Reflection on simple equation teaching

Part 1: Reflection on Simple Equation Teaching

In the teaching of this class, I started from the following aspects:
First, feel the balance of the balance and realize the nature of the equation.
In the study, I present the nature of the equation in the balance of the balance in the multimedia. The students can understand the nature intuitively. The balance condition is that both sides add or reduce the same weight to maintain balance. However, the specific application to the equations allows students to feel that activities are an effective way to obtain true knowledge. Through the above activities, students can smoothly conclude that the balance is balanced on both sides of the balance.
Second, the equation of the nature of the equation - the initial understanding of its magical use
In the classroom, students are unfamiliar with the equations to solve the equations. In their original experience, they prefer to use the relationship between the various parts of the addition and subtraction. Therefore, we must pay special attention to guiding students to recognize the nature of the equation. To solve the superiority of the equation, and to develop the habit of solving the equation by the nature of the equation.
In the whole class of teaching, in fact, students are very active, they always feel that the balance can inspire them to solve such a magical equation, the children have a difficult curiosity about the equation.
The reform of the new curriculum has made the knowledge of the small country more integrated with the middle school. A new reform was carried out in the fourth unit of the fifth grade, "Solution of Simple Equations". The solution to the equation is required to be solved according to the principle of the balance, that is, to solve the equation by the nature of the equation. Although this method makes the solution of the equation find the essential thing, it also makes me feel a lot of confusion.
1. From the arrangement of the teaching materials, the overall difficulty is reduced, and it is intentionally avoided, in the form of 45-X=23 24÷X=6 and other types of topics. Simplify the method solved by the equation. In the actual teaching, we require students to use the equation method to solve the equation more skillfully. However, after solving the equation in this way, the book no longer has the equation of X minus the number or the divisor. The student is in the column. When the equations are actually applied, we can't deliberately emphasize that students will not list the equations in the back of X. We have more headaches than the students' practical ability to solve. This situation is unavoidable in practical equations. Obviously this has current limitations. For good students, we will let them try to accept - answer X's solution to the equations in the latter, that is, add X to the equal side, then change the position left and right, then subtract one from the other, it's a bit Trouble. And some students still have a hard time mastering this method.
2, the content seems to be less practical to teach. After the difficulty has dropped, it seems that the content that the teacher has to teach has become less, but it can actually be more. Teachers should give them a solution to the equation in which X is preceded by a divisor or minus sign. To teach them how to avoid the appearance of an equation with a divisor or minus sign before X and so on.

Part 2: Reflection on the teaching of simple equations

Remember that when I was in school, the way to solve the simplest equations was this: x+5=8 is x=8-5, x=3. I felt very good at that time, but now the fifth grade textbook is like this: x+5=8, x+5-5=8-5, x=3. It looks more complicated. When I first came into contact with this course, I saw that the solution in the textbook example was very confusing and puzzling. Why is the "solution to the equation" teaching of the new curriculum "around the road"? If we simply look at the equation of simple addition, subtraction, multiplication and division, the first method is undoubtedly simple and easy to understand, and the second method is relatively complicated. What is the purpose of the textbook change? After studying the teachings in depth, I realized that I have a deep understanding of the mathematics teaching of the new curriculum.
The reform of the new curriculum pays more attention to the transfer and connection of knowledge, so that the knowledge of the small country should be more integrated with the middle school. A new reform is carried out in the fourth unit of the fifth grade, “Solution of Simple Equations”. The solution to the equation is required to be solved according to the principle of the balance, that is to say, the equation is solved by the nature of the equation. This method allows the solution of the equation to find the essential thing. The teaching of solving equations in old textbooks is solved by the relationship between addition, subtraction, multiplication and division. Students only need to master an addend = and - another addend, subtraction = subtraction - difference, subtraction = difference + Subtraction, a factor = accumulation of another factor, divisor = dividend quotient, dividend = quotient × divisor, these relations, whether simple or complex equations can be used to solve. However, our new textbook is not this method at all. It is based on the balance principle of the balance to obtain the basic property of the equation, that is, the two sides of the equation are simultaneously added or subtracted by the same number equation, and both sides of the equation are simultaneously Multiply or divide by the same number, and the equation does not change the equation. If the new textbook can get the regular teaching of the balance, then the nature of the equation can be mastered, and the nature of the equation can be well understood. Therefore, when I was teaching, I made full use of the balance and the courseware to let the students understand the balance law of the balance deeply, thus smoothly revealing the nature of the equation. This makes it easy for students to master the method when solving simple equations. Knowing the unknown plus a number, as long as the same number is subtracted from both sides of the equation, the unknown is multiplied by a number, as long as the same number is removed on both sides of the equation. Generally, there is no such thing as a mistake in the operation symbol. So although complicated, it is easier to master.

Chapter 3: Reflection on Simple Equation Teaching

In the previous version of the textbook, before learning to solve the equation, students first need to grasp the relationship between the parts of addition, subtraction, multiplication and division, and then use the relationship between addition, subtraction and multiplication to find the unknowns in the equation. The design of the PEP textbook breaks the traditional teaching method, but borrows the balance to make the students first understand the "equation" and knows that "the equation adds or subtracts the same number on both sides, the equation is still established", so It is possible to reveal the meaning of the equation well in the true sense, and then learn to solve the equation, and also to establish a connection with the equation of the shift equation in the middle school. In the teaching of this class, I started from the following aspects:
First, feel the balance of the balance and realize the nature of the equation.
1. In the study, I present the nature of the equation with the balance of the balance. The students can understand the nature of the image intuitively. The balance condition is that both sides add or reduce the same weight to maintain balance. But when applied specifically to the equation, students feel more abstract. I guide students to understand the purpose and basis of adding and subtracting a number in repeated operations.
I put a 5 gram weight on the left side of the balance and a 5 gram weight on the right side.
2, the students hands-on and continue to operate.
On this basis, I will make further guidance.
Activities are an effective way to gain true knowledge. Through the above activities, students can smoothly conclude that the balance is balanced on both sides of the balance and the balance is still balanced.
3. Teacher: Please ask the students to think about it. If the balance is subtracted from the same quality on both sides, what will happen to the balance? Can you list a few such equations? If both sides of the equation are subtracted from the same number, the equation is still true. Through guidance, students can fully derive the nature of the equation. Finally, we combine the nature of the above findings into one by the students' own collation and summary. It is concluded that the same number is added to both sides of the equation and the equation is still true.
Second, use the equation to solve the equation - the initial understanding of its magical use
In the classroom, students are unfamiliar with the equations to solve the equations. In their original experience, they prefer to use the relationship between the various parts of the addition and subtraction. Therefore, we must pay special attention to guiding students to recognize the nature of the equation. To solve the superiority of the equation, and to develop the habit of solving the equation by the nature of the equation.
In the whole class of teaching, in fact, students are very active, they always feel that the balance can inspire them to solve such a magical equation, the children have a difficult curiosity about the equation.
Telling students to use the nature of the equation to solve equations is especially quick. At the same time emphasize the writing format. Through teaching, students can solve simple equations by using the nature of equations, but I think that the method of solving equations by using equations is simple, and the content is less problematic. Its performance is:
1. From the arrangement of the teaching materials, the overall difficulty is reduced, and the type of problem such as 66-2X=30 is intentionally avoided. Simplify the method solved by the equation. In the actual teaching, we require students to use the equation method to solve the equation more skillfully. However, after solving the equation in this way, the book no longer has the X equation in the following, and the student solves the problem when the column equation is actually applied. We can't deliberately emphasize that students will not list X's equations in the back? We are more a headache for the students' practical ability to answer. This situation is unavoidable in practical equations. Obviously this has current limitations. For good students, we will let them try to accept - answer X's solution to the equations in the latter, that is, add X to the equal side, then change the position left and right, then subtract one from the other, it's a bit Trouble. And some students still have a hard time mastering this method.
2, the content seems to be less practical to teach. After the difficulty has dropped, it seems that the content that the teacher has to teach has become less, but actually it is more. Teachers should give them a solution to the equation in X. To teach them how to avoid the appearance of X in the following equations, etc. Therefore, I simply handed over the old method to the students in order to reserve or ask them to choose the appropriate solution method according to the specific situation.
3. I personally think that some areas of the current textbooks have yet to be further improved and improved.

Chapter 4: Reflection on Simple Equation Teaching

Many times, most of us like to use equations to solve problems. This is because I have learned a lot of equations in middle school, one yuan, one yuan, two times, etc., but there is one more important reason is the equation. When the problem-solving ideas are liberated and the formula is used to solve practical problems, the problem-solving ideas often turn around, and he fundamentally allows students to break away from the cumbersome analysis of ideas, while the column equations solve practical problems, and the problem-solving ideas are often straightforward, reducing the difficulty of thinking. It allows students to solve problems from a simple idea - find the same amount of relationships. Therefore, it is very important to teach the knowledge of this unit so that students can learn well.
First, use the letters to represent the number to pay attention to the understanding of the quantitative relationship
The use of letters to represent numbers is the beginning of the initial knowledge of students learning algebra. In arithmetic, people only study some specific and individual quantitative relationships. After introducing numbers in letters, they can express and study quantitative relationships with more general meanings. It can be said that learning algebra begins with learning to represent numbers in letters.
For primary school students, abstracting the number from specific things is a leap in understanding, and the transition from specific and certain numbers to the use of letters to represent abstract, variable numbers is a leap in understanding. Moreover, based on the use of letters to represent unknowns, the mathematical tools that enable students to solve practical problems, from the formulation of formula solutions to the listing of equation solutions, is a leap in the understanding of mathematical thinking methods, which will enable students to use mathematics. The ability to solve practical problems has increased to a new level. In the teaching practice of teachers, because the format is very important when solving problems with equations, teachers often emphasize the format when teaching. However, from the follow-up study of the students, I slowly discovered that in the teaching of this part of the knowledge, the teacher should pay attention to the students' understanding of the quantitative relationship, that is, to strengthen the training of the students with the number of expressions containing letters. That is, writing algebraic training. Because this is the basis of the column equation. Therefore, the teacher here must emphasize and repeat the practice to express the number with the formula containing the letters, so that the students understand that all the quantitative relationships learned in the past can be used in the expression of the formula containing the letters. Such as: the original has 100 yuan, use X yuan, the same to use subtraction to find out how much money left, bought 3 exercise books, each A yuan, the same multiplication to find a total amount of money. Let students know that the number of formulas containing letters is the same as before in such a large number of exercises and reinforcements. However, the symbols used now are different. In fact, in a broad sense, letters are a kind of symbol, and numbers are also a kind. symbol.
Second, pay attention to the teaching of the meaning of the equation.
What is the equation, as it is said in the textbook, the equation containing the unknown is called the equation. In fact, this is just a definition of the equation from the form of the equation. That is to say, from the appearance, if an expression is an equation and contains an unknown number, we say that the expression is an equation. But what is the meaning of the equation in essence of mathematics? Each of us can skillfully solve the problem by solving the equations. So, what is the core of your grasp every time you solve the problem? Is the same amount relationship. Therefore, the most essential teaching meaning of the equation should be that the same quantity is expressed in different forms. But many times, teachers often only study the surface form of the equation when teaching the meaning of the equation, which is what the book says: the equation containing the unknown is called the equation, so the teachers usually start with the equation. Let students introduce unknowns on the basis of understanding equations, and then tell students that equations with unknowns like this are called equations. In this class, students will not know whether a relationship is an equation or not. What do you know? Does such learning really help solve the problem in the following column equations? I think everyone should calm down and think about it, there should be an answer.
Third, the solution to the equation should not be influenced by the previous textbook layout.
The arrangement of the new textbook for solving the equation is very variable. Previously we solved the equation based on the relationship between the various parts of the four arithmetic operations. At the beginning, I did not explain the equation to the students, calling for the unknown number X. However, the current textbook layout is based on the nature of the equation. Of course, the nature of the equation is not summarized in the textbook. After all, in the student’s national stage, as long as the students understand, add both sides of the equation. , subtraction, multiplication, and division by the same number, the equation is still true, which is not the nature of the equation in the full sense. From the perspective of students' learning, I think that students are more likely to accept this method, especially the simpler equations. Students only need to understand who to offset and how to offset. Basically, the problem is not big. However, there are some problems with the slightly complicated equations. This may be because I am teaching this part of the content, because I always consider that students don’t like column equations, so I want to let students write less words, so, The specific writing format and steps are slightly different from the textbooks. I didn't write the nature of how to apply the equations like the textbooks, but let the students directly write the results of this step, so that after the end, there are some There are some problems in the students, especially the equations like 5=55. The students are poorly mastered. It may also be that students are not well established when they use the formula containing letters to indicate the number. A whole, representing a number of such concepts, although some emphasis has been made. On the other hand, specific steps may also have an impact on students. Therefore, I personally think that it may be more helpful for students to follow the steps in the book, although it is a little troublesome.
In general, I think that the simple equation unit, as long as the students have a good use of letters or letters to represent the basis of the number, plus a clear understanding of the essential meaning of the equation, know how to solve the equation, Others should not be a problem. After all, the above is the basis for solving the problem of the column equation. After the foundation is laid, the latter problems can be solved.

Part V: Reflection on Simple Equation Teaching

This lesson is the fourth component of the PEP version. The method of solving the equations of this textbook utilizes the principle of balance balance and uses the nature of the equation to solve the equation. Equations such as x±a=b use the basic properties of the equation. Students can easily solve the equations such as ax=b and x÷a=b. Using the basic properties of the equation, students can easily solve them. However, if the equations such as ax=b and a÷x=b are used, the students will not be able to start. If the basic properties of the equation are used, the process of deformation and the explanation of the equations are more troublesome. When solving a problem, when it is necessary to list equations of the form ax=b or a÷x=b, I ask the students to form equations such as x+b=a or bx=a according to the quantitative relationship of the actual problem. But I think it is not a good way to avoid these two kinds of problems. Otherwise, our teaching will be one-sided and narrow. For example, a total of 128 people are divided into groups of ,, each group of 8 people, students do not hesitate to list 128÷x=8, but students will not solve the basic nature of the equation, but you can not say this equation The column is wrong.
Therefore, when I have a student with an equation of ax=b or a÷x=b, I took the opportunity to teach the method of using the arithmetic idea to solve the equations of the boss textbook. Children with good foundations are easy to accept new methods, and children with poor foundations are still unable to answer such questions.
In addition, the textbook requires that when the students use the basic properties of the equation to solve the equation, the deformation process of the equation should be written, and then wait until the proficiency, and then gradually omit. Such a requirement brings tedious writing in actual operation. Because the equation is solved by the basic properties of the equation, the deformation of the equation can be completed every two steps. This is nothing compared to simple equations, but for some slightly more complicated equations, the process of solving them is too cumbersome.
It seems that the textbook uses the basic properties of the equation to solve the simple equation. There are still some problems. Do you know that teachers have any good methods to solve these problems? Please let me know!