Reflection on the teaching of addition exchange law

Part 1: Reflection on the Teaching of Addition Law

The time of this lesson is well grasped, and the degree of mastery of the students is also ok, reaching the teaching goal of this lesson. Inadequacies: In class, my status is not very good, and students are not very active. Basically, several people are answering questions. The classroom atmosphere in the class is very active, but I don’t know what is going on in this class. Even the children who are learning well are wrong on the blackboard. It may be that the children are a little timid. There is also a self-evaluation language that is too single, and we will work harder in this area in the future. Try to make your class more vivid and perfect.

Part 2: Reflection on the Teaching of Addition Law

This lesson is the first lesson of the "Operational Law", and before this unit, the students have gone through four arithmetic studies for more than three years, and have some basis for these perceptual knowledge: such as the addition within 10, Students looking at a picture can list two addition formulas; in the addition within ten thousand, through the teaching of the verification method, the student already knows the position of the adjustment plus and adds it again, and the added result remains unchanged. This lesson is further guided by some examples to guide students to a summary.
In teaching, I first created a familiar life situation for students, allowing students to freely ask questions based on information in social practice. This not only cultivates the students' divergent thinking, but also the problem consciousness, and also conforms to the new curriculum "creative use of teaching materials". Through the observation and comparison of the two formulas in the teaching, the students' existing knowledge and experience are awakened, the students perceive the additive exchange law, and the students are written to write similar equations to help students accumulate emotional materials, enrich the students' appearance, and encourage students. Using their favorite methods to sum up the law of addition and addition, students can quickly understand the two algorithms, so that students can understand the simplicity and generality of symbols and develop students' sense of symbolism. Through several levels of practice, all the students are involved in the fun mathematics learning, experience the mathematics everywhere, fully enjoy the fun of learning mathematics, and consolidate the content of the whole class, and make it easy to apply the operation law in the future teaching. Calculate the paving.
Through the teaching of this class, I found that there are still many shortcomings.
First, the evaluation of students' classroom performance is not timely enough. For example, in the teaching addition and exchange law, when students write "6+2=2+6,1+9=9+1...", they do not have a good interpretation of the students' psychology. The reason why the student wrote a one-digit calculation was because he felt that writing an equation with one digit plus one digit was very simple and convenient for calculation. However, as an incomplete induction method, the formula he wrote has certain limitations and is not representative. At this time, if you ask the students, "Is there only one person plus one digit to have such a law?", "What advice do you have for this classmate?" This can guide students to think further and cultivate their thinking. The rigor.
Second, there is no good distinction between the additive exchange law and the nature of the addition law. This has led to the inability of students to accurately discriminate in later exercises. It is possible to increase the contrast between the addition commutative law and the additive commutative law, and compare the essential characteristics of the additive commutative law: the addend has no change, the result has not changed, and the arithmetic symbol has not changed, but the position of the addend has changed.
In general, this class has achieved good results, but at the same time, many problems have been discovered. Some of these problems are objective, and many of them are not enough because of their teaching wit and teaching design.

Part 3: Reflection on the Teaching of Addition Law

In the teaching addition and exchange law, I used the situational introduction--exploration of new knowledge-feedback practice three teaching links. The situational introduction link uses the situation of Li Shushu's bicycle travel in the textbook to introduce the known conditions and problems; explore the new knowledge link, let The students complete the study independently. When the group exchanges, the results are the same. Use the equal sign to connect and get 56+28=28+56. Then let the students follow the example and finally guide the students to draw the rules. The feedback is very positive for the students. High, the teaching of this lesson is very smooth, and the teaching tasks are easily completed. However, I feel that there is too little knowledge in this lesson. Can you combine the addition and exchanging laws into one lesson? In the course of teaching this lesson, I am going to try the following aspects in the "Exchange Law" lesson.
Improve the way materials are presented. The textbook only provides the basic content and basic ideas of the teaching. On the basis of respecting the teaching materials, the teacher should make a purposeful selection, supplement and adjustment according to the actual situation of the students. In addition, in the order in which the materials are presented, the order of textbooks is changed: the teaching addition and the law of addition and addition, and then the teaching of the commutative law and the law of integration, but simultaneously presented and studied at the same time. Because when students extract effective information related to new knowledge in the existing cognitive structure, it is impossible to reflect the order of the textbooks, but to reflect them at the same time, and fully respect the cognitive rules of students.
Find the prototype of life. The essence of the additive commutative law and the multiplicative commutative law is to exchange positions, and the results are unchanged. This mathematical thought exists everywhere in life. In this lesson, I will first guide students to observe the phenomena around them in a dialectical manner, and to permeate and change the dialectical materialism. Then, take the example of life mathematics: the two students at the same table exchange positions, and the results remain unchanged. Leading students to ask questions: Is there a change in the result of this exchange position in our mathematical knowledge? Can you give one or a few examples to illustrate? In this way, using the captured "life phenomenon" to introduce new knowledge, students have a sense of closeness to mathematics, feel that mathematics and life are in the same place, not mysterious, but also arouse the interest of students to explore boldly.
Find the starting point for teaching. The correct estimation of the student's learning starting point is the basic point of designing the teaching process suitable for each student's self-reliant learning, which directly affects the learning level of new knowledge. The addition commutative law and the multiplicative commutative law are the contents of the third unit of the eighth volume of the National Education Mathematics, first teaching the additive exchange law and the combination law, then the application of the exchange law and the combination law, followed by the multiplication law and the multiplication law. , multiplication law. In the past, students have a lot of perceptual knowledge of the addition and multiplication exchange laws, and can use the position of the exchange addends to check the addition. Therefore, the focus of this lesson should be on guiding students to discover and express mathematics in mathematical language. The law and the method of summarizing how to obtain the law make the students' understanding rise from sensibility to rationality.

Part 4: Reflection on the Teaching of Addition Law

Freudenthal, a world-famous mathematician and mathematician, points out that the way mathematics learns is to re-create, that is, the students themselves discover or create what they want to learn. According to this guiding ideology, I believe that mathematics teaching should pay more attention to students' "experience" and implement the "subjectivity" of teaching while paying attention to knowledge and skills, and pay attention to the process of students learning mathematics and doing mathematics. The above teaching process breaks the traditional classroom teaching structure and focuses on cultivating students' innovative consciousness and practical ability. Through the actual state of the existing knowledge and experience, the students experienced the process of exploring the mathematics problem of the additive exchange law and the multiplication exchange law through questioning, conjecture, illustration, observation, communication and induction, and experienced the successful solving of mathematics problems. The joy or the emotion of failure.
1. Focus on the integration of teaching objectives.
According to the development and requirements of the times, the value orientation of mathematics teaching is not only limited to students' access to basic mathematics knowledge and skills, but more importantly, in mathematics teaching activities, understanding the value of mathematics, enhancing the application of mathematics, and obtaining mathematics. The basic method of thinking, the process of problem solving. In the teaching, we should deal with the integration of intellectual and developmental goals and balance, promote students' development in the process of knowledge acquisition, and implement knowledge in the process of development.
In the "Exchange Law" class, teachers set procedural goals in the target field, not only with students to study the "exchange law" "what is", but more importantly, let students experience the generation of mathematical problems, encountered The question "What to do" and "How to solve the problem." Spend more time paying attention to the student's learning process and consciously guiding students to experience the process of “doing mathematics”. Guide students to look at things around them with a mathematical eye and ask questions: Is this phenomenon of changing positions and results unchanged in our mathematical knowledge? Encourage students to extract effective information from the existing knowledge structure, observe and analyze, and actively obtain the "addition exchange law and multiplication exchange law". In the process of problem solving, both the method of solving the problem and the success are experienced. emotion.
2. Focus on the reality of teaching content.
In teaching, according to the age characteristics and teaching requirements of students, we should adapt from the familiar situation and existing knowledge of students to carry out teaching activities. This points out the direction of our teaching reform on the operational level. This lesson has been tried in the following aspects.
Find the starting point for teaching. The correct estimation of the student's learning starting point is the basic point of designing the teaching process suitable for each student's self-reliant learning, which directly affects the learning level of new knowledge. The addition exchange law and the multiplication exchange law are arranged in the seventh and eighth volumes of the textbooks for the small and medium-sized mathematics of Zhejiang Education. In the past, students have a lot of perceptual knowledge about the addition and multiplication laws. Using the position of the exchange plus number to check the addition, the teachers of this class focus on guiding students to discover and use mathematics to express mathematical rules and summarize how to obtain the law, so that the students' understanding increases from sensibility to rationality.
Find the prototype of life. The essence of the additive commutative law and the multiplicative commutative law is to exchange positions, and the results are unchanged. This mathematical thought exists everywhere in life. In this lesson, the teacher first guides the students to observe the phenomenon around them with dialectical vision, and to permeate and change the dialectical materialism. Then, take the example of life mathematics: the two students at the same table exchange positions, and the results remain unchanged. Leading students to ask questions: Is there a change in the result of this exchange position in our mathematical knowledge? Can you give one or a few examples to illustrate? In this way, using the captured "life phenomenon" to introduce new knowledge, students have a sense of closeness to mathematics, feel that mathematics and life are in the same place, not mysterious, but also arouse the interest of students to explore boldly.
Improve the way materials are presented. The textbook only provides the basic content and basic ideas of the teaching. On the basis of respecting the teaching materials, the teacher should make a purposeful selection, supplement and adjustment according to the actual situation of the students. In the course of teaching materials, this lesson changed the phenomenon of using textbooks as “the Bible”, allowing students to participate in the provision and organization of teaching materials, creating an innovative and practical learning environment for students, which not only stimulated students' learning motivation. And to explore the desire, but also to make students' body and mind have a successful experience. In addition, in the order in which the materials are presented, this lesson changes the order of textbooks: in the seventh volume of teaching addition and exchange laws, in the eighth volume of teaching multiplication and exchange laws, but at the same time, simultaneously research. Because when students extract effective information related to new knowledge in the existing cognitive structure, it is impossible to reflect the order of the textbooks, but to reflect them at the same time, and fully respect the cognitive rules of students.
3. Focus on the exploratory nature of the teaching process.
In the "Teaching Requirements", the content of "exploring the students' exploration consciousness through observation, operation, guessing, etc." has been added; in the "Several Problems in Teaching Should Be Paid", the "Exploration Consciousness and Practice of Students" “Capability” is discussed as a question, requiring teachers to “design exploratory and open questions based on their age characteristics and cognitive level, and provide students with opportunities for independent exploration, allowing students to observe, operate, discuss, communicate, guess, In the process of induction, analysis and organization, understanding the presentation of mathematical problems, the formation of mathematical concepts and the acquisition of mathematical conclusions, and the application of mathematical knowledge, "form the initial ability to explore and solve problems"
In the course of exchanging law, teachers encourage students to understand the situation according to their "mathematical reality", discover mathematics, break the closed teaching process, and construct "problem - inquiry - application - new problem - re-exploration" The open learning process reflects that students are the masters of learning, and teachers are the organizers, guides, and participants of teaching activities.
Create a living situation and stimulate the desire to explore. In this lesson, we will first guide students to observe the teaching environment around them with the perspective of “changing and unchanging”, and then picking up an interesting phenomenon in real life, allowing students to initially perceive problems, thereby causing cognitive conflicts and stimulating students' desire to explore. This arrangement not only helps the students to eliminate the psychological barriers in thinking, but also prepares the psychological, knowledge, and ability for the acquisition of new knowledge, and achieves the purpose of activating students' original knowledge, attracting attention, and inducing students to participate in consciousness. So that teaching is always in the recent development zone of student thinking.
Guide students to explore and develop their potential. Teachers skillfully use life prototypes, activate old knowledge related to new knowledge learning, guide students to extract effective information from the original knowledge base, organize, observe, classify, communicate through self-organizing formulas, gradually abstract and summarize, form conclusions, and Apply. In this process, through a series of mathematical activities such as student exploration and creation, observation and analysis, induction and verification, correction and exchange, self-discovery, independent exploration of the addition and exchange law and multiplication exchange law, so that students feel the exploratory nature of mathematical problems And challenge, and recognize the certainty of the mathematical thinking process and the certainty of mathematical conclusions.
Reflect on the exploration process and experience the emotions of success. After the problem is solved, guide the students to reflect on the process of inquiry learning: How do we solve the problem in the face of a practical problem? From this, we extract the mathematical thought methods and effective strategies for solving problems, gaining new knowledge, and consciously point the thinking to mathematical thought methods and learning strategies to obtain a positive emotional experience.
Promote teaching and learning, and encourage innovation. At the end of this lesson, the teacher consciously vacated a certain amount of time to make the students difficult. On the one hand, students are asked questions about the knowledge that this lesson does not understand, and solved with the help of teachers and students; on the other hand, let students ask valuable questions, which not only cultivates students' ability to ask questions, but also enables students' cognitive psychology. Create a new "uncoordinated" and form an atmosphere of re-exploration.
In short, in the course of teaching, this lesson highlights the systematic nature of knowledge, the experience of students, and tries to cultivate students' subjective consciousness. The problem allows students to reveal themselves. The method allows students to explore themselves, and the law allows students to discover and knowledge themselves. Let the students get it themselves. In the classroom, students are given enough time for thinking and activities, and at the same time give students the opportunity to express themselves and the successful experience, cultivate students' self-awareness and play the main role of students.

Part V: Reflection on the Teaching of Addition Exchange Law

Get: Through the imitation example, infiltrate the mathematical method of equal substitution.
According to the imitation, the students learned to write the two equations into the same method according to the equality of the results. This is a new knowledge for them, in fact, it is the process of undergoing equal replacement. This mathematical method is very important for the following to learn other various operating laws, and to use the law to perform simple operations, and to solve the equations.
Through the comparison of a large number of mathematical facts, we found that the law is not fully inductive.
After the independent examples, the students exchanged the rules of discovery within the whole class and concluded that no matter how the positions of the two addends are exchanged, their sums will not change. Teacher guidance: All the examples given by the students can write such a conclusion. It can be seen that there is a law in our four calculations. Who can accurately summarize this law? ... From individual to general, the discovery of special cases is raised to a law and nature of universal significance. This is the "incomplete induction method" of the national ministry, allowing students to experience this inductive process and experience the scientific nature of the conclusion.
Loss: The shortcoming of this lesson is that there is some shortcoming in dealing with the "representation of the law by letters". After the students cite the law of letters to express the law, the a+b=b+a formula is used to express the law, and there is no further expansion. For example, how can the three numbers be expressed? Does this rule still apply? This kind of link design will make students more familiar with the law of letter representation, so as to cultivate mathematical ideas and strengthen the goal.
In the future of mathematics, pay attention to strengthen the difficult points of this lesson, and infiltrate and expand the mathematical ideas for the most difficult points, especially for the students who are worse, should repeat the reinforcement, try to let every child learn.