Reflection on the nature of the equation

Part 1: Reflection on the nature of the equation

In the teaching, I first use the courseware to demonstrate that the balance is added or subtracted from the same weight at the same time. At the same time, the same multiple is enlarged or reduced, and the balance is still balanced. The purpose is to let the students intuitively feel the balance of the balance and classify the student migration. The basics are laid out in the equation. Then, let's take example 1, let the students list the equation x+3=9, use the courseware to demonstrate x+3 squares=9 squares, and ask: “If you want to name x, how do you change it?”, guide students to think, As long as you subtract 3 squares from both ends of the balance, the balance is still balanced, and an x ​​is equivalent to 6 squares, resulting in x=6. Can you express the process of the formula with the formula? Most of the students quickly wrote the answer I wanted: x+3-3=9-3, so I asked: Why do you want to subtract 3 from both sides of the equation without subtracting other numbers? The students were silent, and finally two pairs of small hands were raised. "In order to get a x," I emphasized again. Our goal is to find a number of x, so we must subtract the extra 3, in order not to delay. More time, I did not continue to delve into it. Next, in the teaching example 2, I also use the principle of the balance to help the students understand. When the student says that he wants to divide the average of the two ends into three points, and the basis of each is 6, I use the courseware to demonstrate the process of the points, so that the students can The demonstration process is written to solve the equation. On this basis, I guide the students to summarize the balance of the balance, and get the basic nature of the equation: the two sides of the equation are added or subtracted by the same number, divided or multiplied by the same number that is not 0, and the equation remains on both sides. equal.
It stands to reason that students should be able to master the solution of the equation with a little extrapolation. But the next exercise was surprisingly unexpected. Except for a few well-achieved students who were able to finish as required, most of them would hardly do or even move. where is the problem? After careful reflection, the following is summarized:
First, the transition from the balance to the equation, the analogy process students can not understand, the balance is reduced by three squares at the same time, which is equivalent to subtracting 3 from both sides of the equation. When writing this process, it is necessary to emphasize that the original state of the left and right sides remains unchanged. Change, write it down as it is, if this is the case, it will not cause some students not to format.
Second, it is not enough to discuss why it should be subtracted. Although some students answered, I should be able to detect that students have difficulty understanding. Courseware and balances can let students understand that both sides of the equation should be subtracted from the same number. Why is it reduced here? Going to 3 still seems to understand, if the example at the time may be very effective, such as: x-3=6, what should we do? Through comparative discussion, students will find out that we are asking for an x. According to the specific situation of the equation, if it is more than x, it will be subtracted. If it is less than x, it will be enough.
Third, there is a mistake in the student's link. This part of the content should not be difficult, but the existing foundation of the student is the basis for determining the teaching method. From the perspective of teaching effect, I obviously do not do enough.
Fourth, the content of the teaching is not determined properly. Originally, I thought that if there is a certain capacity in class, I will put together the examples 1 and 2, teaching addition and subtraction, multiplication and division, only teaching addition and multiplication, subtraction and The solution to division allows students to solve the problem by migration analogy. Since my class students are new to me in this issue, they don't know enough about the students, the students' foundations are uneven, and the overall level is poor. Therefore, it is difficult to arrange two examples.

Part 2: Reflection on the nature of the equation

The nature of the equation is based on the student's grasp of the nature of the equation. Students have mastered certain learning methods and formed certain reasoning skills. Therefore, in this lesson teaching, make full use of the original knowledge, explore and verify, so as to gain new knowledge, provide each student with opportunities for thinking, expression and creation, so that he becomes the discoverer and creator of knowledge and cultivates students to explore themselves. And practical ability.
I. Conjecture to start, to stimulate learning interest Conjecture is a preliminary unconfirmed judgment of students' perception of things. It is an important link in the process of students acquiring knowledge. Therefore, students are encouraged to think boldly in teaching: If you multiply or divide the same number on both sides of an equation, will the result be an equation? At this time, the students will be eager to try, which will stimulate the interest of learning. Once a student makes some kind of guess, he will connect his own thinking with the knowledge he has learned, and he will eagerly know whether his guess is correct, so he will take the initiative to participate in the development of knowledge, so as to achieve half the effort. Teaching effect.
Second, operational verification, cultivating exploration capabilities When exploring the nature of the equation, two operational activities were arranged. First let the students multiply or divide both sides of the equation by the same number, and then think about the discussion: Will the result be an equation? Guide students to find that the results are still in the equation. Then let the students multiply or divide both sides of the equation by "0". What happens? Through two practical activities, the students personally participated in the process of discovering the nature of the equation, truly "knowing it, knowing why", and thinking ability, spatial sensibility, and hands-on ability have been exercised and improved.
3. Divergent thinking, cultivating problem-solving ability When students verify that their ideas are correct, encourage students to express their ideas boldly, to promote thinking, to open the "gate" of students' thinking, and to evaluate students' various ideas without rushing to evaluate Should not lose the opportunity to guide students to talk about it, discuss and discuss, exchange ideas and reach a consensus. On this basis, let the students rationalize and generalize the nature of the equation. Through the activity process of “writing and thinking”, students are allowed to diverge in activities, develop in activities, learn actively and solidly, and more importantly, cultivate students' ability to seek different thinking, creativity and solve practical problems.
In the teaching of this lesson, there are also questions worthy of further discussion. For example, let students use the method of “conjecture-verification” to explore the law and the nature of the equation. Such a learning style is more like a bystander. What should teachers do?

Part 3: Reflection on the nature of the equation

The textbook "The Nature of the Equation" has designed four observational experimental activities to explore the laws of simultaneous addition, subtraction and simultaneous multiplication and division on both sides of the equation. While using the formula to express the experimental results, the students are made aware of the law that "the equation is added, subtracted or multiplied by the same number, and the equation is still true."
Since the nature of the equation is the basis and basis for solving the equation, I pay special attention to the teaching. Activities 1. Using the operation of the balance diagram to provide students with serious observation, positive thinking, and exchange of their own space, and practical understanding. The nature of the equation. Activity 2, use the courseware to demonstrate, on the basis of activity one, guide students to explore independently, cooperate and exchange, and summarize the nature of the equation. In the basic training, the arithmetic symbols and numbers are filled in the balance, and the simulated solution equations are filled in the classroom exercises. During practice, let the students understand the requirements of the topic, especially the training questions in the first question. What is the meaning of the training question, that is, according to the basic nature of the equation, the basic foundation is the basic nature of the equation below. Solve the equation to prepare.
After the lecture, I feel that the students' learning effect is not bad. I think that using pictures and demonstrations for teaching is very helpful for students' learning. Putting forward refinement thinking questions and proper point-and-click will increase classroom teaching efficiency. The compact teaching process makes classroom teaching smoother. Respecting students, giving students more opportunities to speak, exposing their thinking, leaving their thinking to students is the best way to teach, focusing on the standardization and accuracy of the language expression of students, and the neatness of writing.
In short, mathematics teaching should give students a lot of exercise time for exercises, it is necessary for students to digest and familiarize with the opportunity of consolidation, so in the future teaching, I will always remind myself to concentrate on more practice, try to give more Time and space for independent practice.

Part 4: Reflection on the nature of the equation

This is a math class about China's small convergence: the nature of the equation, the teaching method of experiential inquiry is adopted in the teaching, and under the guidance of the teachers, the students can do their own hands, brain, operation, observation, and induction. Nature, experience the formation process of knowledge, and strive to reflect the teaching philosophy of "subject participation, independent exploration, cooperation and exchange, guidance and exploration". Providing students with the opportunity to personally operate, guiding students to use existing experience, knowledge, methods to explore and discover the nature of the equation, so that students directly participate in teaching activities, students gain a perceptual understanding of the abstract mathematical theorem in hands-on operation, Then, through the teacher's guidance processing, it rises to rational knowledge, so that new knowledge is obtained, and the student's learning becomes a process of re-creation. At the same time, the students learn the ideas and methods of acquiring knowledge, and realize the cooperation with others in the process of solving the problem. Importance, laying the foundation for students to acquire knowledge and explore and discover in the future.
The following is a brief recap of the teaching process:
The whole teaching process is divided into two parts: the first part is the nature of the equation. The teaching method of experiential inquiry is firstly demonstrated by the teacher. The balance is placed on both sides of the balance to balance the balance and transform the experiment into mathematics. Question and list the mathematical formula; let the formula listed by the student ask questions: Can you think of the nature of the equation by the formula obtained from the balance experiment? The students independently think about the nature and nature of the equation, and then abstract the nature of the equation into the symbolic language of mathematics and express it. Finally, through exercises to consolidate the two properties of the equation, and let students think about the nature of the equations from practice. The second part is the use of the nature of the equation. Through two examples and two exercises, the symmetry and transitivity of the properties of the equation are revealed, which paves the way for the study of the one-time equation and the binary equation.
Looking back at this lesson, I feel that there are still some problems in the grasp of some teaching design and teaching process:
1, can not correctly grasp the operation time, resulting in a delay of about 5 minutes to class. The ease of experimentation demonstrated by the teacher should be proportional to the time of discussion given. This not only ensures the effectiveness of the experiment, but also does not waste time. The time left for the students to think and discuss after using the balance to demonstrate the experiment in the nature of the exploration equation is not sufficient, so that the activity did not really have the initial effect. The time left for students to think and solve problems during training is also insufficient.
2. The teaching did not pay attention to the cultivation of students' thinking diversity. In the process of inquiry in mathematics teaching, the final result of the problem should be a process from “seeking difference” to “seeking the same”, instead of letting students follow the teacher’s pre-set direction in the first place, thus controlling The development of student thinking. For example, in the process of studying the nature of the equation 1, the teacher is step by step, and the layers are pulled out, lest there are some flaws, which makes the students' thinking restricted.
3. In the classroom, the handling of unexpected incidents was not decisive, and there was no timely feedback on the students' responses. For example, in Exercise 2, when students are asked to compose a new equation according to the two properties of the equation, the student's answer has many results, and the teacher's comments and guidance take too much time, disrupting the next arrangement.
4. The "form" in the nature 1 failed to make a reasonable explanation.
5. For the use of nature, the teacher asks the student to answer the form, lacks the student boarding session, and does not take care of the participation of all students.
6. Reduced the time for group cooperation and study, and failed to reflect the advantages of group cooperation.

Part V: Reflection on the nature of the equation

"The nature of the equation" is basically handled in this way: the first lesson directly introduces what is the equation, what is the nature of the equation, as an introductory content, ten minutes or even a few minutes, and then teaches the students How to solve the equation. Some simple application of the equation is supplemented by looping exercises in subsequent learning. However, this part of the newcomer's edition has arranged two classes, in addition to introducing the concept and nature of the equation, and directly applying the nature of the equation to discuss some simple one-dimensional equation solutions. Considering that this part is an important theoretical basis for the subsequent learning solution equation, it also provides a basis for the algebraic constant transformation in the transformation between quantity and quantity in algebraic geometry, and lays a foundation for later learning inequalities. I still plan to use a class time to specifically study this part, and to use the equation of the nature of the equation as a focus of this lesson.
In teaching, I introduce content with the balance as an intuitive image, increase or decrease the objects or weights in the left and right trays, so that students can define the nature of the equation and express the nature of the equation by column method. Then through three examples, students will learn how to use the nature of the equation to solve some simple equations.
Even though I noticed the gradient of difficulty when arranging the examples, in the end, students generally think that solving the equations with the nature of the equation is quite cumbersome and not easy to grasp. In contrast, they prefer to use the various parts of the national small formula to solve the problem. It can be seen that this lesson did not achieve the expected goals. Students seem to have insufficient understanding of the nature of the nature of the equation, so this class uses the nature of the equation to solve the equation and they accept it quite passively.