Reflection on the meaning of the equation

Part 1: Reflection on the meaning of the equation

The meaning of the equation is a mathematical concept class. It is based on the fact that students are familiar with the common quantitative relationship and can use the letters to represent the number, but it is difficult to understand. Let's talk about the practices and opinions in teaching in the course of "The Meaning of Equations" that I teach.
Looking back at the teaching process, I think there are several characteristics as follows.
First, review the introduction, excite the topic
This section mainly reviews the old knowledge that is indirectly related to new knowledge, paves the way for learning new knowledge, and introduces the new one. The equation is a mathematical model that expresses the relationship between the number of actual problems. It is familiar with the common quantitative relationship and can be used by students. The letters represent the number based on the teaching, so at the beginning of the class I presented a set of questions in conjunction with some of the life phenomena related to the students, asking the students to express them in a formula containing letters. The emergence of these questions will enable students to review and consolidate the knowledge they have learned before. It will also enable students to realize that there are many phenomena in our lives that can be expressed in style, which stimulates students' interest in learning and leads to the learning content of this lesson. This kind of course is very practical, very simple and very useful.
Second, practice operations, establish equation models
The inquiry exchange in this lesson is mainly reflected in the concept acquisition process of “equal with unknowns, called equation”. In this process, I first let the students observe the balance “balance phenomenon → imbalance to balance → uncertainty Phenomenon "three intuitive activities, abstracting related mathematical expressions, and then observing the characteristics of these mathematical expressions, abstracting the concept of the equation, that is, the abstract process from "formula → equation → equation", and then through the necessary Practice consolidation to deepen understanding and application of the concept of equations. Through this series of observation, thinking, classification, and induction, we will break through the difficulties of this lesson.
Third, return to life, experience the equation
After establishing the meaning of the equation, the corresponding equations are designed according to the situational map, and life examples are introduced at the end to find different equations. In this process, students look for the equations of equal relationship in life practice, further understand the meaning of the equations, deepen the understanding of the concept of equations, and lay the foundation for solving the practical problems by using equation knowledge in the future.
Fourth, the lack of teaching
1. From the perspective of the students' existing knowledge reserves, they will use the formula containing letters to indicate the quantity. Most students know the equation and can give examples to provide students with a problem situation indicating balance between the left and right sides of the balance. Most students use arithmetic. Method column. However, the students use the arithmetic method to solve the problem, causing some interference to the column equation.
2. Although it is more interesting to use the balance to solve practical problems, it is difficult to ask students to convert the life situation they see into using mathematical language and expressing it in a quantitative relationship containing unknown numbers.
3. I should leave enough time for the students to think, instead of saying the answers quickly for the students.
V. Improvement measures
In the future class, I think the first step is to prepare for the lesson in the lesson. The key knowledge should be carefully prepared. It must be detailed, specific, and fully consider all kinds of possible situations. Prepared students are sometimes more important than preparing textbooks. Preparing lessons that are out of touch with students will have a significant impact on classroom instruction. The task requirements in the class must be specific. Each description will have different understandings. Students will also be completed at different levels. They should be clear and easy to understand, so that students can operate and complete according to requirements.

Part 2: Reflection on the meaning of the equation

In designing this lesson, I took the meaning of the equation as the focus of the teaching, not only letting students understand the concept of the equation, but also what is the equation. More thinking is the student's subsequent learning and thinking about the equation, focusing on the penetration of knowledge. Such as the nature of the equations learned later, the use of equations to solve problems and so on.
In the class, I asked the students to ask mathematics questions according to the created situation. The students could hardly mention the problem of expressing the relationship between the two. They were all questions of unknown numbers. At this time, the teacher directly presents the required questions, and then asks the students to find the same relationship first. I found that only a very small number of children can find the same relationship. Because of the first appearance in the same amount of relational textbooks, students don’t know where to start. The students thought about it for a while, and I found that there was no result. I led the students to analyze the information and find the same relationship. Finding the equivalent relationship and then listing the formula with letters is much simpler. My analysis under the class is mainly because I overestimated the students when preparing lessons, and how to guide them requires more research. This is also the focus of my next training.
In order to let students figure out the relationship between equations and equations, I use the demonstration of the balance to let students understand the meaning of the equation. It is easy for students to list the formula according to the balance. Then the teacher pointed out that the formulas we just listed are called equations. What do you find in these equations? It is easy for students to come up with two equations: one is an equation without an unknown number, and the other is an equation containing an unknown number. On this basis, let the students compare the concepts of the equations and then judge which ones are the equations through practice. Not an equation? Finally, let the students express the relationship between the equation and the equation in the form of drawing. This content does not appear in the textbook, but I added it. I think this helps students to deepen their understanding of the meaning of the equation. From the overall perspective of the class, most of the students' thinking is clearer and will be expressed, but some students are unclear and the speech is not positive enough. It seems that classroom teaching should also activate the students' thinking and mobilize the students' enthusiasm. As teachers, they should think more ways.
“Self-independent inquiry” has always been the way we learn, but how to implement it effectively? I believe that "self-learning" must be realized under the scientific guidance of teachers and through creative learning. "Cooperative inquiry" must be carried out on the basis of students' independent thinking. Otherwise, students will not have their own opinions, and communication will be in the form without depth. With the independent thinking of students, when students show exchanges, different ideas and methods will collide. Teachers should respect the results of students' exploration, guide students to reflect on and improve their own results and methods, and encourage all participation and life. An understanding of the process of knowledge formation and the ability to sort out the generalized knowledge.
Throughout the teaching process, teachers as the leader should inspire students to discover knowledge, give full play to the students' potential, and gradually guide students to think and solve problems in depth, which is conducive to cultivating students' listening habits and cooperation consciousness.

Part 3: Reflection on the meaning of the equation

"The meaning of the equation" This is a brand new knowledge point. It is based on the fact that students are familiar with the common quantitative relationship and can use the letters to represent the number, but it is difficult to understand. The mathematics teaching process should first be a process for students to have a rich emotional experience. To let students learn and learn, and let students get a positive emotional experience in the teaching process, let's talk about my practices and opinions in the teaching of the "The Meaning of Equations" taught by me.
Looking back at my teaching, I think there are several features as follows.
First, set up situational guidance to promote students' independent learning
Through the demonstration of the balance in the course of teaching the meaning of the equation: Recognize the balance, the students said the role and usage of the balance. In this link, we must give full play to the low-vision ability, but we must pay attention to the guidance of students with learning difficulties. In this respect, students with learning difficulties should be given more opportunities to contact the balance, at least let them establish a preliminary understanding of the balance.
Second, cooperation and exchange, summary and summary
The concept of the equation is derived from the observation of the balance, and then the students should think independently. By comparing the equation with the equation, and the difference between the inequality and the equation, the concept of the equation is obtained, which reflects the ability of students to learn independently. Instead of speaking the answer quickly, the student should be given the concept of the equation. Through variant training, it is understood that not only X can represent unknowns, but other letters can represent unknowns. In this teaching process, teachers should act as a guide, standing at the fork of knowledge, inspiring students to discover knowledge, giving full play to students' learning potential, putting problems with certain difficulties into groups, and adopting cooperative communication. To solve it, and gradually guide students to think and solve problems in depth, it is conducive to cultivating students' listening habits and cooperation consciousness.
Third, return to life, experience the equation
After establishing the meaning of the equation, the corresponding equations are designed according to the situational map, and life examples are introduced at the end to find different equations. In this process, students look for the equations of equal relationship in life practice, further understand the meaning of the equations, deepen the understanding of the concept of equations, and lay the foundation for solving the practical problems by using equation knowledge in the future.
From the perspective of the students' existing knowledge reserves, they will use the formula containing letters to indicate the quantity. Most students know the equation and can give examples to provide students with a problem situation that indicates the balance between the left and the right of the balance. Most students use arithmetic methods. formula. However, the mathematics problem solving method that students have solved to solve mathematical problems will cause certain interference to the column equation. It is more interested in using the balance to solve practical problems. However, it may be difficult for students to translate the life situation they see into using mathematical language and expressing relationships. It is necessary to find the same amount of relationships and use mathematical language from various specific situations. The expression shows that teachers need guidance and mutual help, and it is necessary to combine independent thinking and cooperation and exchange.

Part 4: Reflection on the meaning of the equation

"The meaning of the equation" is a mathematical concept class. Concept teaching is a kind of theoretical teaching. It is theoretical and academic, and it tends to be boring, but at the same time it is a basic teaching. It is to learn a deeper knowledge and solve more in the future. The knowledge support of practical problems, so this class I pay attention to the openness of concept teaching, the nature of autonomy and the formation of concepts. This lesson is based on the fact that students are familiar with the common quantitative relationship and can teach on the basis of letters, but it is difficult to understand. The mathematics teaching process should first be a process for students to obtain a rich emotional experience. Students should be happy to learn and be eager to learn, so that students can get a positive emotional experience in the teaching process. Let's take a look at this lesson and talk about my practices and opinions in teaching:
First, guess the digital game import, excitement
Before the class begins, let's play a game of guessing numbers. The teacher knows that the student uses the number on the playing card to "multiply 2, add 3, use the sum and multiply 5, and finally subtract 25". The result was 50, and it was quickly guessed that the student’s playing card was 6. At this time, the students were very surprised. At this time, the teacher asked, “Would you like to know why the teacher can guess so fast? It is the “equation” of the mathematics kingdom that helped the teacher. Do you want to know what is the equation? Let’s Learn from it first.” The way the game provokes students' curiosity about the equation and stimulates interest in learning this lesson. The “game revealing” in the last part of the lesson not only communicates the connection between mathematics activities, but also makes students understand the value of the equation as a mathematical model in solving practical problems.
Second, cooperation and exchange, summary and summary
Through the demonstration of the balance: Recognize the balance, the students said the role and usage of the balance. In this session, we must give full play to the low-vision ability, pay attention to the guidance of students with learning difficulties, and give students more opportunities to contact the balance in this aspect, at least let them establish a preliminary understanding of the balance. A lot of formulas are derived from the observation of the balance. Let the students cooperate and exchange observations to classify and derive the concept of equations. By comparing the equations with equations and the inequalities and equations, the concept of equations is obtained, reflecting the students' ability to learn independently. From the actual situation, the equations and inequalities are listed, so that students can express the words to be spoken with mathematical symbols, so that students can experience the process of expressing life phenomena in a simple way of mathematics, which not only makes students initially perceive the expressions of the equations, but also Infiltrated the modeling idea. In this teaching process, teachers inspire students to discover knowledge, give full play to students' learning potential, put problems with certain difficulties into the group, solve them by means of cooperation and communication, and gradually guide students to think and solve problems. In-depth development is conducive to cultivating students' listening habits and cooperation awareness.
Third, return to life, experience the equation
Incorporating abstract equation definitions into a vivid speculative context, students are able to form a deep impression of the external features of the equation in a reasonable interpretation of the equations that are obscured by ink. In addition to providing students with an understanding of the concept of equations, students are provided with an open space for thinking. Students not only show the results of learning, but also the diversity of equations. At the same time, in the judgment of the equations listed by myself, the understanding of the essence of the meaning of the equation is deepened. After establishing the meaning of the equation, the corresponding equations are designed according to the situational map, and life examples are introduced at the end to find different equations. In this process, students look for the equations of equal relationship in life practice, further understand the meaning of the equations, deepen the understanding of the concept of equations, and lay the foundation for solving the practical problems by using equation knowledge in the future.
Fourth, in the "look", "say" and "write" experience equation
When the meaning of the equation is established, I ask the students to observe a set of equations to judge whether they are equations. By judging whether these equations are "equations", why "not equations", understanding the relationship between equations and equations, deepening the equation Understanding of meaning. Let the students write some equations and show their own methods.
V. Practical application, sublimation and improvement
I designed the practice form of picking up the wisdom star in the game and started the exercise. In the practice design, from easy to difficult, from shallow to deep, the students' thinking develops continuously, which makes students understand the meaning of the equation more deeply, especially for the students to freely create the equation, which allows students to apply knowledge. It also cultivates students' innovative thinking.
The teaching design of this lesson has changed the traditional learning style, and used the static resources of the textbook to modernize the mathematics scene through modern teaching methods, which greatly stimulated the students' interest in learning, fully reflected the students-oriented, allowing students to think independently and continuously summarize. To transfer students from passively receiving knowledge to self-exploration, providing students with the space for independent inquiry and cooperation. In the study, I realized the joy of learning mathematics, while gaining knowledge, emotional attitudes, and abilities.
Of course, there are still some problems in this class:
1. The relationship between the equation and the equation is not prominent enough. The two necessary conditions of "containing unknowns and equations" in the definition of the equation are not emphasized, resulting in individual students choosing y+24 as an equation in the choice of questions.
2. The training of “speaking” to students is not enough, and students should be given more opportunities to express themselves.
3. Your own classroom language is not accurate enough, not rich enough, and needs to be improved.
It is often said that "classroom teaching is a regrettable art". Only by continuous summarization and constant reflection can we make continuous progress and lower regrets to a minimum.

Part V: Reflection on the meaning of the equation

This time, the school carried out activities. During the event, we collectively prepared the lesson of the meaning of the equation as a seminar. The difficulty of this lesson is to distinguish between "equation" and "equation". In order to break through this difficulty, we have carefully designed the teaching process of this lesson.
Before the new class, I showed the card:
Then in the process of teaching the meaning of the equation, in order to enable students to understand what is equal, we first use a ruler with a uniform length of 1 meter and put it on the finger. Through this simple game, students can understand what is balance and Unbalanced, balanced situation is when the weight of the left and right sides are equal, followed by the introduction of the balance, placed 20 + 30 two squares, 50 weights on the left and right sides of the balance, and according to the balance relationship An equation, 20+30=50; then one of the 30 is converted to one direction, but the 30 mark is a "?" balance is still in equilibrium. Got another equation 20+? = 50, marked? After re-converting one direction, the above is marked x, and the balance is still in equilibrium, so that an equation 20+x=50 can be written. The whole process focuses on guiding students through a series of activities such as demonstration, observation, thinking, comparison and generalization. From shallow to deep, stratification advances, and gradually draws the "equation" - "equal with unknowns" - "equation" .
Although the entire teaching task seems to be completed. However, from the students' practice, we found that there are still some students who have not really figured out the relationship between "equation" and "equation". For example, there is a discussion in the exercises: "Equations are all equations, and equations Not necessarily an equation." Is this sentence correct? But through the cooperative learning and arguments of the groupmates, the answers are different. Although the students who did the wrong thing were finally convinced by the classmates who did the right thing, it also shows that there are still problems in the teaching process of "equation" and "equation". In fact, we ignore the direct contrast between "equation" and "equation".
The introduction of our oral calculations was originally intended to pave the way for the study of this lesson, but in the first class, we did not go back and make full use of the oral calculations. After class, after everyone's evaluation and the guidance of the coach of the Science and Technology Center, it seems to be a very simple question, which hides the relationship between the equation and the equation. In the second lesson, we improved, and after returning to the "equation" and "equation", we returned to the oral calculation card and passed the change of the problem of the card - just the equation |, - is both an equation and an equation. This comparison makes the relationship between the "equation" and the "equation" clear.