, I mainly use the students' observation, verification, induction, application and other forms of learning, using heuristic teaching methods, from shallow to deep, from intuitive to regular, let students feel the exploration of mathematics problems, cultivate students to learn Mathematical interest.
Inadequacies:
1. The amount of practice is not enough. Because the communication time did not control the time, the communication time was too long, the problem was not completed, and the students did not better consolidate and understand.
2. Student exchange time is too long. In the classroom communication session, the students are active and enthusiastic. I have the heart to dispel the enthusiasm of the students to speak, and simply let the students report them one by one, which wastes a lot of time. In this part, I can let the students verbally repeat the same ideas, instead of one-on-one, and pick up some time.

Part V: Reflection on the Teaching of Multiplication and Combination Law and Exchange Law

1. Imagine a method of learning. Many of the world's problems and the solution of these problems benefit from the conjecture of such a learning method. The first part of this lesson is to associate the law of multiplication and multiplication with the law of addition and addition, and then to guess the content of the law of multiplication and multiplication. Then I wonder if we have a way to solve a real problem. Usually we can't know which direction we should guess, we need to search, sometimes it will pop up. So I think the point of conjecture is how to find out the objects of Lenovo. This should be the key to this lesson.
2, the process of verification
The process of this class verification is this: because all the equations written by the students prove that the law is correct, this law is correct. Is this process correct? In fact, this process is not necessarily correct, although the deductive method and the incomplete induction method are mainly used in the national ministry. The process of verification should be the student's understanding of the content of the law. The example can only explain the student's understanding of the surface of the law. It is very specific. It should guide the students to understand the multiplication commutation law in the sense of multiplication, so that students can exchange the multiplication. The understanding of the law is further, that is, on the abstract level. I later thought it was possible to do this: When the student introduced the alphabet formula, the teacher: We can know by example that this law is correct, then you have other ideas? Teacher: Can you understand the multiplication commutation law according to the meaning of multiplication? ?
3. Lack of depth.
From these aspects: 1 understanding of the two laws, staying on the surface without deep understanding of the content from the student side, lack of challenges, no difficulty. Especially the understanding of the law of multiplication is not timely Summarizing, so that when the content is not consistent, the students feel a little difficult. The understanding of the combination law should let the students understand that the combination law is the multiplication of three numbers, no matter the two numbers multiplied and the third Multiply the numbers and their products are the same. Let the students understand this. First, by way of example; second, through the reality of life to understand how the multiplication of three numbers is going on. Finally, I can ask: What do you think is the use of these two laws? I think if this is the case, one of the most striking features of this class is to use a learning method to complete the whole lesson: Lenovo_Conjecture_Verification_Abstract.