Reflection on the teaching of multiplication law

Part 1: Reflection on the teaching of multiplication law

The law of multiplication is taught on the basis that students learn the law of addition, union, multiplication, and law. Its teaching focus is to let students perceive the law of multiplication, know what is the law of multiplication, and the difficulty is to understand the meaning of the law of multiplication. Therefore, in this class, I used various methods such as oral calculation, reading formula, and writing similar calculations to let students perceive the law of multiplication, and finally the students summed up the concept of multiplication law. This is the only place I feel satisfied with in this class. It is to give the students the main body of the class. The students are actively involved in the study, but there are many shortcomings.
First, my teaching program in this class is: first let the students calculate, then present the scene map, according to the information given on the scene map, the formula: × 25 = 4 × 25 + 2 × 25 and let the students talk about the two formulas Meaning, then let the students read the formula, and then let the students write two similar formulas, then write the formula written by several students in the book and select a classmate's formula to let him say why the left side of the formula is equal to Right ×5=6×5+2×5); and I also asked the students to use different methods, through the previous programs, and then let the students summarize the characteristics of the left and right sides of the formula to get the multiplication. The law of distribution, and finally through the practice to consolidate and deepen the students' understanding of the law of multiplication. I thought that there would be a better effect in this way, but it was counterproductive. When I asked the students to write two similar calculations independently, I found that a small number of students would not write, so the latter part of the class would not be smooth. It is. After class, I asked Liu Siyi to learn that there was a problem in my teaching program----contrary to the students’ cognitive rules. It should be guided by the teacher to summarize the multiplication law and let the students write similar The formula, experience the law of multiplication, and finally practice to consolidate and deepen the students' understanding of the law of multiplication.
Second, when the students were asked to sum up the concept of multiplication law, the teacher did not have a good guidance, which led the students to have a vague understanding of the characteristics of the law of multiplication.
3. When the students summed up the concept of multiplication law, I just took the multiplication law and showed it to the students through the courseware. It did not repeatedly emphasize the characteristics of the law of multiplication, which led to the students not having a good grasp of multiplication. law.
Fourth, classroom language is not concise.

Part 2: Reflection on the Teaching of Multiplication Law

The multiplication law is a new operation law after the multiplication law and the multiplication law. In arithmetic theory, it is also called the multiplication property of addition, because it is different from the multiplication law and the combination law is a single operation. To a certain extent, the degree of abstraction is higher. Therefore, it is more difficult for students. How to make students master better and remember more? I think the knowledge that students get themselves is more secure than the ones that are instilled. So I designed a shopping situation at the beginning, letting students enter life and start learning new things in a relaxed and pleasant environment. In the process of teaching, there is a slope that allows students to constantly understand and experience the law of multiplication and multiplication, and then summarize the law of multiplication. I designed this like this:
First, let students understand the law of multiplication law from life examples
A total of 25 groups participated in tree planting activities, with 8 people in each group responsible for digging and planting trees, and 4 people responsible for lifting water and watering trees. Reorganizing the teaching materials and changing the number of people in each group, from 25 to 25, can highlight the convenience brought by the application of the law of multiplication, and also lay the foundation and foundation for the application of the law of multiplication. And the change of "pitting, planting trees", "lifting water, and watering trees" to "pitting and planting trees" and "lifting water and watering trees" reduced the difficulty of words on students' understanding.
Students are given two calculations by introducing problem solving. First capture its meaning and then highlight its form of performance.
For example, the meaning of ×25 is 6 25 and 4×25+2×25, which is also 4 25 plus 2 25 or 6 25. Their meanings are the same. Therefore, the number is the same. Then observe the characteristics of their form changes. The sum of two numbers multiplied by a number can be written into the form of two products, and then the characteristics of the factors are captured for analysis. On this basis, I am not eager to let students speak the rules, but continue to provide students with challenging research opportunities.
Students can appreciate the rationality of the law of multiplication by means of different solutions to the same practical problem. This is what I have encountered in life. Students can understand the meaning of the two formulas and can solve the problem of equalization of the two formulas.
Second, the difficulty of teaching the breakthrough of the law of multiplication
Let students experience the formation process by witnessing the rules. The value of the process of exploring the simple distribution law is no less than the mastery value of knowledge. Since it is a "law of law", it is a scientific process design that allows students to experience the law. Without the traces, students can continuously observe, compare, guess, and verify, thus summarizing the law of multiplication, and infiltrating in the process of exploration and induction. From special to general, from general to special mathematical ideas and methods.
Compared with other laws in multiplication, the structure of the multiplication law is the most complicated, and the equation is changed.
The ability of shape is the difficulty of teaching. In order to break through this teaching difficulty, starting from the practical problems in life, and opening up the situation, a total of 25 groups participated in the tree planting activities, and each group was responsible and responsible. How many students participated in this tree planting event?
Students take the initiative to design, solve, and motivate students. Let students choose their favorite programs according to their own ideas, open them to students, give full play to students' subjectivity, and verify their internal laws by discovering, guessing, questioning, understanding, adjusting, verifying and perfecting, thus summarizing the multiplication law. Let students freely use their knowledge, experience, and thinking to try to solve problems, and explore the activities of this series of equations that have something in common.
On the basis of the students' existing knowledge and experience, study the abstract formulas together, find their respective characteristics, and summarize their laws. In the process of finding the law, some students are in the horizontal observation, and some students are longitudinal observation. The purpose is to let the students start from their own mathematical reality, try to solve the problem, and enable the students with different levels of thinking to get corresponding satisfaction and obtain corresponding Successful experience.
Of course, the meaning of the law of multiplication law needs to be more complex and combined, which is more conducive to the establishment of the model.

Chapter 3: Reflection on the Teaching of Multiplication Law

The Law of Multiplication Law is the seventh unit of the fourth grade. Before that, the students have learned the addition and the law of association, the law of multiplication and the law of integration in the last semester, and also the fourth unit of the semester. I used the learned algorithm to make simple calculations. Before class, I thought that students were familiar with this part of the knowledge. So I simply designed the review, reviewed the learned algorithms, and let the students find the algorithm simple. The application in the calculation, then shows the example of the class, let the students find the shadow of the law of multiplication from the example, and then through examples, compare the law of multiplication and show it with the alphabet, and basically complete the new teaching of this lesson. Through the consolidation exercise, students can understand the application of the law of multiplication in calculation and practical life problems. Before class, I thought that the students would follow my thoughts and would go through the complete class smoothly. But after finishing the class, I found that there were a lot of problems in my own class. After summing up, I felt that I was not doing much in many ways.
At the beginning, when students reviewed the law of operation, there was a small problem, which made me feel helpless, resulting in the later review questions being forgotten and the classroom links were omitted.
When teaching a new lesson, the student's column is not the form of the formula I want. I will directly write the form of the formula I want. In fact, this time I can use the multiplication commutation law to become the form I want. I also think that knowledge should be flexible. I should also write the form that the student said, because this is the formula that the students listed themselves. He can certainly understand it, but my approach in class is a bit I am eager for success, and I am a bit hard-working.
There were a lot of problems in the group discussion. I thought that this class students should quickly discover the characteristics of the two sides of the equation, and they can quickly say what they have in common, but when they are in class, the group discussion I found that students simply don't know how to find out the commonalities of these formulas. Even if some students find some features and don't know how to express them, after reflection, I find that my problems are not well designed and students can't understand. Knowing where to start, is to compare the relationship between the numbers, or to observe the relationship between the expressions, or to see the relationship between the symbols, so that the students do not know what to say, there is another important reason is that I compare before the discussion The equation in the example does not clearly tell the students to observe the order of the equations, so that the students will not say. On the other hand, it is not difficult to abstract the equation into a single letter, but it is also an abstract process. It is a bit difficult for students in the fourth grade. Students can feel that it is written like this, but said It is really difficult to justify it. Therefore, in our teaching, we must consider the level of students' cognition. It is good for students to say what they should have. In the future teaching, we should try our best to let the students discuss the ideas and discuss their own ideas. It is necessary to pay attention to the degree of group discussion and to propose effective questions that are suitable for students.
In practice, we should pay more attention to the development of students' abilities. Let students express their own ideas, understand the design intent of each question, calculate correctly according to the meaning of the questions, and master the methods of doing the questions.
After a class, I found that I had a lot of problems, and I hope to gradually reduce the emergence of such problems in future teaching.

Part 4: Reflection on the teaching of multiplication law

The law of multiplication is the content of the fourth grade mathematics book. It is a relatively abstract concept class. It is based on the students learning the law of addition, addition and addition, multiplication and multiplication. The law of multiplication is also a difficult point in learning these laws. Therefore, for the teaching of multiplication law, I did not focus on the expression of mathematics language, but focused on allowing students to fully perceive through the calculation of various methods, and observe, compare and summarize the listed formulas. Boldly raise your own guess and give examples to verify...
Therefore, the teaching objectives of this lesson, I am positioning: from the students' existing life experience, through observation, analogy, induction, verification, application and other methods to deepen and enrich the understanding of the law of multiplication. Infiltrate the method of understanding things from "special to general, then general to special", and cultivate students' ability to independently, actively explore, discover problems, solve problems, and improve the application of mathematics.
A striking feature of this unit's textbook is that it no longer only gives some examples of numerical calculations, allowing students to find out the rules through calculations, but to help students understand the realistic background of the operating law by combining the familiar problem situations. This makes it easy for students to analyze and compare different methods for solving problems based on existing knowledge and experience, and to introduce the operating law.
The textbook provides such a main picture: in the spring, the students carried out tree planting activities, a total of 25 groups, each group of 4 people responsible for digging and planting trees, and 2 people responsible for lifting water and watering trees. The question that needs to be solved is: How many people participate in tree planting activities? Students will use two different methods to list the formulas separately, and then find through calculations that the two formulas can be connected with "=", that is, 25 ×=25×4+25×2. I will present it to the students first, in order to help students understand the realistic background of the law of operation in combination with the familiar problem situations.
Then design the "suspense", throw four sets of questions, and lead the students to the "equal results of the two calculations". Ask the students to guess first, then verify, then ask the students to edit the questions, so that each student can participate in the research. In the process of editing, many students have handed in the correct “answers”, which enhances their self-confidence and desire to continue research. Then, ask the students to find a way to verify in life. With the four-person group as the research unit, the students' thinking activities are suddenly active and they explore the mysteries. The way in which the group is discussed encourages students to communicate with each other and motivate students to succeed. Through practice and discussion, the law of multiplication law is revealed. Then internalize by expressing the law of multiplication in the way you like. In doing so, students learn positively, learn actively, learn to be happy, do their own hands-on editing, explore their own brains, and learn the rules from the multiple analogies of quantitative relationship changes, “help” less, students create more, students It is not only a law that is learned, but more importantly, students learn to automate themselves, learn to cooperate, learn to think independently, and learn to study and discover like a mathematician! For the children around the age of ten, the motivational effect is undoubtedly enormous, and the learning habits of "love, think, think" will benefit the child throughout his life. Throughout the teaching process, students learn easily and learn actively.
Through the teaching of this class, I feel that: seriously studying the teaching materials and in-depth exploration of the valuable resources in the textbooks will make the content of the textbook more broad and deep, and provide a broader space for cultivating and developing the flexibility of students' thinking. .
The teaching of this lesson has better implemented the concept of the new curriculum standards, mainly reflected in the following points:
First, take the initiative to explore and realize personal experience and experience
The learning process of students should be the process of learning text criticism, questioning and rediscovery. It is the process of whole body and mind devoted to learning activities in specific situations, to experience and experience the formation of knowledge, and also the process of realization and development of various aspects of body and mind. In the teaching of this section, I started with the theme map and brought out 25×=25×4+25×2. The purpose of the design is to obtain an example of the multiplicative conjunction law from the two algorithms that solve this problem. Next, four sets of questions were thrown, and the students were introduced to the case where the results of the two formulas were equal. Then let the students pass the verification method's feasibility, and then let the students to verify the universality of the method. Finally, the students can observe the multiplication law by observing, discussing, discovering and summarizing. Throughout the process, I did not present the law directly to the students, but let the students explore and discover through self-exploration, so that the subjectivity is fully exerted. In this process of inquiry, students experience a rigorous process of scientific discovery: conjecture—verification—conclusion—connecting life and solving problems. It lays the foundation for students' sustainable learning.
Second, multi-directional interaction, focusing on cooperation and communication
In mathematics learning, students' thinking style, intelligence, and activity levels are all different. Therefore, in order to enable different students to develop in mathematics learning, teachers in this lesson are based on multi-directional interaction between teachers and students, especially through mutual enlightenment and supplement between students and students to cultivate their sense of cooperation. The active construction of the algorithm of "multiplication law" is realized. The construction process of the “multiplication law of the students” is the process in which the individual methods of the students are turned into common learning results, and the joy of success and the vitality of life are developed.
In short, the new teaching concept is reflected in this class, but the enthusiasm of some students is not fully mobilized. Although the students are very invested, they seem to have mastered it, but they still found some problems during the practice. For example, when the student calculates a×, the formula is wrongly written as: a×b+c, and I also remind everyone to pay attention, but in practice, many people still forget to go separately, this question is waiting for me in the future teaching process. Continuous improvement and improvement.

Part V: Reflection on the Teaching of Multiplication Law

The law of multiplication is the difficulty and focus of the third chapter. The design of this lesson. I started with the students' life problems and started using the milk tea that students are interested in. In this lesson, I try to teach students to learn knowledge and become a guide to students to learn. By letting students experience the process of knowledge formation such as “observation, preliminary discovery, case verification, re-observation, discovery of rules, generalization and induction”. Looking back at the entire teaching process, the highlights of this lesson are mainly reflected in the following aspects:
First, the introduction of life issues, interest exploration
In teaching, I created a large number of vivid, concrete and vivid living situations for students, so that students feel that mathematics is from the life around them, and stimulates students' enthusiasm for learning. First, I created a scenario and asked the question: “How many students have participated in this tree planting event?”. Let the students solve the problem according to the conditions provided, and find the equation ×25=4×25+2×25. Then ask the students to observe that the order of operations on both sides of the equation makes the students initially perceive the "multiplication law." Let the students "observe the difference between the two sides of the equation" and perceive the "multiplication law." At the same time, the use of scenarios allows students to fully perceive the "multiplication law", which provides a powerful guarantee for the later exploration of the law of multiplication.
Second, provide students with the opportunity to explore independently
I asked the students to observe the two equations and ask "What did you find?" At this point, the students have a little bit of their own perception of the "multiplication law". I immediately asked the students to imitate the equation and write a few similar equations. In the students' own imitation, the guessing and verification are naturally completed, and a relatively "fuzzy" understanding is formed.
Third, create conditions for the transformation of students' learning style
In order to "change the way students learn, let students conduct exploratory learning" is not an empty talk. In this class, I grasped the students' existing perceptions and immediately proposed "observing this set of equations. Can you find the mystery?" In this way, students are provided with a wealth of perceptual materials and challenging research materials, providing space for guessing and verification, discriminating and communicating, and returning the active power of learning to students. The students’ enthusiasm for learning is high, which naturally sparks the spark of inquiry. The learning style of students is no longer single and boring. The whole teaching process adopts a learning method that allows students to observe, explore, and communicate. I think: Only by changing the way of learning can students improve their ability to find, analyze and solve problems.