Reflection on the estimation of multiplication

Part 1: Reflection on the estimation of multiplication

1. The situation should be created in conjunction with the actual life of the student. Let students learn mathematics in the context of life-related situations to reflect the value of mathematics. The situation in this lesson is a very common thing, and most of the students have experience, so students will not feel useless when they study.
2. Students should be given enough time to think independently about the problem. Only enough time for independent thinking, the students' thinking can be opened, and they can take the initiative to think about the problem. For example, in this lesson, I gave everyone ten minutes of independent thinking time, and the students came up with so many methods.
3. Students should be made aware of the purpose and meaning of learning. When students learn some new knowledge, they often have the idea of ​​“learning what kind of knowledge and methods are useful.” As teachers, if they can't let students know the role of learning estimates, they will not take the initiative to think about the method. How much is it prepared?” This question points out that the money the teacher prepares can only be the money to buy tickets. Must be very precise? When the store owner goes to purchase, is it necessary to calculate each expenditure very accurately? There are many times in life as long as you know the approximate number. Therefore, estimates are often used in life. When students understand the role of estimation, they will think about how to estimate more easily.
4. How to effectively play the main role of students in forty minutes? In this lesson, I used the independent thinking group of the students to discuss the form of the whole class communication and achieved good results. The students are basically involved in the activities of exploring the estimation methods, and there are also gains in the optimization methods. Through student exchanges, it can be seen that students can migrate to new knowledge based on their existing knowledge. This lesson is based on the students' learned to add and subtract, and consciously adopts the method of “rounding off” to obtain various estimation methods. .
5. The advantages and disadvantages of mindset influence the learning efficiency of students. In this lesson, students can use the “rounding off” method to come up with Method 1, Method 3, but there are also many students who insist on the first method when optimizing the above five methods because of the “rounding up” mentality. I am sure that the second method, then how to guide students out of the mindset, I think that based on practical experience, using life experience to verify is a good way. It is more natural for me to ask students to calculate the actual price of the tickets and then let the students talk about which methods are not practical. However, at this time, there is a cognition conflict about the old knowledge of the students' rounding. Why can't we use the rounding method here? If this problem is not solved well, some students will be confused. Therefore, when I organized everyone to compare Method 1 Method 3, I found that when using "rounding" to estimate, the fare and the number of people were less, and the result was of course smaller than the actual one. The ticket was bought here, and the teacher took the money. Actual tickets should be prepared more, so that the reason for learning mathematics should be based on reality, and emphasize that the "rounding off" method is a general rule. When solving practical problems, it is also necessary to flexibly choose methods according to actual conditions.
Through the study of this lesson, students not only master the method of estimating multiplication, but also make students feel that solving practical problems can not be too dogmatic, but should carefully analyze and select the method according to the actual situation, so that students' thinking is more flexible and more Diverse.

Part 2: Reflection on the estimation of multiplication

The teaching design of the course "Multiplication Estimation" has the following characteristics:
1. Create a living situation and highlight the key points of teaching.
From the point of view of calculation methods, students are more accurate in calculating, estimating consciousness, and have no real experience and feelings on the role and value of estimation. They feel “not used to” in their understanding and behavior, and often estimate for estimation. Therefore, I contacted the actual situation of life and created the problem situation of Xiao Ming’s trip to Beijing. I will visit the zoo, watch the dolphin show, and assemble bicycles for tourists. Let the students experience the estimation in the situation, not only let the students understand the mastery. The method of estimating the number of digits by one digit is more important to encourage students to explain the idea of ​​estimation, to feel the actual application of multiplication estimation in life, to understand the difference and connection between actuarial and estimation, and to experience the value of estimation. It really highlights the key points of estimating teaching, from simple skill training to estimating awareness.
2. Strengthen variants and comparisons, focusing on the induction and improvement of estimation strategies.
The first semester of the "Syllabus" estimates the requirement of cultivating consciousness: "It can be combined with specific situations to estimate and explain the process of estimation." In this lesson, Teacher Dong expanded the content of the example, combined with life, creating problems, paying special attention to the analysis and comparison of different issues, such as the comparison of "enough" and "not enough" in the problem of creation, the comparison between prototype examples and creation problems, "Visit the zoo" and the prototype examples, "watching the dolphin show" and the creation of the problem, the "assembly of some bicycles" selection algorithm comparison, etc., encourage students to explain the reasons and ideas. Guide students to choose a reasonable estimate of “less” strategies based on actual problems, and focus on the induction and improvement of estimation strategies. Therefore, the idea of ​​specific analysis of specific problems is infiltrated, allowing students to flexibly select appropriate algorithms according to different situations and cultivate students' ability to solve problems.
3, pay attention to the organic integration of presupposition and production, the classroom is full of vitality.
Presupposition is the basic requirement of teaching, and teaching is the process of interaction between people. Therefore, it is a process of continuous generation. Presupposition is the premise of generation, and the generation needs a good and relaxed atmosphere. Without careful presupposition, it is impossible to have wonderful generation. Only when preparing lessons, fully estimate the various situations that will occur in the classroom, and consider the strategies to deal with. Capture and grasp the fleeting and productive resources in the classroom. In this lesson, students have different opinions about 32 students with enough money for 250 yuan. They are constantly sparking the spark of students' thinking. The students' understanding of the meaning of estimation and the limitations of estimation show students' inspiration. The whole lesson reflects the organic unity of presupposition and generation.

Part 3: Reflection on the estimation of multiplication

"Multiplication Estimation" is a section on the 60th page of the fourth grade book of the compulsory education curriculum standard experimental textbook. After I finished this section according to the plan, I reflect on the whole teaching process. The key to success is to break the traditional teaching mode. Using the life materials around the students, the students can ask questions and communicate with the students, students and teachers, let the students actively participate in every aspect of the study, and boldly say what they want to say, thus experiencing teaching and learning. Happy, serious reflection, this lesson has the following characteristics.
1. The material is derived from life, allowing students to generate estimated needs.
Calculations should be used every day to estimate the existence of the day. But when we estimate the teaching, we find that sometimes students don’t estimate at all, or they can calculate an exact number before writing an approximate number. One of the reasons for this problem is that the material that the teacher gave to the student did not combine with the actual life. The student faced such information, and did not resonate emotionally. There was no estimated demand, and it was simply an accurate result. The main three sets of materials in this class come from the reality of life or social life. E.g:
1 Estimate the number of people to choose the venue, the number of participants can not be counted one by one, and the seats in the event venue are not necessary for one place, then it is estimated based on experience.
2 When writing a text, the number of faces to be written is determined by the specified number of words. Generally, it is not counted and accurately calculated one by one, but only needs to be estimated according to the number of rows per row and the number of grids per row.
3 orange day sales can only be estimated based on the sales situation of a certain day.
In this way, the estimation becomes a kind of demand in life in the eyes of the students, rather than the unreachable mathematical knowledge. It allows the students to feel the connection between mathematics and life and enhance the awareness of mathematics application. At the same time, such materials are conducive to students' active activities such as observation, guessing, exploration and communication.
2, the same problem from the students, let the students master the mathematical thinking method.
We must see that although the ideological method of mastering mathematics is not the only goal of this class, it is still an important goal. Some teachers in traditional teaching often give closed questions, only the answer to the questions, let the students answer and then proceed. Mechanical memory and repeated training. In this lesson, I gave some information from the actual life, mainly asking questions from students, and then questioning and communicating with each other. At the intersection of their respective viewpoints, let us see the joy of success in the dark, and the basic method of multiplication estimation is naturally natural. Although some students are not mature enough in communication, this process has made students feel that they are the masters of learning. The summary of methods also has their own merits, satisfying the psychological needs of students' self-esteem, communication, and success. Let them always put into the mathematics learning.
The new mathematics curriculum concept tells us that mathematics teaching should let students experience the close relationship between mathematics and nature, human society, understand the value of mathematics, learn to use mathematical thinking to observe and analyze relevant phenomena in real life, and solve daily life and I will try to implement this concept in mathematics teaching in the study of other subjects and to establish good emotions for further study.

Part 4: Reflection on the estimation of multiplication

According to the work arrangement of the teaching and research group, each teacher teaches the lectures in the upper part of the preparation group, and selects a teacher to represent the preparation group to participate in the school's annual “Quality Course Competition”. As a member of the preparation group, today I coached the "Multiplication Estimation" of the fourth grade of the People's Education Edition. Rethinking the entire teaching process, there is a feeling of "please make people happy."
Throughout this part of the knowledge, the textbook was written with the intent of teaching multiplication by letting students estimate the specific question of how much money to purchase. To further understand the problem: the solution of many problems in life needs to be estimated; choose the appropriate estimation method according to the specific problem to be solved, so that the estimated result is in line with the actual problem and close to the accurate value, so that the estimation process is as simple as possible. Guide students to master the basic methods of estimation in communication and comparison. And the definition of the basic method is clearly: close to the exact value; easy to calculate. The Mathematics Curriculum Standards also clearly require the estimation of the second semester: in the process of solving specific problems, we can choose the appropriate estimation method and develop the habit of estimation. Its focus is on "combining the actual situation and choosing the appropriate estimation method."
In giving me the above ideas, I chose the materials in the real life of the students when designing the teaching. By going to the Beijing Olympic Park to visit the Olympic venues to buy tickets, the teaching focused on allowing students to ask questions and solutions independently, so that the solutions are in students and students. The communication between the students and the teachers is clear. Through the question “Why do you want to estimate this?” “Which plan do you think is more appropriate?” “Which plan is more reasonable and more realistic?”, so that students can gradually construct estimates. Methods. Learn to encounter problems on the basis of understanding the problem, determine the strategy, and then solve the problem. In order to make the children feel the boring and boring practice in the math class, I put the practice into the context of the game, mobilized their enthusiasm for learning by setting the “Lucky Pass” game, and also let the students actively participate in the process of consolidating the practice. Among them, experience the joy of mathematics learning.
The fly in the ointment is: the beginning of the class let the children guess the age of the teacher, giving them a guess of the scope "about 30 years old", the result is that a student guessed 24 years old, I did not go further to ask "24 years old is not in line with the teacher Given such a range?", nor did it guide the students to understand the function of the estimate - to determine the range of values, directly into the exploration of the new lesson, without maximizing the introduction of the default situation. Furthermore, the beginning of the lesson lacks the knowledge of the estimation, and the child's knowledge base and ability are overestimated, so I should continue to work hard to understand the students.
When estimating in class, most students use the rounding method to approximate the number. (1) Think of 49 as 50, 104 as 100, 50 × 100 = 5000, should be prepared 5,000 yuan. There are also students who use the first method to estimate, there are two estimation strategies (2) to see 49 as 50, 104 as 110, 50 × 110 = 5,500 yuan, should be prepared 5,500 yuan. (3) Perhaps influenced by the pen-multiplication training, individual students use the pen to calculate the result directly - accurate value. In fact, the method of approximating the number, there is a further method, the tail method, etc., when estimating, it is often estimated according to the specific situation, using different methods of approximating the number. When students basically use the (1) estimate, there is a cognitive contradiction: How is the estimated result compared with the actual accurate value? The student spontaneously discussed why this happened, and thus understood that there was an error between the estimation and the exact value calculation. The multiplication estimation we have learned today is based on the actual situation to choose the most appropriate estimation method to solve the problem. Therefore, when we encounter the money for preparation in the future, when should we estimate it bigger, and when it should be estimated to be smaller, it should be determined according to the actual situation. It is not necessary to use rounding to get the number. The question of “How much is appropriate?” is the question of how to use the estimation strategy to solve the problem. At this time, there is (2) the wonderful generation of the strategy. At this point, I feel that the treatment is not enough. Subsequent exercises also produce "chain" errors that occur because they do not understand the estimated strategy.
Due to the delay in the practice of too much time, the end of the teaching summary of the end of the course. Grasping the rhythm of classroom teaching and carrying out effective teaching will also be the direction for me to study and practice in the future.
In teaching, I also found that the language used by students to express their own calculation ideas and problem-solving ideas is not so refined and clear. Therefore, cultivating students' mathematical language expression ability and promoting students' mathematical literacy will be the focus of my future thinking and research. Subject
The value of mathematics is to let students learn to use mathematical thinking to observe and analyze relevant phenomena in real life, to solve problems in daily life and other subjects, and to establish good emotions for further study. I will also Practice this concept in the future of mathematics teaching.

Part V: Reflection on the estimation of multiplication

Estimation is a mathematical idea. "Evaluation of multiplication" is a simple, rough calculation that can be performed without the need for precise calculations. To let students understand this kind of mathematical thinking, with the estimated consciousness and ability, the teaching should be combined with the students' actual life, so that students can adopt different estimation strategies according to their own needs, thinking habits and individual differences, so as to understand the practical significance of the estimation. Learn different estimation strategies and use your own estimation strategies to solve practical problems. Return the class to the students. In the classroom, not only should students develop a good habit of actively speaking, but also cultivate students' awareness and ability to argue, let students express their opinions, and let others learn to be recognized when others do not agree. My own point of view argues, even if it is the wrong view, so that our children can experience deeper, learn more firmly, and understand what they have learned while learning new knowledge and experiencing the formation of knowledge. The following points should be done when designing this lesson:
1. Enhance students' awareness of estimation and reflect the connection between mathematics and life.
The new curriculum standard emphasizes the need to strengthen the estimation, pay attention to the cultivation of students' estimation consciousness and estimation ability, and the estimation has a wide range of applications in daily life. Therefore, teachers must create certain situations and closely link mathematics with life. Students feel the great practical significance of learning mathematics knowledge in real life, thus enhancing the motivation of students to learn and generating positive mathematical emotions.
2. Infiltrate multiple methods to develop students' ability to analyze specific problems.
After asking questions, let the students try to solve the problem first. The students' methods can be described as diverse. On this basis, the teacher can ask, “Every method is well-founded. For this question, which estimation method is better? Some?" At this time, students will express their opinions and compare the most appropriate methods based on a variety of algorithms, thus cultivating students' ability to solve problems flexibly.
In the process of teaching, teachers should also pay attention to creating a good psychological environment for students to fully relax and fully respect their thoughts and feelings, so that their thoughts and opinions can be fully revealed and expressed. The views and conclusions can be improved in a step-by-step expression, and each child's thinking and emotions are also developed. Once again, the design of the whole class reflects the selectivity, openness, hierarchy, and diversity. It gives the students the space to explore, not only the openness of the form, but also the opening of the concept, the progress of the layers, the amount of information, and the embodiment. The diversity of algorithms. What is important is that it reflects the characteristics of mathematics. From life to life, it solves the problems in life. The acquisition of knowledge is not the teacher’s hard work for the children, but the children’s positive in the specific situation. Thinking, constantly discovering problems and solving problems. In the classroom, the exchange of students, teachers and students is harmonious and natural, and the collision of thoughts ignites the spark of knowledge. The children's desire for learning naturally rises, and the enthusiasm and initiative of learning are fully exerted. The initiative to learn knowledge has also been best reflected