In the teaching of this part of the textbook, starting with the games that students are interested in, let students experience coin toss, practice by themselves, observe the possibility of events, study the fairness of the rules of the game, express the possibility with scores and experience the formation process of knowledge. In teaching activities, in order to let every student experience the formation process of knowledge personally, I adopted the learning method of group cooperation, so that every child can feel the characteristics of the possibility of things happening, so that they can learn in happiness and have the following feelings:

Let students learn mathematics in operation activities. In teaching, I give students the initiative to learn. Students experience the process of exploring random phenomena in teaching activities, and guide students to guess the possibility of the results first; Then let the students do the experiment by themselves. Through the process of counting the number of coin flips in front of the group and the whole class, let the students find that when the number increases, it gradually approaches the average. Finally, the experimental results of scientists are displayed, which makes students feel that when the number of times is increasing, it is almost equal to half, indicating that the rules are fair.

Let students feel in cooperation and communication. Throughout the whole class, various activities such as "throwing coins", "throwing dice", "designing a turntable" and "little designer" run through, which fully embodies the life of mathematics in the curriculum standards, allowing students to solve problems through cooperation and communication, and the communication is natural and effective. The whole class enables students to obtain a lot of mathematical information and knowledge in an active, democratic and harmonious atmosphere, making mathematics learning possible. It embodies the effectiveness of mathematics teaching.

Attach importance to the emotionalization of mathematics learning. Changing students' learning state is one of the core concepts of the new curriculum reform. In the classroom, teachers should learn to respect and guide students to express their inner thoughts boldly, create an equal, democratic and harmonious relationship between teachers and students, encourage students to find problems, ask questions, dare to question, be willing to communicate and cooperate, taste the joy of success in learning activities and build self-confidence.

After this class, my feeling is that if students are only allowed to move, sometimes it may be difficult to understand knowledge, because the possibility of an event still has some errors in actual operation. The size of the possibility is difficult to get through experiments. Because if we do experiments, we must build on enough experiments, and it is impossible to do a lot of experiments in class. After studying other teachers' classes, I think if we leave the coin toss experiment before class, we can make students understand that they have the same possibility in class. Finally, we can improve students' problem-solving ability through examples, so as to achieve our learning goals.

This is the first time that students are exposed to decimal multiplication. I boldly changed the situation map in the textbook and sorted out the changing rules of the review. Through the example of 1, let students master the calculation method of multiplying decimal by integer in the process of solving practical problems, and then arrange some exercises to consolidate. In the actual learning situation, most students will calculate decimal multiplication, knowing that it is calculated as an integer and then pointing to the decimal point. However, the vertical writing is still very vague about why it should be done. I think if we follow the arrangement of the textbook, such questions will not be challenging and students will not be interested, so we will arrange them from the following aspects:

1, highlighting the change law of products.

The law of accumulation and change in teaching materials is review, but I will regard it as new knowledge in teaching, guide students to discover the law and experience the fun of discovery. Fully understand how many times one factor is constant and another factor is expanded (reduced), and the product will be expanded (reduced) by the same multiple. Guide students to directly use this law to calculate 0.3×2, and at the same time verify and feel the correctness of this law by multiplying decimal by integer.

2. Highlight the vertical writing format.

With the previous understanding of arithmetic, students no longer find it difficult to calculate 3.85×59 vertically, but some children still can't understand why they write like this, so I grasp why decimal points are not aligned to guide students to think. We expand 3.85 by 100 times, and the calculation is 385 times 59, so we calculate it according to the calculation method of integer multiplication, not decimal multiplication. Finally.

3. Highlight the change of decimal number.

The change of decimal places is the difficulty of this lesson, so I arranged two exercises for this, one is to calculate decimal places, and the other is to judge decimal places. After judging the decimal places, I chose two questions for students to calculate, and realized that the decimal places that are not products are the same as the decimal places of factors.

After the whole class, students begin to be interested in learning, think positively, solve problems by using the discovered rules, and correctly calculate decimal times integer. What puzzles me is that in the previous part, I asked students to find the rules, do oral calculations with the rules, and then do written calculations. Everything is in my arrangement, the teaching process is smooth, and the students are guided to transfer and expand their knowledge smoothly, and the situation is also very good.

But do too many hints constrain students' thinking? If they don't pave the way, would it be better to just show the students the problem of multiplying decimals by integers and let them think? In the second half of the class, students were no longer interested in calculation, and several children deserted. After investigation, they found that the problem is too simple, that is, the decimal point position of the product, just move the decimal point position.

Do it. The calculation is of little significance. The students are telling the truth. They have recently studied calculation and discussed calculation methods. However, the discovery of calculation methods sometimes does not require them to go through the process of discovery and exploration, but is more reminded and told by teachers. How can curious children like passive acceptance? It seems that computing teaching needs teachers to enrich the practice forms to attract students' eyes and brains.

Reflections on the teaching of the first volume of fifth grade mathematics (Part III) "Division of fractions" is an important and difficult point in this textbook. Fractional division is taught on the basis that students master the related operations of integer division and learn fractional multiplication.

The calculation rule of fractional division is based on the law that the quotient of dividend and divisor multiplied by the same number (except 0) in integer division remains unchanged, and the decimal point position moves, which leads to the change of decimal size. In the trial and error method of fractional division, the steps of division are basically the same as those of integer division. Pay attention to reviewing and applying the related knowledge of integer division, so as to lay a foundation for learning new knowledge.

In the teaching of this unit, I emphasize students' independent thinking and try to make each student have a unique experience of new problems in textbooks. On this basis, the communication and mutual assistance between students will produce sparks of thinking collision, and only in the collision of thinking will students have real development. Students' innovative ability can not be separated from the guidance of teachers, from the transmission, analysis, induction and association of knowledge, and find new methods from it. In order to broaden students' thinking and improve their innovative ability, students can recall their existing knowledge through association and communicate the internal relationship between knowledge.

Of course, in the process of opening up, the role of teachers can not be ignored. Reflecting on the teaching of a unit, I think the guiding role of teachers can be strengthened a little, and perhaps better results can be achieved.

Because of the teaching experience in the first unit, I am fully prepared for the second unit "Fractional Division". Sure enough, although students have the calculation basis of integer division, when it comes to the calculation of decimals, students' thinking begins to be confused, and unexpected and unexpected problems come out.

1. Decimals are out of sync. Move the decimal point of the divisor into an integer, and all the students know that it can be done smoothly. The key is to forget to move the decimal point of the dividend, especially when the decimal point of the dividend is not enough to make up 0. Or the number of bits moved is inconsistent with the divisor. Although they know that the decimal point movement of divisor and dividend is based on the invariance of quotient, they forget it when they do their homework.

2. The unit of quotient is not enough 1, and the point of quotient 0 is ambiguous, especially if the unit of dividend is not in the lower right corner, write 0. (For example, what is done next to the textbook 18, 24 15)

3. The decimal point of the moved quotient is not aligned with the decimal point of the dividend.

Emphasize arithmetic, practice quotient decimal point more, and analyze and comment on the mistakes in students' homework.

4. When checking, multiply the quotient after the decimal point is moved by the divisor.

5. Forget to write 0 in the quotient position when it is not enough, and then pull down a number. Some students divide by the remainder again. (For example: textbook 18+0.438+08)

Reflections on the teaching of the first volume of fifth grade mathematics (Part IV) Before learning the knowledge of this lesson, students know the fractions and decimals respectively, and they will also compare the fractions and decimals. The content of this lesson is based on this development. In the introduction of the question, I showed two children the time they spent reading extracurricular books, one was the score and the other was the decimal, and then asked the students to compare who spent more time. The second is to solve problems and compare two numbers expressed in different forms, which is new knowledge and a new conflict in students' cognition. How to solve this conflict requires students to explore for themselves. After heated discussion, the students also came up with the same four comparative methods as in the book. Even if they are not as complete as in the book, it will not affect their exploration. The first method is to compare the reading time of two children intuitively by drawing pictures; The second method is to find out who spends more time through simple reasoning; Third, the conversion of time expressed by fractions is divided into decimals, and then the time is compared; The fourth is to convert decimals into fractions and then compare them. In the process of exploring the problem, the discussion on the conversion between fractions and decimals runs through it. It is easier for students to accept and master fractions, and it is difficult for individual students to convert decimals into fractions. After some discussion, students can realize the basic method of converting fractions into decimals. Therefore, the design of this lesson embodies the following characteristics.

1, let students learn mathematics in specific situations and solve practical problems as a means.

This lesson focuses on the realistic and interesting life problem of who spends more time, and organically links various learning materials, so that students are always in the process of discovering, asking and solving problems, and their learning enthusiasm can be fully mobilized.

2. With students' independent exploration as the main line, guide students to find the method of mutual transformation between fractions and decimals.

Only through students' active participation and independent exploration can mathematical knowledge be transformed into students' own knowledge. When students explore the method of fractional reciprocal, teachers provide students with time to explore, let students explore in the form of group cooperation, and compare and integrate on the basis of students' various methods, so as to get the method of fractional reciprocal. In this process, students have experienced the whole process of forming knowledge through their own efforts and the efforts of their peers.

The teaching in this class is satisfactory.

1, to stimulate students' strong thirst for knowledge

Problems, contradictions and questions are enlighteners of thinking, which can change students' thirst for knowledge from potential to initiative, and effectively adjust students' enthusiasm and initiative in thinking. In each link of this class, students are arranged to hold talks with each other, and sometimes even some suspense is set, which not only mobilizes students' enthusiasm for learning, but also stimulates their strong thirst for knowledge.

2. Let students seek development through independent exploration.

In teaching, I fully respect students' personality differences and provide them with opportunities to exchange ideas from their existing knowledge background, so that students can choose their own methods through communication. When comparing fractions with decimals, students think from many different angles, which fully shows that students are the masters of learning.

3. Promote the development of students' original cognitive level.

The content of this class is relatively simple, and the students have had a preliminary understanding before class. Therefore, in the classroom, students are completely free to explore and learn by themselves, and to experience and appreciate the process of knowledge formation and acquisition. In the exploration of comparative methods, let students choose their own comparative methods according to their own characteristics, so that students of different levels can achieve different degrees of development. The amount of harvest may be different, but everyone can get a successful experience.

Reflections on the teaching of the first volume of fifth grade mathematics (Chapter 5) In the previous textbooks, the area of irregular figures was not arranged. Irregular graphics can be seen everywhere in our real life, so the textbook of Beijing Normal University Edition has incorporated this content into the textbook, requiring students to master the estimation and calculation of irregular graphics area, which not only helps to cultivate students' spatial concept, but also helps to improve students' problem-solving ability. Growth footprint is one of the contents in this field.

Every child has experienced infancy, but now looking back at his birth footprints, he feels incredibly small. So I started this class with excitement and curiosity: What is the footprint area of Xiaohua when she was born? In this case, students' enthusiasm for learning is fully stimulated, and they actively participate in finding a more suitable method to correctly estimate the area of irregular footprint graphics. So the methods obtained are different, and some use several grids; Some people calculate footprints as approximate rectangles; Some are calculated by approximate trapezoid; Some are calculated as approximate triangles ... Although the methods are different and the results are also wrong, the child's thinking is in an active state. In order to make the results more accurate, some students who use the method of counting grids actually count carefully in units of half grids, and the results are accurate to ten. In this way, with the children's active exploration, the teaching goal was easily realized. Therefore, at the age of 2, it is no suspense to explore Xiaohua's footprint area, and students learn easily and happily.

Reflecting on the teaching of this course can give children the initiative to learn and create time and space for exploration. Children are active in learning, open-minded and diverse in methods. Although there will be temporary difficulties in the process of learning, under my implicit guidance, children can complete their learning activities well. This makes the classroom become a classroom generated by interactive discussion and problem solving between teachers and students. The disadvantage is that there is still a certain error between the estimated value and the accurate value of the child. How to effectively narrow the error range needs to be further strengthened.

Reflections on the teaching of the first volume of mathematics in grade five (Part VI) The content of "using letters to represent numbers" seems simple and clear, but it is an important part of learning algebra knowledge and a leap from concrete numbers to letters for primary school students. For fifth-grade children, this course is abstract and boring, and it is difficult to teach. I have seriously considered the objective requirements of the letter representation in the curriculum standard, and noticed that it is very important for students to fully experience and appreciate the process of expressing numbers by letters in their original knowledge and skills. So I designed a teaching link, trying to let students fully experience the process of expressing numbers with letters. Mainly adopts the teaching method of combining teaching with practice.

First, pay attention to guide students to experience the process of expressing numbers with letters, and have a preliminary feeling about algebra.

Using letters to represent numbers plays an irreplaceable role in the history of mathematics, but how to make students understand why and under what circumstances letters are used to represent numbers? In the whole teaching activity, I attach importance to using what I have learned to solve practical problems, which makes students experience the transformation from symbols to letters. In this process, firstly, students observe and solve problems by themselves, and then students inspire and complement each other, thus deepening their understanding of mathematical knowledge in the process of solving problems.

Second, pay attention to the close relationship between mathematics and life.

In this class, I chose Introduction to Conversation. Let the students practice the interesting topic of arranging numbers according to the law. Based on students' existing life experience, I will transition from symbol representation of numbers to letter representation of specific numbers, so that students can understand and realize the wide application of letter representation of numbers in real life and study. Then let the students talk about the examples that you have seen in your life in which numbers are represented by symbols or letters, so that students can feel that mathematics is around, which reflects the connection between mathematics and life.

Third, combine teaching with practice, increase encouraging language and arouse students' learning enthusiasm.

When I teach the law of operation by letters, I adopt the mode of teaching+self-study. First of all, I instruct students to learn to express multiplication and method of substitution by letters, and tell them the process of abbreviation multiplication between letters, and then let them try to write other algorithms themselves. Because some mathematical concepts are established by convention and stipulated by predecessors, we don't need to delve into them. Therefore, teachers need to teach some knowledge points, so that students can consolidate their cognition through meaningful acceptance, save teaching time and resources and optimize teaching procedures. In class, I didn't ignore or interrupt the students' speeches, but paid attention to the students' speeches and gave them encouragement and praise. Students' learning enthusiasm is higher and their learning status is better.

Disadvantages:

One, an algorithm can be described in words, can also be represented by examples, can also be represented by letters. In the teaching process, the design is not good enough, and there is no sharp contrast, which makes students feel the superiority and necessity of using letters to represent numbers.

Secondly, in the teaching process, in order to let students learn and understand the numbers expressed by letters within the specified time, I teach according to my own intention, which leads to students' blind listening, limiting students' thinking activities to the specified time and space and suppressing students' creative thinking.

Teaching reflection on the first volume of fifth grade mathematics (Chapter 7) The parallelogram area is the content of the first volume of fifth grade mathematics. The idea of textbook design is: first, calculate the base, height and area of parallelogram by counting squares. Then through the observation of the data, a bold guess is put forward. Through operation verification, the calculation method of parallelogram area is deduced. Then use the learned formula to solve the problem. I think it is not difficult for students to recite the formula simply, but it is difficult for students to understand the formula. Therefore, every student must go through the process of knowledge formation. On the basis of independent thinking, I personally cut and paste, combined with my own operating experience to discuss and communicate in the group. The class was full of unknowns, and I summed up the lesson carefully after class.

(1) Count the gains and losses in the grid.

The process of counting squares designed in the textbook closely follows the flower bed in the picture above. Draw two flower beds on grid paper after scaling down. Ask the students to count 1 grid on the grid paper as 1 square meter. This is slightly different from the students' previous mathematical methods. In addition, there are less than 1 squares in the parallelogram. How to accurately calculate the area is a problem that students need to seriously consider. At that time, Qiu Zehao was asked to count the squares in front, but the result was not very smooth. If I guide the students to cut the left side along the grid line, move to the other side at this time and count after completing all the squares. And tell the students that this method of cutting and filling to the other side of the figure is called cutting and filling method. This kind of teaching can prepare students for converting parallelogram into the calculation of graphic area they have learned in the future, so I don't handle this place very well.

(2) Students must go through the process of knowledge formation in math class.

Before class, I asked each student to prepare a parallelogram learning tool and let each member of the group cut a parallelogram in different ways. The operation of the class is: first measure the base and height of the parallelogram, record the data of the parallelogram in your notebook, convert the parallelogram into a rectangle through cutting, measure its length and width, and calculate its area. Then think about what has changed and what has not changed after the transformation, and then find the relationship between parallelogram and rectangle through thinking and reporting. The area calculation formula of parallelogram is obtained. In this process, students summed up the area calculation formula of parallelogram through their own operation and thinking, which not only made them understand the formation process of knowledge, but also improved their hands-on ability and brain ability. This provides a method and direction for learning the knowledge of graphics in the future. In class, I still feel that the density and treatment of exercises are not clever enough, so we should pay attention to the design and treatment of exercises in the future.

Reflections on the teaching of the first volume of fifth grade mathematics (Chapter 8) This lesson is to measure the distance between two points that are far apart in practical activities.

A ruler is a tool for measuring length. Whether it is a ruler or a tape measure, it is difficult to directly measure the distance between two points that are far apart. Generally, the distant place is divided into several sections, the actual length of each section is measured with a ruler, and the distance between the two places is added up. To do this, we must first determine a straight line passing through two points, and then measure the length along this straight line. The focus of practical activity "actual measurement" is to guide students to measure such a straight line. The textbook shows three students measuring a straight line between point A and point B. Two boys insert a pole vertically at point A and point B, and one girl inserts a pole at point C and point D between point A and point B in turn. As long as the four columns are inserted in the same straight line, the distance between A and B can be divided into three sections: AC, CD and D B. The boy in the hat is observing and guiding the adjustment, and measuring the straight line between A and B with four pillars ... The textbook guides students to understand the situation map and what the three people in the picture are doing, especially how the boy in the hat judges that the four benchmarks are not on a straight line. Then use this method to carry out similar practical activities on the playground.

There are also step measurement and visual inspection in this exercise. To know the step size, the step size is generally not obtained by measuring the length of a step, but calculated by the number of steps = average step size. The textbook guides students to choose a distance and walk three times, and calculates the average step size by filling in a table. This distance can't be too short or too long. Generally, about 20 meters is enough. Because the step measurement is to measure some lengths according to the number of steps you usually walk, you need to walk three times at this distance with natural and even steps, and the average step size obtained by averaging the number of steps you walk each time is close to the normal state. Visual inspection can only estimate the distance between two points, which often has a big error with the actual distance. The textbook only introduces the method of practicing visual inspection, so that students can experience it in practice and try to do some visual inspection.

Reflections on the teaching of the first book of fifth grade mathematics (Chapter 9) Decimal multiplication is the content of the first unit of the first book of fifth grade mathematics. The teaching focus of this content is the calculation rules of decimal multiplication; The difficulty in teaching is the location of decimal places and decimal points in decimal multiplication. If the number of decimal places of the product is not enough, it should be preceded by 0.

Decimal multiplication by decimal is taught on the basis of students' learning decimal multiplication by integer. I think students have a certain foundation in this knowledge point. As long as they master the arithmetic of fractional multiplication, it should be easier to learn, but the facts are not satisfactory. In after-class exercises, students make many mistakes: 1, and the method is wrong: for example, in teaching example 3(2.4×0.8), students can fluently say that the product multiplied by two factors will be expanded by 10 times, and in order to keep the product unchanged, the product will be reduced by 65438 times. But in the process of calculation, some students can't combine arithmetic with method, and can't solve the decimal point problem of product correctly. Some students confuse decimal multiplication with decimal addition, or just look at the decimal places of a factor. 2. Problems about 0 in calculation; Some students have zero at the end of the product, so cross it out first and then point the decimal point; Some students with learning difficulties have to multiply by 0 again when the factor is a pure decimal or there is 0 in the middle of the factor. 3. Calculation error: When there are many digits in the factor, individual students directly write the numbers (for example, 4.5 15 is directly in the vertical form of 2. 1 without calculation process), and then complete the vertical form without writing the numbers in the horizontal form.

Faced with the mistakes made by students, I have to re-examine my classroom and my students, and I deeply reflect on this: this unit is not as simple as I thought, not only should we pay attention to the connection between old and new knowledge, but also highlight the changing law of product, vertical writing format and the relationship between decimal places in factors and decimal places in products. To this end, I decided to improve from the following aspects:

1. Analyzing and judging students' mistakes as teaching resources, the effect of correcting mistakes is better than that of correcting books by students.

2. Vertical thinning of columns. Key points: ① "last bit alignment" when decimal multiplication column is vertical. (2) After calculating the product, count two factors * * * with several decimal places, and count the same decimal places from the right to the left of the product. (3) Calculate the result by counting the decimal point first, and then cross out the 0 at the end of the product.

3. We should strengthen the comparative practice of decimal addition and subtraction and decimal multiplication.