Reflection on basic inequality teaching

Part 1: Reflection on Basic Inequality Teaching

Usually, many of our lectures are newly taught. We also have a lot of lectures. This section should be regarded as a problem class in terms of class type. Why is this class type mainly proposed a method for the colleagues to discuss? Several patterns were derived. The content of this section is "the application of basic inequalities". It is based on the basic inequality skills of students. The application of basic inequalities is mainly two aspects: one is to find the most value, and the other is its actual application. The teaching process is designed into four parts: one is to sort out the knowledge points of basic inequalities; the other is to practice the maximum value of the basic inequality; the third is the application of basic inequalities in practice; the fourth is the typical question of basic inequalities in the college entrance examination. . The schedule is like this: the first link is about 5 minutes; the second link is about 10 minutes; the third link is about 15 minutes; the fourth link is about 10 minutes. In actual operation, there may be timeouts in the first and second links, so the final class content cannot be completed in 40 minutes. Of course, my purpose is only to propose a classroom mode of the problem class. At specific time, we can achieve the coincidence by increasing or decreasing the problem. For the fourth link, there may be different opinions among colleagues. It is considered that it is only for students to look at the college entrance examination questions, and it is not as effective as it is. My design intent is to let students understand the form of this content in the college entrance examination in recent years, and to practice and consolidate it as a data preservation class. Teachers and students in the first and second grades of high school should have three years of thinking and action in a game of chess. After each content is finished, the classic college entrance examination questions in recent years will be taken out for analysis. I think it is very beneficial to students or teachers. Can allow students to develop this habit, three years of accumulation, so that students will have more or less will focus on the content of the college entrance examination content, the form of propositions and the rules of propositions have their own research or ideas, I believe that their review of the third year and The exam is very helpful.

Part 2: Reflection on Basic Inequality Teaching

According to the requirements of the new curriculum standard, the focus of this section is to understand the basic inequalities by using the combination of numbers and shapes, and to explore the proof process of basic inequalities from different angles. The difficulty is to find the most value by using basic inequalities. This lesson is the first lesson of the basic inequality.
In the course of the new lesson, I studied the textbook carefully and found that this lesson is mainly to let students understand how to use the basic inequality to find the most value. How to use basic inequalities requires students to understand the six-character policy: one is equal to three. This is a more abstract content. In particular, the relevant changes in “fixed” are more flexible and cannot be solved in one lesson. Because I put this part in the second lesson. This lesson is designed to give students the meaning of “positive” and “equal”.
I designed to start with the first example, the first small question can explain "accumulation and minimum", and the second small question shows "and maximum accumulation". Through the explanation of this example, let the students understand "one positive, two thirds, etc." Then use the six-word policy to get the most value. This is to explain the second example, let the students familiar with the steps to solve the problem with basic inequalities. Then let the students solve the problem themselves.
In the consolidation exercise, the judgment questions were designed to let the students understand the connotation of the six-word policy. The related exercises were also designed from the aspects of “and fixed” and “accumulated”, so that students gradually became familiar with the basic inequality to find the most value.
Students are the main body in the process of class implementation. Including pre-class preparation, examples to let the students do, as well as exercises to let students go to the board and other links, let students take the initiative to think, and show typical errors in the process of finding problems, timely correction, and achieve good results.
The downside is that the introduction of the review is too difficult, and it is not quite in line with the reality of liberal arts students. And the time spent reviewing is too much, the problem of repetition is too much, and the triviality is explained; the analysis of the example is not deep enough. Because of the lack of time, some questions are always stopped. The exercises explain the time rush and there is no explanation.

Part 3: Reflection on Basic Inequality Teaching

After reviewing the second lesson of the basic inequality, I made the following reflections on this lesson:
One. Give full play to the subjective status of students in the teaching process
In the classroom, both new teachers and old teachers usually regard themselves as the masters of the class and too much will ignore the subject status of the students; or students will forget that they are the masters of the class because they are used to listening to the teacher for a long time. .
In this lesson, I designed a number of sessions for students to discuss, but when I said that students can discuss their own conclusions with their own tables, the classroom will still be quiet. After a minute of such class activities, I had to explain my own problems. At this point I feel that this section has failed because I have occupied the time that should belong to the students.
two. To design a teaching problem
In the teaching, we should reasonably design the questions to be used in the teaching. Why did the student interactions I designed fail to succeed? I think the big reason is that I didn't design the problem. I didn't know what kind of result I asked them to give me when I asked the question. In this lesson, most of my questions are asked this way: Ask the students to do this topic first, and then discuss with their own table whether their results are correct. When students hear such questions, they will first complete the problem by themselves, rather than working with their partners. Moreover, in the mathematics teaching, the gradient design of the problem is very important, because the new curriculum emphasizes the formation process of the concept, and the generation of the concept is an abstract process, so it is very good to show how the concept of the student is produced during the teaching. This teaching session requires teachers to design a gradient of the problem.
three. Learn to design deep questions
In the teaching of this lesson, the most common question I asked was: The students understood that there is no, or right? Is it such a superficial problem? From the perspective of classroom effects, these questions did not motivate students' enthusiasm for learning. Students only answered mechanically: yes or no, right or wrong. Making communication between students and teachers becomes a mechanical question and answer process. Therefore, in the future teaching, I should pay more attention to the requirements of the depth of the problem.
The above is my reflection on the teaching of this lesson: give full play to the subjective status of students, design teaching problems and learn to provide in-depth teaching problems.

Part 4: Reflection on Basic Inequality Teaching

The chapter on inequality is difficult for students. It is very important to grasp the teaching well. I will see through the reflection of teaching.
1. When teaching the "solution set of inequalities", it is the most easy to understand method and the most suitable method to find the solution set by finding the common part by means of the number axis by using the method of combining numbers and shapes. I use the phrase "larger size, smaller size, smaller size, smaller size, larger size, smaller size" to solve the inequality. I think that it is easy to train students' ability to combine numbers and shape. In teaching, I ask students to use both.
2. Strengthen the teaching of mathematical modeling ideas that abstract the quantitative relationship in practical problems, embodying the curriculum standards: the principle of spiraling up important concepts and mathematical ideas. In teaching, on the one hand, strengthen training and exercise students' self-solving ability. On the other hand, through the "correction" problem type exercises and students' mutual learning and analysis, the correctness of the problem solving is gradually improved.
3. Grasp the teaching objectives, prevent excessive demands when solving the actual problems by using one-time inequality, focus on strengthening the connection between words and symbols, use the sentences with different languages ​​in the questions to find the unequal relationship, and list the one-time inequality. Solve the problem, pay attention to the difference between the method of using the equation to solve the actual problem, and prevent the students from applying the equation to solve the practical problem of the unequal relationship.
4. The class size of this class is too large, and there are also special places in thinking, which leads to insufficient time for students to think in class and class time is relatively tight. Therefore, in the future, we should arrange more class hours in the class schedule to reduce the classroom capacity of each class, give students more time and space to think, and improve the classroom effect. At the same time, we must pay attention to the role of thinking questions, because some students in the class reflect the foundation is solid, and they are also interested in mathematics. Some difficult questions can make this part of the students who have spared ability to improve. .
5. From the perspective of the effect of the classroom, the problem of the objective object of the student object is not enough to solve the problem with a special method. They are always worried that there will be problems, especially the lack of ability to compare and analyze the multiple-choice questions, because the multiple-choice question is a special one. Question type, its particularity is that the answers to such questions are known. Some students do not look at the four choice answers in the title when they are doing the exercises. In the actual problem-solving process, they can put four for the multiple-choice questions. The analysis of the answer options is very good for improving the speed and accuracy of the problem solving. However, some special methods for solving objective problems appearing in this lesson are particularly effective in solving problems related to inequalities. However, if there is a case of classification discussion in the problem of inequality, the special method has its limitations. Students need to be flexible. The problem of classification discussion in the problem is generally a difficult problem. My treatment in teaching is to explain the problem to the students in the process of teaching. to sum up. Therefore, students are required to use a special method to reflect on education by using inequality teaching.

Part V: Reflection on Basic Inequality Teaching

Yesterday I talked about the basic inequality of the third chapter of Compulsory. The opening of the church first recalled the inequality knowledge learned in the middle school and explained the geometric meaning of the basic inequality. Then there are several major issues involved in the college entrance examination in the inequality. However, after a class, it didn't feel very good.
Although a class has a few college entrance examinations, but for students, just getting in touch, understanding is not very thorough. I think it should be done in the following way: First, the first section only talks about basic inequalities and their geometric meanings. Let the students fully understand the specific meanings and application of “one positive, two fixed, three-phase, etc.” in the inequality. And supplemented by the college entrance examination questions, is the student's mastery of the college entrance examination trend. Second, the second section will talk about patchwork and separation of these two types of questions related to the previously learned function. It reflects the inequality and function, explains the importance of the function in high school mathematics, and by the way, reviews the two methods of patchwork and separation. Third, the third lesson will talk about the substitution of "1" and the image method. These two methods examine students' flexible changes in knowledge and the application of the combination of numbers and shapes, and are deeper than the knowledge in the second section. In this case, the knowledge of the three classes will be deepened, so that students can understand the relationship of knowledge and clarify the specific application of each knowledge point in the college entrance examination. In the initial method, a class firstly gives all the key points of the college entrance examination to the students, making the students easy to be confused. I don't know what the focus of this lesson is, and the students are not easy to master. After all, if the capacity is large, the amount of practice will be reduced accordingly. When I wait until the second quarter, when I talk about it in the third quarter, the students are unskilled and have to review again. It feels like a "hot leftover".
Therefore, when it comes to new courses, especially the new lessons that involve little knowledge before students, we must be steady and steady. We must not only ask for large capacity, post college entrance examinations, but also prepare appropriate content, order and teaching methods from the perspective of students’ thinking. .