In addition to continuing to complete the proportional knowledge, common three-dimensional figures and preliminary statistical knowledge in primary school mathematics, the twelfth volume of Primary School Mathematics should systematically sort out and review the main contents of primary school mathematics, consolidate the learned mathematical knowledge, and comprehensively apply the learned mathematical knowledge to solve relatively simple practical problems. The detailed analysis of the knowledge points in the textbook of the twelfth volume of primary school mathematics is as follows:

In the study of proportion knowledge, we can understand the meaning and basic nature of proportion, know solution ratio, see the scale, understand the meaning of positive proportion and inverse proportion, judge whether the two quantities are directly proportional or inversely proportional, and solve relatively easy application problems with proportion knowledge.

In the study of common three-dimensional graphics, we can know the characteristics of cylinders and cones, have a preliminary understanding of the radius and diameter of spheres, and calculate the surface area of cylinders and the volumes of cylinders and cones according to the actual situation. For example, a circular pool requires its floor area to be the bottom area; Require the length of a circle around the pool, that is, find its bottom circumference; To cement the periphery and bottom of the pool, it is to find its surface area (a bottom area plus lateral area); To know how much water a pool can hold, you need to know its volume. Students are required to make a concrete analysis according to the actual situation and specific problems, which should not be confused.

In the study of preliminary statistical knowledge, everyone will read and make composite statistical tables with percentages, understand the drawing method of simple statistical charts, and initially read and draw simple statistical charts.

Finishing and reviewing is a key point of this book. Through systematic arrangement and review, we can deepen our understanding and mastery of the mathematical knowledge learned in primary schools, better cultivate reasonable and flexible computing ability, develop our own thinking ability and spatial concept, and improve our ability to solve simple practical problems by comprehensively applying the learned mathematical knowledge. The general review part is divided into three areas: number and algebra, space and graphics, statistics and probability, and each area is divided into four aspects: consideration and communication, consolidation and application. Among them, the general review occupies a large space, accounting for 5 1 page in the 90 pages of the book, accounting for 56.7%. It can be seen that the general review occupies a great weight in the second volume of the sixth grade. The main purpose of review is to reflect and improve through reflection. How to teach the general review part?

1, be familiar with the textbook and master it.

What we are teaching now is the first class of textbook. Every teacher is in contact for the first time, and some teachers are not systematic. Influenced by the previous syllabus textbooks, teaching will also be interfered by the original textbooks, so we should be familiar with the textbooks systematically and grasp them, otherwise we will not be able to grasp the objectives, for example, question 5 on page 42, "What have we learned about multiples and factors?" Please tidy up. "The current textbooks and previous textbooks have changed a lot in the handling of this content. If our teacher is not familiar with it, we can't master it, and we don't know what we have learned, so it is difficult to achieve our goal in review. As far as the overall review is concerned, the narrative is very coherent and concise. If our teachers are not familiar with the teaching materials, they will not be able to concretize the coherent narrative and detail the concise sentences, and they will always feel tired or do nothing when reviewing, and will not achieve the due results. Familiarity with textbooks requires teachers to know about the whole set of textbooks, the teaching content of each textbook, the source of each knowledge point and the content of the textbook, and the relationship between books in the same field. Familiar with the teaching materials, teachers are required to have a thorough understanding of the knowledge points involved in each field and each part, and make its structure chart clear.

2. Truly reflect the subject.

The curriculum standard (revised edition) clearly points out that "students are the main body of learning mathematics". "Review communication" should reflect subjectivity, let students review and let students communicate, and can't make mistakes. Such as: 40 pages of review and arrangement of relevant figures. "Review and communication" should not only be able to answer some specific questions, but also rise to how to solve what kind of problems from special to general according to the law, such as "Calculation and Application" on page 53 of the textbook. "Review and communication" occupies a small space and seems simple. In fact, there are many knowledge points and it takes a lot of time. Teachers must not rush by, for example, the first topic of stereoscopic graphics on page 7 1 and the second topic of graphics and transformation on page 78 "Review and communication", which requires our teachers to prepare lessons carefully before class. "Review and communication" should make necessary notes according to the knowledge content. I think each student should have 1 review notebook.

"Consolidation and application" should reflect the subjectivity, let students do the questions and let students say the questions. The evaluation of exercises reflects subjectivity, allowing students to talk about ideas and methods.

3. Pay attention to the internal relationship between knowledge dissemination and help students build a good knowledge structure.

Through general review, a knowledge system is formed. General review *** 19 has three topics, and there are several knowledge points under each topic. The knowledge points of the same kind of knowledge are internally related, but they are scattered in the teaching process. In the general review, we should find out the internal relationship between them, make them connect into a line, form a network and establish a knowledge structure.

According to the content, some knowledge structures can be represented by network diagrams, some by tables, and some by graphs. For example:

"Digital knowledge" is a network representation.

Decimal notation is a tabular representation.

The relationship between graphics in Understanding Graphics is represented by graphics (set graphics). The development we advocate is based on inheritance, not total negation. In the arrangement of knowledge, teachers can review the knowledge structure diagram in the original syllabus.

4. Pay attention to the training of basic skills.

The study of any knowledge is not completed at one time, and skills depend on training. Therefore, in addition to the necessary basic exercises, we should also carry out some variant exercises and comprehensive exercises. The characteristics of mathematics decide to do more problems and practice more. Practice is not repetition. Find problems through practice, consolidate knowledge and methods through continuous problem solving, and improve the ability to solve problems through continuous problem solving.

If you want to train, you must have information and practice. The exercises in the general review of syllabus textbooks are divided into two parts: "do one thing and do one thing" and "practice". There are 55 exercises in "Do One, Do One" and 154, and 209 exercises in * *, while the exercises reviewed in the new century edition of curriculum standard textbooks are only "consolidation and application".

5. Pay attention to effective help for students with learning difficulties.

Learning from China students is a relative concept. Every class has students with learning difficulties. In order to "improve the teaching quality in an all-round way", we must do a good job in helping students with learning difficulties. Primary education is universal education. Only by paying attention to helping students with learning difficulties can it be said to be "for all students". To help students with learning difficulties, it is necessary to analyze the causes of students with learning difficulties, help them build up their confidence in learning, and carry out targeted work. A person's growth needs constant repetition, and the transformation of students with learning difficulties cannot be achieved overnight. Long-term persistence takes time and energy, and teachers' professionalism and sense of responsibility should be reflected in effective help for students with learning difficulties.

In addition to continuing to complete the proportional knowledge, common three-dimensional figures and preliminary statistical knowledge in primary school mathematics, the twelfth volume of Primary School Mathematics should systematically sort out and review the main contents of primary school mathematics, consolidate the learned mathematical knowledge, and comprehensively apply the learned mathematical knowledge to solve relatively simple practical problems. The detailed analysis of the knowledge points in the textbook of the twelfth volume of primary school mathematics is as follows:

In the study of proportion knowledge, we can understand the meaning and basic nature of proportion, know solution ratio, see the scale, understand the meaning of positive proportion and inverse proportion, judge whether the two quantities are directly proportional or inversely proportional, and solve relatively easy application problems with proportion knowledge.

In the study of common three-dimensional graphics, we can know the characteristics of cylinders and cones, have a preliminary understanding of the radius and diameter of spheres, and calculate the surface area of cylinders and the volumes of cylinders and cones according to the actual situation. For example, a circular pool requires its floor area to be the bottom area; Require the length of a circle around the pool, that is, find its bottom circumference; To cement the periphery and bottom of the pool, it is to find its surface area (a bottom area plus lateral area); To know how much water a pool can hold, you need to know its volume. Students are required to make a concrete analysis according to the actual situation and specific problems, which should not be confused.

In the study of preliminary statistical knowledge, everyone will read and make composite statistical tables with percentages, understand the drawing method of simple statistical charts, and initially read and draw simple statistical charts.

Finishing and reviewing is a key point of this book. Through systematic arrangement and review, we can deepen our understanding and mastery of the mathematical knowledge learned in primary schools, better cultivate reasonable and flexible computing ability, develop our own thinking ability and spatial concept, and improve our ability to solve simple practical problems by comprehensively applying the learned mathematical knowledge. The general review part is divided into three areas: number and algebra, space and graphics, statistics and probability, and each area is divided into four aspects: consideration and communication, consolidation and application. Among them, the general review occupies a large space, accounting for 5 1 page in the 90 pages of the book, accounting for 56.7%. It can be seen that the general review occupies a great weight in the second volume of the sixth grade. The main purpose of review is to reflect and improve through reflection. How to teach the general review part?

1, be familiar with the textbook and master it.

What we are teaching now is the first class of textbook. Every teacher is in contact for the first time, and some teachers are not systematic. Influenced by the previous syllabus textbooks, teaching will also be interfered by the original textbooks, so we should be familiar with the textbooks systematically and grasp them, otherwise we will not be able to grasp the objectives, for example, question 5 on page 42, "What have we learned about multiples and factors?" Please tidy up. "The current textbooks and previous textbooks have changed a lot in the handling of this content. If our teacher is not familiar with it, we can't master it, and we don't know what we have learned, so it is difficult to achieve our goal in review. As far as the overall review is concerned, the narrative is very coherent and concise. If our teachers are not familiar with the teaching materials, they will not be able to concretize the coherent narrative and detail the concise sentences, and they will always feel tired or do nothing when reviewing, and will not achieve the due results. Familiarity with textbooks requires teachers to know about the whole set of textbooks, the teaching content of each textbook, the source of each knowledge point and the content of the textbook, and the relationship between books in the same field. Familiar with the teaching materials, teachers are required to have a thorough understanding of the knowledge points involved in each field and each part, and make its structure chart clear.

2. Truly reflect the subject.

The curriculum standard (revised edition) clearly points out that "students are the main body of learning mathematics". "Review communication" should reflect subjectivity, let students review and let students communicate, and can't make mistakes. Such as: 40 pages of review and arrangement of relevant figures. "Review and communication" should not only be able to answer some specific questions, but also rise to how to solve what kind of problems from special to general according to the law, such as "Calculation and Application" on page 53 of the textbook. "Review and communication" occupies a small space and seems simple. In fact, there are many knowledge points and it takes a lot of time. Teachers must not rush by, for example, the first topic of stereoscopic graphics on page 7 1 and the second topic of graphics and transformation on page 78 "Review and communication", which requires our teachers to prepare lessons carefully before class. "Review and communication" should make necessary notes according to the knowledge content. I think each student should have 1 review notebook.

"Consolidation and application" should reflect the subjectivity, let students do the questions and let students say the questions. The evaluation of exercises reflects subjectivity, allowing students to talk about ideas and methods.

3. Pay attention to the internal relationship between knowledge dissemination and help students build a good knowledge structure.

Through general review, a knowledge system is formed. General review *** 19 has three topics, and there are several knowledge points under each topic. The knowledge points of the same kind of knowledge are internally related, but they are scattered in the teaching process. In the general review, we should find out the internal relationship between them, make them connect into a line, form a network and establish a knowledge structure.

According to the content, some knowledge structures can be represented by network diagrams, some by tables, and some by graphs. For example:

"Digital knowledge" is a network representation.

Decimal notation is a tabular representation.

The relationship between graphics in Understanding Graphics is represented by graphics (set graphics). The development we advocate is based on inheritance, not total negation. In the arrangement of knowledge, teachers can review the knowledge structure diagram in the original syllabus.

4. Pay attention to the training of basic skills.

The study of any knowledge is not completed at one time, and skills depend on training. Therefore, in addition to the necessary basic exercises, we should also carry out some variant exercises and comprehensive exercises. The characteristics of mathematics decide to do more problems and practice more. Practice is not repetition. Find problems through practice, consolidate knowledge and methods through continuous problem solving, and improve the ability to solve problems through continuous problem solving.

5. Pay attention to effective help for students with learning difficulties.

Learning from China students is a relative concept. Every class has students with learning difficulties. In order to "improve the teaching quality in an all-round way", we must do a good job in helping students with learning difficulties. Primary education is universal education. Only by paying attention to helping students with learning difficulties can it be said to be "for all students". To help students with learning difficulties, it is necessary to analyze the causes of students with learning difficulties, help them build up their confidence in learning, and carry out targeted work. A person's growth needs constant repetition, and the transformation of students with learning difficulties cannot be achieved overnight. Long-term persistence takes time and energy, and teachers' professionalism and sense of responsibility should be reflected in effective help for students with learning difficulties.

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