Reflections on inequality and inequality group teaching 1

In this class, I use the method of creating problem scenarios from life to stimulate students' interest in learning, use the method of analogy to guide students to explore independently, teach students the problem research methods of analogy, conjecture and verification, and cultivate students' study habits of being good at observation and thinking.

Activity 1: By reviewing old knowledge, grasp the breakthrough point of new knowledge, and enter the math classroom to prepare for learning new knowledge. In this link, there is less time left for students to think.

Starting from students' life experience, let students feel the existence of mathematics in their lives, which not only stimulates students' interest in learning, but also enables students to intuitively understand some properties existing in inequalities. This link shows students an object, so that students can get an intuitive feeling.

Question 2 aims to analogize the basic nature of equality, study the essence of inequality, let students experience the application of analogy in mathematical thinking methods, train students to study problems from analogy to conjecture to verification, let students complete tasks in cooperative communication and experience the fun of cooperative learning. I talked a little too much about this link and didn't grasp the theme of students well. In the process of guiding students to explore, the time control is not compact and it is a waste of time.

Let students compare the similarities and differences between the basic nature of inequality and the basic nature of equality, which not only helps students understand inequality, but also enables them to understand the internal relationship between knowledge, grasp knowledge as a whole and develop students' dialectical thinking.

Let students reflect on their composition, further guide students to reflect on their own learning methods, cultivate students' habit of summarizing, let students build their own knowledge system, and stimulate students' joy of success.

Activity 3. Help students improve their application through two questions. The first problem is to let students experience the simple application of inequality properties in the form of judgment. The second problem is to simplify the inequality into "x >" a "or" x "

In the process of using symbolic language in the whole class, students will have all kinds of problems and mistakes, so in class, I pay special attention to evaluate and encourage students' performance in time. This not only stimulates students' interest in learning, but also cultivates their symbolic language expression ability.

In this class, I think I have basically achieved the teaching goal and mastered the breakthrough of key points and difficulties. There are still many problems. I will try my best to improve my teaching skills and gradually improve my classroom in the future.

Reflections on the Teaching of Inequalities and Inequality Groups (Ⅱ)

First, the success of the teaching process

1, analogical interpretation makes it easier for students to master.

Learn the solution of linear inequality of one variable by analogy with the solution of linear equation of one variable, so that students can clearly see that the solution of inequality is different from the solution of equation except that the coefficient of the last unknown is changed to 1, and other steps are the same, with special emphasis on the last step of "negative change, positive change".

2. Talk less and practice more.

It reduces teachers' activities and gives students enough time to discuss. Teachers only give appropriate guidance, so as to talk less and write less on the blackboard, so that students have enough time and space to explore and develop independently and urge students to learn to learn.

3. The combination of numbers and shapes is more vivid.

By drawing the number axis, the solution set of inequality is represented by the number axis, which embodies the mathematical idea of "combination of numbers and shapes"

Second, shortcomings and regrets

1, too much content leads to the inflexibility of students' application time.

Obviously, a 40-minute class is eager to accommodate the exploration and application of the three properties of inequality. Practice also shows that it is true. After exploring the three properties, there is not much time left. Students can only simply apply what they have learned to solve some relatively simple problems, and their ability to use knowledge flexibly is not well reflected.

2. The minor faults in the teaching process need to be corrected.

In the course of class, many small problems that are usually ignored are also reflected in class. For example, in the process of answering questions, students often interrupt their answers and deprive themselves of their initiative in order to get their expected answers faster; When students are asked to carry out operation experiments, the instructions given by the teacher are not particularly clear, and they are often supplemented in the process of students' operation, which has a certain influence on students' thinking; It is not very good to sum up students' experiences and gains in class, which shows that this is caused by negligence in class at ordinary times.

Reflections on Inequality and Inequality Group Teaching (Ⅲ)

This week, I talked about "the inequality of one dollar". At first, my design idea was to review the concept and solution of inequality. However, I taught three properties of inequality. After learning the three properties, I will immediately talk about the solution set of inequality and express it on the number axis. Finally, I did a consolidation exercise. However, in the teaching process of the first class, I found that students did not understand the concept of inequality solution set, nor did they know how to express inequality solution set on the number axis.

Therefore, I immediately adjusted my teaching ideas. In the next class, I will ask the students to review the concept and solution of inequality first, and then teach the three properties of inequality. After finishing the three properties, I will ask the students to do related exercises on the application of the three properties immediately. Finally, the solution set of inequality and the solution set of inequality on the number axis are discussed.

By adjusting the teaching ideas in this way, I found that students have a further understanding of the concept and solution of inequality, and understand the three properties of inequality, and will use these three properties to solve related mathematical problems. The solution set of inequality is an abstract concept, but students can understand what is the solution set of inequality through practice because the solution set of inequality is solved by students themselves. On the basis of students' understanding of inequality solution set, students can further express inequality solution set through the number axis. Through the combination of numbers and shapes, students can deepen their understanding of inequality solution set and pave the way for solving inequality in the next section.

My reflection and experience are:

1, full preparation before class is the guarantee. From how to introduce and guide students to explore nature, we are fully prepared.

2. The teaching of natural difficulties 3 is not enough. Students explore property 3 in the form of group discussion, but because I have no clear design intention, several groups multiply two different numbers on both sides of inequality for comparison. It completely avoids the teaching that both sides of inequality are divided by the same negative number (I think division can be done by multiplication, so multiplication is enough), and as a result, students are stuck in such a problem.

3. The three properties of the inequality expressed by the formula have been brushed aside, and lesson preparation needs to be strengthened. I think this knowledge point is not important when preparing lessons. In fact, students' mathematical symbol language ability can be trained here.

4. Pay more attention to students' reaction in class. Adjust teaching ideas in time according to students' classroom reactions.

Reflections on Inequality and Inequality Group Teaching (Ⅳ)

In this class, teachers can better analyze and grasp the teaching content, the teaching design is novel and reasonable, the teaching organization is reasonable and effective, the teaching objectives are well realized and the teaching effect is good. The main highlights of this lesson are as follows:

First, the teaching clues are clear. In teaching, the acquisition and application of basic inequalities are open lines, while the infiltration and experience of mathematical thinking methods are dark lines. In the study and teaching of this class, the light and dark clues echo each other, students constantly experience the role of mathematical thinking methods in the process of knowledge learning, and even try to let students use thinking methods to think and learn strategically in the teaching of examples, so that students can improve their understanding of mathematics while learning knowledge and make the learning process natural and smooth.

Second, pay attention to the necessary knowledge and understanding. In this lesson, as far as the core knowledge of basic inequalities is concerned, the teacher presents students with the opportunity to know knowledge from multiple angles through effective treatment of the teaching materials, especially designing the understanding and thinking link of the relationship between basic inequalities and important inequalities, so that students can experience the harmony of the two inequalities in this lesson. This design promotes students' understanding of the essence of basic inequality, helps students to sort out the core knowledge of this lesson, and teachers highlight the teaching key points in a relaxed and natural way, which also provides some new perspectives for teachers to understand basic inequality.

Third, pay attention to the essence of students' participation and insist on the generative nature of knowledge acquisition. In the whole class, teachers always ensure that students' knowledge comes from substantive mathematical activities and profound generation. In this lesson, we can observe from the three dimensions of students' emotional participation, behavioral participation and cognitive participation that students' participation in real mathematics activities ensures that students' generation is natural and reasonable, and generation becomes the premise of knowledge acquisition. This kind of study is scientific and effective.

Of course, this class still has some shortcomings:

The whole class shows a lack of guiding students to reflect on their own learning in time, thus losing some opportunities for students to experience or form learning strategies. Although teachers have paid more attention to the understanding and understanding of the nature of knowledge in the teaching of core knowledge, they are still a little impatient at some moments in the teaching process and have not kept the knowledge acquisition process perfect. On the whole, the inquiry level of the whole class is still a little low, and it is still at the level of guiding inquiry. The reason is that the traditional teaching habits are inadvertently reflected.

Reflections on the Teaching of Inequalities and Inequality Groups (5)

Yesterday, I talked about the basic inequalities in the third chapter of compulsory five. At the beginning of the class, I recalled the knowledge about inequalities I learned in junior high school and explained the geometric meaning of basic inequalities. Then, several major issues involved in the inequality college entrance examination are involved. However, I didn't feel very good after a class.

Although a class talks about several test sites for the college entrance examination, for students who are new here, their understanding is not very thorough. I think it should be carried out from the following aspects: first, the first section only talks about basic inequalities and their geometric significance. Let students fully understand the specific meaning and application of "one positive, two definite and three phases" and find inequality in practice. Assisted by college entrance examination questions, let students master the trend of college entrance examination. Secondly, the second section will talk about putting these two kinds of questions related to the knowledge of functions learned before together and then separating them. This paper reflects the relationship between inequality and function, explains the importance of function in senior high school mathematics, and reviews two methods of splicing and separation in function. Third, the third class will talk about the substitution and mirror image method of "1". These two methods examine students' flexible changes in knowledge and their application of the idea of combining numbers with shapes, which is a little deeper than the knowledge in the second section. In this way, the knowledge of the three classes is deepened layer by layer, so that students can realize the connection of knowledge and clarify the specific application of each knowledge point in the college entrance examination. In the original method, all the key points of the college entrance examination were told to students in a class first, so that students were easily confused, and it was difficult for students to master without knowing what the key points of this class were. After all, if the capacity is large, the amount of practice will be reduced accordingly. By the time of the second and third period, the students were still not proficient and had to review it again, which was a bit "hot leftovers".

Therefore, new courses, especially those in which students have little knowledge before, must be slow and steady, not only for the sake of large capacity, but also for the sake of students' thinking, to prepare appropriate content, order and teaching methods.

Reflections on the Teaching of Inequalities and Inequality Groups (VI)

In the review of senior three, I specially designed this review course in combination with the examination requirements of the basic inequality in the college entrance examination and the investigation of this part of knowledge points in recent years. Firstly, the knowledge points, problem-solving methods and requirements are reviewed, and then three examples are expounded to help students form the problem-solving ideas and norms of this kind of problems. Next, the students practice, discuss in groups and perform on the blackboard. Finally, teachers and students sum up together and finish this lesson.

After this class, I reflected on the teaching design and teaching process and got the following points:

Teaching advantages:

1. Topic introduction

In the lesson plans and tutoring plans distributed to students, the knowledge points and problem-solving methods of this lesson are presented in the form of questions. By answering questions, let students master the knowledge points applied in this lesson and lay the foundation for solving problems later.

2. Detailed examples

Through three selected examples, review the basic ideas and methods of solving basic inequalities, the commonly used deformation method-collocation method, and the general steps of solving problems, so as to demonstrate for students.

3. Classroom exercises

In this class, I selected five real questions from the previous college entrance examination for students to practice, and asked them to practice in advance, and then exchanged views with classmates in class and put forward their own views on a question. During the discussion, teachers observed and gave on-the-spot guidance on the common problems of students.

4. Students perform on the blackboard

Through discussion, students have their own methods to solve problems. Each group invited a classmate to perform a blackboard writing performance, which improved the students' participation in class and gave them the opportunity to show.

5. Students discuss

In class, students are allowed to have time to discuss in order to improve communication among students. Each student has the opportunity to express his ideas in the group and learn to communicate and improve through listening.

6. Course summary

After learning this lesson, let the students sum up first, and then the teacher inspires the students to supplement, not only to sum up the knowledge points learned, but also to sum up the learning process and the mathematical thinking methods adopted.

Deficiencies in teaching:

In this class, because some students do less exercises in advance, the time for classroom practice seems a bit tight. Some students haven't finished the five exercises assigned by them, and because many college entrance examination questions don't pay much attention to the application conditions, some students may not pay enough attention to this application conditions.

Enlightenment to future teaching;

After this lesson, I discussed it with the teachers of the teaching and research group. I think there are the following points for future work:

1. In teaching, let students use their hands and brains to give full play to students' initiative and enthusiasm in learning.

2. Supervise and inspect the assigned exercises, and let the students do them first, so as to lay a foundation for cooperation and communication among students in classroom teaching.

3. Organize students to discuss in groups, stimulate students' enthusiasm for discussion, guide students to cooperate and communicate with classmates, and share experiences and lessons in the learning process.

4. Senior three review classes can be conducted by reviewing relevant knowledge points first, then explaining typical examples, then students practice, group discussion, blackboard performance, and finally summarizing by teachers and students.

5. When reviewing senior three, you can practice with the real questions of previous college entrance examinations, which not only improves students' ability to do questions, but also enhances students' adaptability to college entrance examinations and reduces the mystery of college entrance examinations.

6. In the class summary, we should not only summarize the knowledge points we have learned, but also summarize the learning process and the mathematical thinking methods adopted.

In short, when reviewing senior three, we should not only consider the requirements of the college entrance examination, but also combine the actual situation of students. In the process of organizing review, it is necessary to combine closely to help students master the knowledge points and questions commonly tested in the college entrance examination and effectively improve the review efficiency of senior three.

Reflections on the Teaching of Inequalities and Inequality Groups (7)

Mathematical knowledge system is a highly coherent knowledge system. In the field of space and graphics, mathematics in primary and secondary schools is mainly reflected in the gradual transition from intuitive geometry and experimental geometry to demonstration geometry. Junior high school math teachers should pay attention to the connection with primary school teaching, review the contents of primary schools appropriately and improve on the basis of primary schools. From the perspective of the connection between primary and secondary schools, this paper makes some thoughts on the lesson "The Nature of Parallelogram" (People's Education Edition).

First, reflect on preparing lessons.

Prepare teaching materials:

When preparing lessons, I first consulted the textbooks that the students had learned in primary school. It is found that the definition of "parallelogram" in primary school textbooks is clearly defined in bold, and the characteristics of "equilateral" are obtained by students through measurement or folding. Convert the area of parallelogram into rectangle by truncation. So students should already know the concept and characteristics of parallelogram and find its area.

"Parallelogram" is one of the key contents of the whole chapter, which is based on students' mastery of the properties of parallel lines, congruent triangles and polygons. Parallelogram is another typical figure of plane geometry, which is not only a comprehensive application of predecessors' knowledge, but also the basis for learning all kinds of special parallelograms in the next step, and has the function of connecting the preceding with the following. The properties and judgments of rectangle, rhombus and square are all developed on the basis of parallelogram, and their exploration methods are also in the same strain as parallelogram. The properties of trapezium and triangle midline theorem are also based on parallelogram related theorems. And "the nature of parallelogram" is the first section of this chapter, and the study of this section plays a key role in learning the judgment of parallelogram and other special quadrangles. In the textbook, the three properties of parallelogram are explained in two parts, namely, "the opposite sides are equal", "the diagonal is equal" and "the diagonal is equal". Because this course adopts the exploratory teaching method, students are expected to get these three properties in the same class, so they are treated in the same class.

Prepare students:

In order to clearly understand students' cognition, I went deep into students and investigated their mastery of parallelogram. It is found that nearly 90% students can define parallelogram. More than 50% students know that the two sides of a parallelogram are parallel and equal. However, only a few students know the nature of "parallelogram diagonal is equal" and "diagonal is equally divided" because of their in-depth study. In view of students' cognitive structure, I put the exploration of parallelogram properties on the angle and diagonal.

Preparation method:

? Mathematics curriculum standard points out that mathematics teaching activities must be based on students' cognitive development level and existing knowledge and experience. Teachers should stimulate students' enthusiasm for learning, provide them with opportunities to fully engage in mathematical activities, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematical activities. I saw a teacher giving an open class on a parallelogram. Teachers may want to mobilize students' subjectivity and let them define "parallelogram". Results The students explained the definition of parallelogram and all the judging methods, and explained the reasons for this definition. It sounds like women are right and men are right. It's hard to say which definition is more appropriate. Finally, the teacher said that it is customary to define "two groups of opposite sides are parallel respectively". After reading this lesson, combined with the primary school textbooks and students' cognitive situation, I think that the "parallelogram" has been clearly described in the primary school textbooks, and if we make a big fuss about how to define the "parallelogram", we can only be trapped in the teacher explaining to the students why we can't define it with parallelogram judgment (students don't know it is judgment), and the definition itself is often a prescriptive thing. So I take this place to let the students prepare two identical triangular pieces of paper in advance, and then let the students spell out the parallelogram in class and display the spelled figures on the blackboard. While arousing students' enthusiasm, I can not only find out students' understanding of parallelogram, but also pave the way for the proof of parallelogram properties below.

In the process of exploring the essence of parallelogram, the conclusion and proof process are filled in the inquiry report sent in advance by means of independent inquiry and cooperative communication, so that students' thinking and implementation are closely linked. Let students know the necessity of proof, understand the basic process of proof, master the format of comprehensive proof and feel the axiomatic thought.

Correct use of multimedia courseware. In order to make students have a clearer understanding of the three properties of parallelogram, I prepared a vivid courseware to explore the properties from the perspective of rotation.

The whole class adopts exploratory proof methods, that is, observation, conjecture, intuitive verification, reasoning proof and obtaining the essence. Infiltrate students with the mathematical thinking method of "transformation" from complexity to simplicity and from new knowledge to old knowledge.

Second, reflection class.

After entering junior high school, with the strengthening of students' logical thinking ability and abstract thinking ability, we can no longer be limited to the acquisition of some conclusions, but should pay attention to the derivation process of conclusions and reveal the ins and outs of knowledge, that is, we should not only know why, but also know why. The textbook also requires students to reason and demonstrate the findings.

The property that the opposite sides of parallel polygons are equal is obtained by observing and measuring the length of the opposite sides in primary schools. Can you prove this conclusion? In the past, students studied polygons by dividing polygons into triangles, so when they proved this conclusion in class, students quickly thought of dividing quadrilaterals into triangles and solving them with congruent knowledge. However, students' symbolic language in reasoning is not smooth, and reasoning still lacks standardization. So, under the students' narration, the teacher makes standardized reasoning on the blackboard and demonstrates it to the students.