? What is the meaning of the equation? The key point of teaching is to let students understand the essence of equation. Experiential equation is a mathematical model that describes the equivalence relationship in the real world and preliminarily experiences the idea of equation. What is an equation? Textbooks say that equations with unknowns are equations. The essence of the equation is to treat the known number and the unknown equally, and obtain the unknown number by establishing the equation relationship between the known number and the unknown number.

Fully understand the essential characteristics of the equation with the help of the balance

To understand the essence of the equation, students must first understand the meaning of the equation. At the beginning of the course, show the balance and let the students talk about its characteristics. If the pointer that students understand in communication points to the center of the balance, it means that both sides of the balance are balanced. That is, (mass on the left = mass on the right). If the pointer is biased to the left, the mass on the left side of the balance >; The object on the right. If the pointer is biased to the right, the mass on the left side of the balance

On the basis of classification, fully understand the dominant characteristics of the equation.

Guide students to carefully observe the feedback formula and classify it according to certain standards. Think about how to classify and communicate with the class. Clever use of classification means, so that students can actively find the difference between them through observation. Further guidance on the basis of the equation, what else did you find? Let the students observe the equation and think again: What do you think is an equation? An equation is an equation, which contains unknowns. The students themselves come to the conclusion that an equation is an equation with unknowns. Finally, let the students talk about the relationship between equation and equation. Guess whether the original column is an equation through practice?

( 1) 0.36 + = 42

(2) 0.5 + 1.2? 5.3

(3)- 20 > 5

(4) 6? + = 78

The main characteristics of the equation, namely? Including unknowns? And then what? Equation? . This lesson uses the method of classification to help students understand the external characteristics of equations through comparison: first, it is divided into equality and inequality according to whether it is an equation, and into formulas with unknowns and formulas without unknowns according to whether it contains unknowns; Secondly, considering the two classification criteria comprehensively, all formulas are divided into four categories by cross method, and the difference between the equation and other formulas is clear at a glance. Then further understand the dominant characteristics of the equation through practice.

Return to the situation, highlight? Equation model? The value of

When the students know the equation and browse the equation, in the last part, I designed an exercise to let the students make up different situations according to the same equation. Show pictures 2 and 3 and say:? These two problems can be listed as equation 5x= 100. Can you compile other mathematical situations and list the equation 5x= 100? At this time, it aroused the students' thinking, waited quietly for a while, and many students raised their hands. Some students said:? There are five identical books, each with X yuan, and five books 100 yuan. ? Some students said:? A car travels an average of x kilometers per hour, 4 hours 100 kilometers. ? Others said:? On average, each person is divided into 4 notebooks, and X people are divided into 100 notebooks. ?

The essence of the equation is: the unknown quantity is required, and the equality relationship between the unknown quantity and the known quantity is established. Professor Chen Zhongmu, a doctoral supervisor of algebra in Southwest University, once pointed out:? An equation with unknowns is called an equation? This definition does not reflect the essence of the equation, so this definition should be diluted, not recited, not recited, not tested. The key is to understand the essence, value and significance of equation thought. Therefore, the focus of this lesson is to establish the equation model, truly understand the essence of the equation, and let students experience the equation modeling process.

?

Reflections on the Teaching of Equation Meaning (Ⅱ)

I. Introduction

What should our teaching give students? Is it knowledge or method? I think method is more important than knowledge. Once students master the scientific learning methods, they will play a positive role in the follow-up study. So how to teach students to learn in math class? How to embody it in classroom teaching? High participation, high autonomy, high coordination, high pleasure and high efficiency? Teaching philosophy? Considering this, I designed the course "The Meaning of Equation" and won the first prize in the 20 13 Xixiang Quality Class Competition.

Second, the introduction of teaching background

1. Students' cognitive level and cognitive characteristics.

Cognitive level: the meaning of the equation is the content of Unit 4 in Book 9 of the textbook for six-year primary schools with nine-year compulsory education. It is based on the fact that students have learned some arithmetic knowledge and been exposed to some algebra knowledge. Before this class, I learned to use letters to represent common quantitative relations, algorithms, calculation formulas, use letters to represent quantities, and find the value of formulas according to formulas containing letters.

Cognitive characteristics: children in the fourth grade are sensitive to knowledge, and they must link mathematics with life before they are interested. Children in this period have gradually learned to distinguish between essential things and non-essential things in concepts, learn to master preliminary scientific definitions, and make logical arguments independently. At the same time, to achieve such a level of thinking activity, it is also inseparable from direct and perceptual experience, so it still has many concrete images.

2. The role and position of teaching content.

The significance of the equation is the content of Unit 4 in the first volume of the fifth grade of the compulsory education standard experimental textbook "Primary Mathematics". It was taught by students after learning to solve problems with arithmetic thoughts for four years, and they can learn at the same time? Solve the equation? The foundation of.

The meaning of equation is a brand-new mathematical concept course for children, which is an improvement of arithmetic thinking and a leap in digital understanding. On the basis of using letters to represent unknowns, students' mathematical tools for solving practical problems have developed from listing the solutions of formulas to listing the solutions of equations, from seeking results from unknowns to participating in operations with unknowns, and their thinking space has increased. This is another leap in mathematical thinking method, which will improve students' ability to solve practical problems by using mathematical knowledge.

Third, reflection on the teaching process

The book "Teaching Site and Teaching Details of New Curriculum" says? Which is more important, the role and function of details in the teaching process, and the significance and value in promoting students' development? ? Indeed, to a certain extent, the course is composed of countless details in the classroom. These details are like stars dotted with the dark night sky, and the night sky will be more dazzling because of the stars. In the lesson "The Meaning of Equation", I carefully designed a teaching detail. It is with these little details that this lesson can shine in the Xixiang quality class competition. And I think these details are just right? High participation, high autonomy, high coordination, high pleasure and high efficiency? The best embodiment of the classroom.

Detail fragment 1: the connection between teaching materials and reality

After showing the balance, the students say two equations according to the balance of the balance. Next,

The teacher asked a student; How tall are you? Student: I don't know.

Teacher: What letters can we use to express it?

Student1a: X. Health 2, a?

Teacher: The teacher invited a teacher to compare height with you. The teacher asked a teacher to stand back to back with his students. )

Teacher: Is there any way to make them look the same height?

Health 1: Let Xiao Zhao stand on the stool.

Teacher: Well, whatever you say. (The teacher takes out the stool on the spot) Teacher; The teacher has measured this stool, and its height is 25 cm.

Teachers and students stand back to back, exactly the same height. )

Teacher: Can you write an equation according to this situation?

The atmosphere suddenly enlivened, and the students raised their hands to ask for answers.

Health 1: x+25 = 162, the height of Xiao Zhao plus the height of the stool equals the height of the teacher.

Health 2: 162-x = 25, the height of the teacher minus the height of the stool equals the height of Xiao Zhao.

.

Reflection:

An important idea of the new mathematics curriculum standard is to highlight the reality of mathematics, and mathematics teaching should be based on reality and applied to reality. I don't think mathematics should be an intellectual game on calculus paper anymore. It should be around us, living in the fact of life. In fact, this clip is an exercise on page 98 of Grade Four of Beijing Normal University Edition, but I skillfully combined the reality when designing it, and arranged a student to stand on a stool 25 cm high in advance, as high as the teacher, and cooperate with me to complete the teaching of this clip (but other students didn't know that I had arranged it in advance, so they all thought it was amazing). This has also become a highlight of this class. Let the mathematics on paper enter the children's world, truly become a tool for children to know the world, and let children know the true face of mathematics knowledge. Students not only know the real existence of knowledge in life, but also cultivate the quality and accomplishment of their own inquiry in this process, which is more important than acquiring knowledge itself. Practice has proved that this kind of teaching and learning is easy for teachers and easy for scholars.

Detail Segment 2: Classification and Analysis

The teacher asked the students to classify all the formulas on the blackboard according to the remainder of the balance.

Teacher: Who wants to be the first to report?

Health: According to the balance of the scales, I classify those with equal symbols. Those without an equal sign are classified into another category. (talking and moving the formula on the blackboard)

Teacher: Does that make sense? What other students have the same classification standards as him?

Teacher: In mathematics, there is a formula equal to such a symbol. We call it an equation (blackboard writing). A class like this is called "a match made in heaven": inequality. It seems that you really got the point.

Teacher: Now let's look at these equations again. Can we get another point on the basis of the equation?

2. Reveal the meaning of the equation:

Teacher: Please observe this kind of formula carefully. What are their characteristics compared with other formulations?

Health: They have unknowns and equations.

Teacher: In mathematics, equations with unknowns like this are called equations. (blackboard writing)

Teacher: Today, the students did a good job. They summed up the meaning of the equation through their own efforts. The fruits of labor are hard-won. Let's read the meaning of the equation together.

Read all the students together

Teacher: You read really well, but the teacher feels a lack of imitation. Read it again and emphasize the words you think are important, ok?

After listening to the teacher's prompt, the students read well.

Teacher: Which word did you emphasize?

Health: Unknown number, equation.

Teacher: Your reading voice is really nice. This is just the sound of the sky. Then these are not equations, so let's take them away, but there must be a reason for taking them away. Why should I say that I am not an equation?

One by one, the students went to the stage to pick up the formula newspaper. (Note that the student reports are wonderful. Some children have not only used them? Nevertheless. .. but this kind of related words, the teachers praised the children's language expression ability in time. )

Reflection:

Equation teaching is concept teaching. If concept teaching leaves children's independent exploration and self-summary, then concept teaching will fail. Although you can learn by rote, it will be boring and children will lose interest in learning. In this lesson, I borrowed from other teachers' teaching methods and supplemented my own understanding. Pay attention to what? Quote? Work hard on writing, follow the teaching principles of from shallow to deep, from easy to difficult, from concrete to abstract, guide children to sum up the concept of equations with their hands, brains and mouths, and deepen their understanding of the meaning of equations in the process. Natural? Naturally? .

Detail 3: Integrating into Life

Teacher: Equations are widely used in our lives. Let's see what this equation shows in our daily life.

The courseware screen shows four words: basic necessities of life. Who do you want to accept the challenge first?

Each word is linked to a picture.

(Clothes: The picture shows a dress of RMB X and three clothes of *** 120 yuan. Write an equation according to the picture. )

(Food: a hamburger, 7 yuan, two cokes, one coke, X yuan, *** 17 yuan, as shown in the figure. )

A big pot of water just fills two small kettles and a cup. Cup 200 ml, small kettle x ml. According to the graphic equation)

(OK: A bus arrives at the station, eight people get off and six people get on. At this time, there are 45 people in the car. How many people are there on the bus? )

Reflection:

The famous mathematician Hua said: for a long time, people's impression of mathematics is boring and mysterious, and one of the reasons is that it is divorced from reality? . Indeed, mathematical knowledge is highly abstract, which conflicts with the concrete image of primary school students' thinking. If we teachers can't better integrate knowledge into life, extract life situations from life and apply them to teaching, how can students be interested in those lifeless and boring figures? Life itself is a vast mathematics classroom, and there are a lot of mathematical phenomena in life. In this class, I successfully integrated the exercise of equation into people's daily life, so that children can experience equation and understand life in daily life. In this class, children are exposed to life situations in class, and their emotions are high, and they actively participate in exploration. Classroom teaching is very active and the teaching effect is very good.

Detail Segment 4: Application of Motivation Language

German educator Stuart said:? The art of teaching lies not in imparting skills, but in inspiring, awakening and encouraging. ? In classroom teaching, teachers often use some praise language to motivate students, which is helpful to stimulate students' learning motivation, narrow the distance between teachers and students and realize spiritual communication. In this class, I pay attention to using a variety of inspiring languages to comment on children's learning behavior and learning process. These warm languages, such as spring breeze and rain, nourish students' hearts, let children find the direction of learning in class, and are willing to explore knowledge with teachers. For example:

When I interact with children before class:

Teacher: Students, today the teacher is lucky enough to come to Huasheng School to study with the students. The teacher is so happy. I have long heard that Watson is good at thinking, active and generous, and has a loud voice. The teacher has long yearned for Watson. Look how straight the students are sitting. Are you all ready?

When students read the concept of equation:

Teacher: Your reading voice is really nice. This is just the sound of the sky. The teacher wants to hear it again, okay?

When students find problems:

Teacher: You can find problems with a mathematical eye. The teacher is really proud of you.

Teacher: Great minds think alike, so does the teacher.

When students express their opinions:

Teacher: Your suggestion is great. Do as you say.

etc

Reflection:

The application of these inspiring languages has played an indelible role in the success of this course, making students in an active learning and learning state. In teaching, after the students discussed the meaning of the equation, I smiled approvingly and the students were encouraged. They immediately rushed to express their opinions, and the classroom became a place for teachers and students to discuss. In class, when I praise students as mathematicians, students must be elated, have more interest in learning mathematics and strengthen their confidence in learning mathematics well. In the process of acquiring knowledge, teachers take students' positive emotional experience as their responsibility, feel it from the students' point of view, and participate in the process of students' exploring knowledge, learning, exploring, acquiring and sharing happiness with students, so that teaching can achieve harmonious coexistence between teachers and students and happy classroom.

Fourth, shortcomings:

1, the students actually thought of many forms of equations when practicing, but because it is a competition class, many students want to show their ideas because they are afraid of not having enough time later. I was so cruel that I went straight to the next question. I really shouldn't think so. After class, the judges and teachers also said it was a little pity. Classroom is the stage for students to show, and teachers should provide this stage for students.

2. It is still difficult for a small number of students to solve problems by listing equations and find out the equivalent relationship in the problems. In the limited time, they still feel that they can't effectively help them understand the meaning of the problem.

3. The meaning of the equation should be an unknown equation, but what I present to the students is an equation with letters. The mathematical concept is rigorous, and it is a thousand miles away. I think we should also make students understand that the expression of this unknown is not just letters.

Five, teach the design concept:

1, Introduction:

I saw many teachers introduce this lesson from multiple scales. I wonder if it can be introduced from other situations? For example:

In a basketball match, the red and blue teams played quite fiercely. Now the score on the field is 26: 33. Can you express the relationship between the scores of the two teams by mathematical formula? (Draw lots: 26)

The coach of the red team also noticed this situation and immediately called a timeout to make tactical adjustments. In the first paragraph, only the red team won in a row? Please guess what will happen to the two teams.

Can mathematical expressions be used to express several possible relationships of scores?

Is it feasible to introduce inequality and equation from the score of basketball game and then divide the equation?

2. Summarize the concept part.

20111kloc-0/October, I was lucky enough to listen to a lecture entitled "The Meaning of Equation" given by Zhao Zhen, a special teacher in Beijing Normal University. When he was dealing with the concept of equation, he was like this:

After the students separated the equation from the equation, he said, students, the topic we are studying today is to know the equation. The teacher can tell you that such equations are called equations. Then, please discuss and see, what does the equation have to have?

In teaching, the results are directly presented to students, and then students find out what the key words of this concept are through discussion, exchange and exploration. I think this inverted teaching method is also worth a try.

3. Practice part:

Because I didn't add the practice of drawing equations with line segments when I consolidated the exercise, I think it is also an exercise to draw equations according to line segments when I teach next time.