Weighted average is a difficult point in teaching. The difficulty lies in the understanding of "right". From small to large, the definition of average in students' minds is the addition and division of numbers. The characteristic of weighted average is that all data do not appear, and the same data only give weight, which causes students' confusion. The following is my reflection on weighted average teaching (generally 5 articles), welcome to refer to it.
Reflections on the teaching of weighted average 1 ** month 2 1 The sixth class is an open class for me. I have made full preparations for this class. Tutorial plans and courseware are carefully considered and revised repeatedly, and even the time required for each link and the transitional language are repeatedly scrutinized. Nevertheless, after a class, I am still very dissatisfied.
Coincidentally, Guangshui's education colleagues were scheduled to visit our school this morning, but due to objective reasons, they changed it to the afternoon, so the sixth class was temporarily transferred to the fifth class. After the nap, it is the fifth class. I am worried about the students' mental state and want them to wake up early, but I am afraid that the students' failure to wake up will affect the class. I can only wait for the passage of time in the office. As soon as the wake-up bell rang, I hurried into the classroom to wake up the students one by one and tell them about the temporary shift, so that they could act quickly and save their strength. Although I urged them urgently, the students' vacant faces and sleepy eyes told me that they might not be able to "live" in this class.
Before the bell rang, Guangshui's teachers came into the classroom one after another. Look at this situation. The teacher who attended the class surrounded the students. I guess new and old classmates may be afraid to talk again ... the whole class began to follow the steps. First of all, I let the students teach themselves in the tutorial part of the tutorial plan. I found that the students' eyes were completely dull, and they had no intention to do the problems on the tutorial plan, which made me lose confidence.
The content of this lesson is weighted average, because it has nothing to do with what you learned before and mathematics knowledge. Students know nothing about what is right and what is weighted average, not to mention that in this class, right first appears in the form of ratio, which makes students puzzled. Based on this, I boldly adjusted the content of the textbook, first throwing out the concept of weighted average and guiding understanding with simple examples. Let students understand what is weighted average and what is weight, and know how to calculate weighted average by using formulas.
In the part of communication and cooperation, four different questions are designed. Starting from the arithmetic average, two different weights are given, and the average scores of two players are calculated respectively. Finally, the importance of weight is obtained through observation and comparison, and the important role of weight and weighted average is realized. Afraid of completing the teaching task, the time for students to communicate is too short. In addition, students seldom see so many strange faces, and they are afraid to express their ideas. Even if students are asked to discuss in groups, few people speak, and even if they do, they just whisper a few words. The usual chatter is gone. Helpless, can only arrange instead. After class, I feel a little too eager for quick success and instant benefit. I should give students more time. Maybe they can't discuss the function of "weighted average", but they can realize that the change of weight will affect the average level of this group of data by observing the different results of calculation.
I designed two questions for the consolidation and expansion. The first question is to review the weighted average algorithm. The first step of this question, if the three scores of the players are equally important, who should be admitted? When analyzing this problem, some students suggested that only the sum of the three scores of the players can be compared. I gave a simple evaluation to guide students to analyze with arithmetic mean. In fact, the guidance in this place is very inappropriate. If we can understand "equal importance" in this position and talk about the connection and difference between arithmetic average and weighted average, students may understand it better. The second question gives the test scores of three candidates' innovation ability, computer ability and public relations ability, so that students can design reasonable permissions for the company to recruit network managers and account managers. This can be said to be not only a comprehensive review of the knowledge learned in this class, but also an improvement of the classroom atmosphere in this class. Here is the wonderful highlight. Unfortunately, I'm not sure, but after the group discussion, let the representative briefly talk about the weight of the design. If we can talk about the matter, let the students tell the different weights of the design institute and then verify it through calculation, it may be the most perfect ending.
Forty-five minutes is not a long time, but I feel it in a dull atmosphere. The atmosphere in the class is dull. Although I used the way of group competition to motivate me, I still didn't improve. The usual chatter has turned into a big eye and a small eye. Now it's pushing around, which makes me feel that the children in the mountains are the children in the mountains. If they can't get into the table, the chain will fall off if there are too many people in class.
This class has been completed in an orderly way as planned, and the teaching tasks have been basically completed, but more is not satisfactory. Through this class, students may have mastered the algorithm of weighted average, but their mathematical ability and thinking have not been well improved, which is enough to show from the omissions in the class. Based on this, I think that in the future teaching, we should not only focus on whether the tasks of the class are completed, but also focus on the whole mathematics, locate the teaching tasks and educational objectives of each class from the perspective of the whole junior high school mathematics, examine the teaching content from a higher and broader perspective, and choose some teaching methods. Only in this way can the classroom be more perfect!
Reflections on weighted average teaching On March 3rd1,our school welcomed the new foundation responsible team of China Normal University, in which Mr. Wu listened to my class, and the content was weighted average. After listening to the class, Mr. Wu made a detailed comment on my class, which gave me a new understanding of this class and a comprehensive reflection on this class, and gained the following results.
First, minor problems.
1, one question is to estimate the unit price range of assorted sugar? Here can be changed into two questions (1), and there are several possibilities for making assorted sweets. (2), in what range? Here, turn one question into two questions, enlarge the questions, and let students have time and space for discussion.
2. In the first search for student resources, the awareness of finding answers is relatively strong, and all students are not concerned. This is also a problem, and focusing only on the results is a fundamental reason.
3. There is no need to estimate the unit price of assorted sweets twice in the first big piece of teaching, which is some problems in transplantation class.
Second, the relatively prominent problem.
1. Ms. Wu made the following explanation on the collection and release of resources. She believes that there are the following types of resources (1), which are different and improved. (2) Organic trench type. (3) processing and substitution. This lesson belongs to the third kind. The first level resource is that when students appear a(60+ 100×4), teachers can ask what this means. Students can answer the price of one kilogram of fruit candy plus four kilograms of chocolate. The second resource is (60+ 100)÷( 1+4), which is mainly to make students realize that the total price is two kilograms, which does not correspond to the quantity of five kilograms. The third level resource is (60+ 100×4)÷( 1+4), which also enables students to experience the corresponding ideas. The other layer means (60+ 100)÷2 is the average price of one kilogram of chocolate and fruit candy, which is inconsistent with the requirements here.
2. How to embody the spirit likeness in a class is mainly reflected in three aspects.
(1), the infiltration of mathematical research methods, reflected in the premise and purpose of research before sugar blending. Step 1: For example, how much fruit candy and chocolate can it be? Let the students speak. Step 2: What should the teacher say first? In order to illustrate the purpose of the study, many research schemes can start with individual cases, and then cite a large number of facts after studying individual cases. The third step is to give examples, and then ask: How to give examples to help find the law?
(2) Stimulate students' habit of active participation. Here, a student can study several situations first, and then summarize them in groups of four. Through this form, one is to stimulate the sense of participation, and the other is to develop the habit of cooperation.
(3) further shift the center of gravity. In the process of cooperation, the first simple requirement can be that I speak and repeat at the same table. The second one is higher. You have to ask two people to talk in turn. The third is to further request that four people cooperate and * * * cooperate with the summary. The last highest requirement is the cooperation between individuals and groups. When one person can say' together', other students can say it softly. Never read together, the center of gravity should move down.
3. Integrate practice with richness in the process of formation. For example, in the third lesson, when there are many chocolates, there are five kilograms of assorted sweets. That is to say, when there is a lot of fructose, assorted sugar can be a variety of kilograms, so that the total price and kilograms can be placed in different environments. Another example is (100+60)÷2. Let the students realize that 5 kg or 3 kg can also be done. In addition, it is necessary to strengthen the explanation of the middle price. What is the middle price is the middle number of two prices. In this way, in the case of more chocolates, it is easier to find assorted sweets with a smaller price range.
The above is my reflection in this research activity, but there are also shortcomings and improvements that need to be further improved in the future teaching research, which is what I urgently need to do now.
The third part of the teaching reflection of weighted average points out that the process of mathematics learning is the process of students' exploration, practice and thinking about related mathematics content, so students should become the main body of learning activities, and teachers should become the organizers, guides and collaborators of learning activities. As a teacher, we should first consider how to mobilize the initiative and enthusiasm of students and guide them to learn to be independent, explore and innovate. Teachers should also be students' collaborators and good friends while playing the role of organization and guidance.
Based on these thoughts, in the teaching of this class, I first introduce practical problems that students are familiar with, so that students can learn with problems. In the following teaching, students are required to think independently and propose solutions to problems. The purpose is to let students use the existing knowledge and experience to analyze and solve new problems, and directly participate in the necessity and rationality of concept generation. Then try to solve the problem. In the process of solving problems, first of all, teachers appear as participants, find and solve problems with students, and share the joy of students' success every time. Secondly, he appears as a guide, and is good at capturing students' thinking highlights every time, giving timely encouragement and giving timely instructions when students encounter difficulties, so that students can learn in a pleasant atmosphere from beginning to end.
In order to truly return the right to study to students and experience the fun of doing mathematics, in the process of re-understanding the concept, I give students the opportunity to solve problems and abstract generalization, let students read and study independently, give them more space and more opportunities to show themselves, and let students feel the charm of mathematics learning in an emotional and harmonious classroom atmosphere. With the encouragement and appreciation of teachers and classmates, we can know ourselves, find confidence and experience the fun of success, so as to establish confidence in learning mathematics well.
The classroom begins to grasp the breakthrough point of new knowledge through the problem situation, so that students can enter a state of "trying to get through, but not getting through", thus entering the mathematics classroom with interest and preparing for learning new knowledge.
Based on students' life experience, let students feel the existence of mathematics in their lives and stimulate their interest in learning. There is no problem in arithmetic average, which increases students' learning confidence. Question 2 aims to lead to the topic of this section and introduce the concept of weighted average. Through these two questions, students can compare the difference between arithmetic average and weighted average, which not only helps students understand average, but also enables them to understand the internal relationship between knowledge, grasp knowledge as a whole and develop students' dialectical thinking.
I feel that I talk more about the introduction of new knowledge, because the concept is relatively difficult to understand, so I am afraid that students will not understand it themselves, which is the place to pay attention to and improve in the future.
In the design of exercises, two exercises appear in a special way, especially the problem of recruiting employees, which is different from the textbook in design. My idea is to decide who to hire after group discussion, and each group gives weight and the calculation is reasonable. The main purpose of doing this is to deepen the understanding of rights, give students a stage to fully display themselves, fully develop their emotional attitude and general ability, learn the value of mathematics from them, and thus enhance their understanding of mathematics. In this link, students will have all kinds of problems and mistakes, so in class, I pay special attention to timely evaluation and encouragement of students' performance. This not only stimulates students' interest in learning, but also cultivates students' ability to cooperate and communicate with each other, and enhances students' awareness of mathematics application.
Let the students reflect by summing up. First, further guiding students to reflect on their own learning methods is conducive to cultivating the habit of induction and summary, so that students can build their own knowledge system; The second is to stimulate students' joy of success, strive to cultivate success with success, cultivate self-confidence with self-confidence, and encourage students to devote themselves to future study with greater enthusiasm.
In this class, I think I have achieved the teaching goal, and I have grasped the breakthrough of key points and difficulties well. In the process of teaching, students' enthusiasm for participation is high and the classroom atmosphere is active. Of course, 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 weighted average teaching Part IV Weighted average is a difficult point in teaching. The difficulty lies in the understanding of "right". From small to large, the definition of average in students' minds is the addition and division of numbers. The characteristic of weighted average is that the data is incomplete, and the same data only gives weight, which causes students' confusion. Here's how I handled it:
First, skillfully quote the word "right". Start with a special case. Give a class a math test score, and some scores appear many times, so that students can get an average score. At this time, there will be different methods, and the teacher will continue to guide. If two classes have the same number of students and each class has an average score, how to find the average score of the two classes? If the number of students in the two classes is different, how do you ask? Give a few more examples around students.
This naturally guides students from different calculation methods to the definition of two averages.
Second, reanalyze the word "right". From three perspectives, (1) indicates the number of times the data appears; (Students have understood) (2) the proportion of data; (3) Represents the percentage of data. Under the guidance of the time of each data in the cited examples, students can rewrite them into ratios and percentages for analysis. )
In this way, the three angles of "power" are organically combined and the essence of "power" is clarified.
Third, practice the word "right" more. On the basis of understanding, let students master the formula of weighted average. It can be concluded that arithmetic average is actually a special case of weighted average, that is, the weight of each data is the same.
As a learning content of junior high school mathematics, this part of knowledge specifically introduces the concept of weighted average and its calculation formula. In specific teaching, I always have a dilemma: I think it is neither difficult nor difficult.
First, when a lot of data in a group of data appear repeatedly, the formula for calculating the weighted average is another form of calculating the arithmetic average, and it is also a relatively simple algorithm. Compared with elementary school mathematics, we can find the sum of several identical addends and replace them with multiplication to achieve the purpose of simple calculation, reduce the amount of calculation and make it easier to understand. When explaining the weighted average of the first kind, we can learn by analogy. The "weight" here is the number of times the data appears, which is not difficult for students to understand. So it's not difficult. For example, the average score of the calculation group is 6.95, 5.84, 3 100, 1 75. What is the average score of the group?
Second, in the textbook, students have experienced the above-mentioned weighted average and given the calculation formula of weighted average, but the "weight" here often reflects the importance of a group of data in the form of even ratio or percentage, and uses an example to change the weight and discuss who will be hired. This example reflects the influence of weight difference on the result (average value), which obviously leads to different results. It is found that the understanding of "weight" is in place, which restricts the application of calculation formula. In class, students can solve similar problems by imitating the model of examples, but they can't understand the truth of doing so in essence. As long as they make a slight change, students will make mistakes. So it is also a difficult point in teaching.
In teaching, I found that when students use the weighted average formula to solve problems, the reason for making mistakes is that they directly mistake which numbers are "data" and which numbers are "weights" of data, thus misusing the formula. This is a difficult point for students and a key breakthrough in classroom teaching. First of all, it is necessary to find out why students' understanding of "force" is not in place: because of the differences in students' understanding ability and learning foundation, their understanding ability of this knowledge point is different; Most students think that the content looks simple and easy to learn, and they are not interested. Primary school students have learned the calculation of (unweighted) average. Influenced by the mindset, students are used to the calculation method of dividing the sum of all data by the total number of data to get the average value. When learning weighted average, it is easy to be limited to the previous ideas.
In view of the learning situation, we should first grasp the breadth and depth of teaching materials, create rich problem situations, connect with reality, mobilize students' learning enthusiasm, give play to their subjective initiative, select typical exercises and fully train them. Deepen students' understanding of the importance of "right" in questions and distinguish "data" from "right", thus reducing the occurrence of mistakes. If students want to accurately understand the "weight" in the weighted average, teachers should pay attention to guiding students to skillfully use the mindset in their studies and compare the differences and connections between the (unweighted) arithmetic average they learned in primary school and the weighted average now. In fact, the unweighted average is not really unweighted, but the weight of all data is equal, which is "1". In this sense, it can be said that all arithmetic averages are weighted averages. Then, through appropriate examples, let students have a deeper understanding of "right". As long as students really understand the meaning of "right", they can also break through the doubts of students' learning and thus break through the difficulties of this class.
Reflections on the fifth part of the teaching of weighted average When teaching the weighted average content in the first section of Chapter 20 of the second volume of eighth grade mathematics of People's Education Press, the teaching mode of "learning before teaching and training in class" was put forward. Because the students in front have already learned the related knowledge of arithmetic average, and the content of this section is relatively easy, so I draw lessons from the teaching mode of "learning before teaching and training in class" in Yang Si Middle School.
Firstly, review the concept of arithmetic average and the meaning of numerator and denominator in its operation formula;
The second is to set up problem situations and introduce new lessons;
Third, use the small blackboard to show the teaching objectives, key points and difficult contents of this lesson;
4. Instruct students to teach themselves the contents of the textbook p 136~ 139 and think about the problems displayed on the small blackboard. Teachers patrol the classroom and give appropriate guidance to students with learning difficulties from time to time;
Fifth, students do problems;
Sixth, announce the answer;
Seven, choose the places where students make more mistakes to comment;
Eight, students summarize themselves;
Nine, homework after class.
Judging from the teaching effect, the success of this course lies in: achieving the predetermined goal. Students actively participate in a wide range, have a strong interest in learning and have a high level of practice. The teacher was liberated and the students were given the opportunity to exercise. Many students have found confidence in self-study, changed their learning methods, changed from over-reliance on teachers to self-study before asking questions, and cultivated students' self-study ability and independent thinking ability. This is very useful for students' future study and development. Disadvantages: Because students have more time for self-study, more exercises and more calculations, students' calculation speed is slow, so it is impossible to arrange several students to do some exercises. Then design: arrange students to preview before class, select exercises and reduce the amount of calculation. Enlightenment: In the teaching process, we can flexibly use the teaching mode of "learning before teaching and training in class" according to the difficulty of teaching content, which not only liberates teachers themselves, but also gives students the opportunity to exercise, thus improving the teaching effect.
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