Reflection on solving simple equation teaching

Part 1: Reflection on the Simple Equation Teaching

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". I can reflect on this activity under my class as follows:
1. At the beginning of this lesson, show the balance and put forward the question “How can we make X balance on the left side of the balance and keep the balance balanced?”, guide the students to maintain the balance of the balance, and introduce the change method of the agenda. This kind of process has achieved the goal of “knowledge in the game, abstraction into the image, and no change to the specifics”, which makes the students' learning meaningful and interesting.
2. If I prepare some “small egg beads” in front of the class instead of the demo weight, the students will understand more intuitively that the equation remains the same as the equation.
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, such as: 45-X=23 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 latter equations, 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.

Chapter 2: Reflections on the Solution of Simple Equations

Solving equations is an important part of mathematics. In real life, after learning the equations to solve problems, many exercises that are difficult to solve with arithmetic methods can easily solve the equations. This is enough to explain the column equations. It has obvious advantages over arithmetic to solve problems.
This year, I taught the fourth grade. The textbook used is the Qingdao version of the May 4th textbook. The first unit has the content of understanding the equation. I have already taught this part of the textbook four times. It is reasonable to say that this part of the fifth teaching should be It is easy and easy to move, but in the face of the design of new textbooks, my five-year-old teacher who does not teach higher grades has a lot of confusion---the teaching design of this textbook breaks the traditional teaching method, and it is beyond me. What is expected is to use the balance demonstration to make the students feel the "equation" and know that "the equations are added or subtracted by the same or a non-zero number, and the equation is still true", so that the students can further Understand the meaning of the equation in a true sense and learn to solve the equation using the properties of the equation. In the previous rounds of textbooks, before learning to solve the equations, students were first required to master the relationship between the parts of addition, subtraction, multiplication, and division, and then use: one addend = and - the other addend; the subtracted = Subtraction + difference; subtraction = subtracted - difference; dividend = quotient × divisor; divisor = dividend quotient quotient and other relations to obtain the solution of the equation, even the solution equation that I learned when I was a child It is also based on the relationship between the parts of addition, subtraction, multiplication and division to find the solution of the equation.
At first, I was somewhat suspicious. I thought that only the version of the Qingdao version of the May 4th edition used the teaching of the nature of the equation, so I eagerly opened the computer to find various versions of the electronic textbooks to look at this part of the content, but found various versions of the textbook design ideas. The same is true, first learn the basic properties of the equation, and then use the basic properties of the equation to solve the equation. In order to thoroughly understand the intent of writing the textbooks, I have found the teaching materials of the teachers in these versions of the textbooks. The new textbook writers generally explain this: For a long time, when the simple teaching equations were used by the national small schools, The basis of the equation deformation is always the relationship between addition, subtraction, multiplication and division, which is actually using the arithmetic idea to find the unknown. In the middle school, we must start another stove and introduce the basic properties of the equation or the principle of the same solution of the equation to teach the equation. The stronger the master's thinking and its algorithms are, the more obvious the negative transfer of the primary school algebra start-up teaching. Therefore, according to the requirements of the Standard, the basic nature of the equation is introduced from the national small, and the method of solving the equation is derived based on this. This completely avoids the two concepts of the same content, two kinds of mathematical explanations, and is conducive to strengthening the convergence of Chinese small mathematics teaching. After reading these contents, I have accepted this design idea from the ideological point of view. It was originally intended to make the method of solving the problem of the elementary school teaching and the method of solving the equation in the middle school teaching consistent.
Understand the design intent of the textbook, I began to force myself to reverse the old teaching ideas. As a result, because the students were first contact, the students in the classroom were so fascinating. However, in the following teachings, I gradually found that using the basic nature of the equation to solve the equations brought to the students is actually a partial convergence, and the existence of local convergence is more difficult for students. From the arrangement of the textbooks, although the overall difficulty has declined, the method of solving the equations using the nature of the equations has been simplified. The textbook intentionally avoids the types of problems such as a-X=b a÷x=b, and does not teach the solution of such equations, because such problems are very troublesome if they are solved by the nature of the equation. Obviously, using the nature of the equation, this method has many limitations in teaching the equations of the national stage.
However, when the teaching column equation solves the practical problem, we can't avoid the students still have equations like ax=b and a÷x=b when they are in the equation. In particular, we can't deliberately emphasize to students that they cannot list X. After doing the subtraction or divisor equation, if this is emphasized, there will be great doubts in the students' minds. When students list such equations, we have more headaches than the limitations of students' ability to solve.
In view of the above reasons, I used the method of combining old and new teaching ideas in the classroom. I first used the basic nature of the equation from the new ideas in the textbook to teach the children to solve simple equations, so that they can smoothly integrate in the future study in the middle school. The “migration” of the middle school can also be successfully received. However, in the face of the thinking and acceptability of the fourth-grade children, I will use the teaching ideas of the old textbooks to “add, subtract, multiply and divide the relationship between the various parts of the method” to teach the children to solve the equations. At least this will enable my students to solve various types of problems. Equations, especially for children to solve equations to solve practical problems, they will not be plagued by the equations of "divide by multiplication" and "additional subtraction", and list them to solve this equation smoothly.
I personally think that using the old and new methods combined with teaching can not only make students connect for future study, form a green channel, but also reflect the diversity of methods and ideas to solve the same problem. Through the classroom work of the students, I found that the teaching effect was surprisingly good.
By solving the teaching of this part of the equation, I feel that no matter how long your teaching age, you have taught the same teaching content several times. Every teaching requires teachers to calm down and study the teaching materials so that they can use the most. A method suitable for students' future development to teach students.

Chapter 3: Reflections on the Solution of Simple Equations

Students experience the process of abstracting the algebraic problem from the specific operations on the balance. The equations can be listed by the nature of the equation. Students are no strangers to solving simple equations.
For example: x+4=7 students can quickly say x=3, but in terms of the writing rules of the equation, it is necessary to strengthen the training from the beginning, and the teacher's standardized blackboard to exert the strong effect of first-time perception of preconception and promote good writing. The formation of habits. For a slightly more complicated equation, let the students try it out, so that inquiry-based classroom teaching can enter an ideal state.
It is not difficult to see that the students experienced the process of mistakenly changing the arithmetic symbol "+" to "-" and correcting themselves. In this process, the students experienced the feelings of nervousness, anxiety, expectation, and success. At this time, mathematics learning has entered. The inner heart of the students, and become the process of student life growth, truly implement the goal of "successful experience in mathematics learning activities, exercise the will to overcome difficulties, build self-confidence" in the "Mathematics Curriculum Standards", in this thinking process Students gain an emotional experience and the opportunity to find faults and solve problems themselves. The teacher is people-oriented, fully respects the students, and is also reflected in patient waiting, eagerly expecting teaching behavior, the teacher's teaching behavior is full of humanistic care, smiling face, anticipating eyes, encouraging words, making students feel all the time. This is not only a process of mathematics learning, but also a process of life communication. Students have a very safe psychological space. Otherwise, how can he say to the teacher, "Teacher, I am too nervous", this is the trust of the students and the teacher. The performance of complex emotions that are uneasy about yourself. Rethinking our teaching behavior, if we have more patience and expectation in the classroom, there will be more love for more students, and students will have more confidence, more courage, and more Reiki.

Part 4: Rethinking the Simple Equation Teaching

The mathematics curriculum standard changes the teaching requirements of the equation method in the national ministry, and uses the nature of the equation to teach the equation. Here are some examples of new and old methods for solving equations:
Old method:
x + 4 = 20
x = 20-4
Based on the relationship between operations: one plus is equal to and minus the other.
new method:
x + 4 = 20
x + 4-4=20-4
According to the basic properties of the equation 1: Add or subtract equal numbers on both sides of the equation, the equation is unchanged.
Reasons for reform:
The new textbook writers have explained that for a long time, when the national small school teaches simple equations, the basis of the equation deformation is always the relationship between addition and subtraction operations or the relationship between multiplication and division operations. This is actually using arithmetic ideas to find unknowns. In the middle school, we must start another stove and introduce the basic properties of the equation or the principle of the same solution of the equation to teach the equation. The stronger the master's thinking and its algorithms are, the more obvious the negative transfer of the primary school algebra start-up teaching. Therefore, according to the requirements of the Standard, the basic nature of the equation is introduced from the national small, and the method of solving the equation is derived based on this. This completely avoids the two concepts of the same content, two kinds of mathematical explanations, and is conducive to strengthening the convergence of Chinese small mathematics teaching.
From this we can easily see that the main reason for this reform is to be consistent with the method of solving equations in middle school teaching.
Then, what kind of situation will occur in the actual operation of the primary school students? Is there any problem with such reform? There was a problem in my teaching process.
1. Unable to solve equations such as ax=b and a÷x=b
The new textbook believes that after solving the equation using the basic properties of the equation, the equations such as x+a=b and xa=b can be reduced to a simultaneous subtraction of a from the equation; solutions such as ax=b and x÷a= Equations of class b can be attributed to the fact that both sides of the equation are divided by a. This is the superiority of the so-called "more unified than the original method." However, it has a corresponding adjustment measure that deserves our attention, that is, it avoids the equations of the form ax=b and a÷x=b. The reason is that primary school students have not yet learned the four arithmetic operations of positive and negative numbers. Using the basic properties of the equation to solve ax=b, the process of equation deformation and the explanation of arithmetic are more troublesome; and the equation of a÷x=b, because its essence is a fractional equation According to the basic nature of the equation, it is necessary to go to the denominator first, and it is not suitable for learning in the national stage.
I think it seems inappropriate to use the basic properties of the equation but to avoid the two types of equations. More importantly, avoiding these two types of equations, the new textbook does not affect the student equations to solve practical problems. Because when it is necessary to list equations of the form ax=b or a÷x=b, the student is always required to form an equation such as x+b=a or bx=a according to the quantitative relationship of the actual problem. But I think that such a treatment method sometimes inevitably contradicts the equation thinking directly.
For example, "3 kilograms of pears is 0.5 yuan more than 5 kilograms of peaches. 2.5 yuan per kilogram of pears, and how many yuan per kilogram of peaches?" A reasonable approach should be to "set peaches per kilogram of X yuan". From the forward thinking, list the equation as " 2.5 × 3-5X = 0.5". However, according to the arrangement of the new textbooks, because the students will not solve such equations now, they should be classified into equations such as “5X+0.5=2.5×3” according to the quantitative relationship. Another example: on page 62 of the textbook, "Dad is 28 years older than Xiao Ming, Xiao Ming is 40 years old, and Dad is 40 years old." Many students list 40-Х=28 according to "Daddy is 28 years old than Xiaoming", but can't solve it, so Then turned into Х +28 = 40.
Obviously, the second equation is contrary to the basic idea of ​​the equation. We know that the biggest meaning of the equation is to let the unknowns participate in the equation, making the consideration of the problem more direct and natural. To achieve this goal, it is important to think as far as possible in order to reduce the difficulty of thinking. This is an inevitable requirement for the superiority of the equation method. In fact, if the student can be listed as “5X+0.5=2.5×3” “Х+28=40”, then he is already very familiar with the quantitative relationship. In this case, you can use the arithmetic method, and there are columns. What is necessary to solve the equation? How can we talk about guiding students to understand the superiority of the equation?
It is not difficult to see that solving problems according to the equation of reality situation, X as a subtraction, as a divisor, should be a very common and necessary phenomenon. It is a normal teaching requirement for students to learn to solve these equations. This should not be avoided. Otherwise, our teaching will be one-sided and narrow.
2. The process of solving the equation is too cumbersome
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.
From these two aspects, Guo Xiaoli learns the basic nature of the equation and uses it to solve the equation. In practice, there are also many practical problems. Then, if we use arithmetic to solve the equation and have a negative transfer to the middle school, we need reform. Now we have changed the equation to solve the equation with the basic nature of the equation. If there is a problem, then how can we be good?

Chapter 5: Rethinking the Simple Equation Teaching

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, such as: 45-X=23 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 latter equations, 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.