People's education publishing house curriculum teaching material institute primary school mathematics curriculum teaching material research and development center
The sixth volume of Mathematics, an experimental textbook for compulsory education curriculum standards, was compiled by the Primary School Mathematics Room and the Research and Development Center of Primary School Mathematics Curriculum Textbooks of People's Education Publishing House. It is based on the basic ideas and prescribed teaching contents of the Full-time Compulsory Education Mathematics Curriculum Standards (Experimental Draft) (hereinafter referred to as the Standards), and on the basis of summarizing the research and use experience of the original nine-year compulsory education primary school mathematics textbooks, the editors try their best to embody the new concept of textbooks, teaching and learning, and pay attention to the adopted concept. On the other hand, pay attention to the relationship between inheriting tradition and developing innovation. It is necessary not only to embody the new concept of current mathematics education reform, but also to maintain the fine tradition of mathematics education in China, so that the teaching materials are basic, rich and developmental.
The arrangement and treatment of the teaching content of this volume is guided by the compiling ideas and principles of the whole set of experimental textbooks, and strives to make the structure of the textbooks conform to the principles of pedagogy and psychology and the age characteristics of students, and continue to reflect the styles and characteristics of previous experimental textbooks. This textbook still has the characteristics of rich content, paying attention to students' experience and understanding, embodying the formation process of knowledge, encouraging diversification of algorithms and problem-solving strategies, changing students' learning methods, and embodying open teaching methods. At the same time, due to the different teaching contents, this textbook also has the following obvious characteristics.
1. Increase the teaching of understanding negative numbers, embody the new concept of mathematics teaching reform, and deepen students' understanding of logarithmic concept knowledge.
Negative number is a new content in primary school mathematics teaching. For a long time, the teaching of negative numbers is generally arranged in the primary stage of middle school teaching. Now, considering the wide application of negative numbers in life, students have come into contact with some negative numbers in their daily lives. With a preliminary understanding of negative numbers, the standards have pushed them to the primary school stage. The understanding of negative numbers is an expansion of the concept of numbers for primary school students. Numbers that students used to know-integers, fractions, decimals, etc. -Are all the numbers within the arithmetic range? The establishment of the concept of negative numbers expands students' understanding of arithmetic numbers to rational numbers, thus enriching pupils' understanding of logarithmic concepts.
The concept of "negative number" is abstract for primary school students, and the standard requires "understanding the meaning of negative number in familiar life situations." Therefore, the arrangement of this textbook should first pay attention to providing students with rich and colorful materials, such as the expression of temperature and the recording method of income and expenditure. Let students feel and understand the necessity of negative numbers and the meaning of positive and negative numbers in real life background. This arrangement not only deepens students' understanding of negative numbers, but also helps to cultivate students to observe reality with mathematical eyes and gradually form the consciousness of mathematical application. On this basis, two examples are arranged in the textbook. Through lively and interesting activities and practical materials, let students learn to express the numbers they have learned by straight lines, initially penetrate the concept of number axis, form a relatively complete cognitive structure of numbers, initially understand the relationship between negative numbers, zero numbers and positive numbers, and initially understand the order of numbers on the number axis, thus deepening students' understanding of the knowledge about numbers.
2. Improve the arrangement of proportion, highlight the concept of proportion, enrich the content combined with practice, and cultivate practical ability.
Proportion is one of the traditional teaching contents, and it is also an important basic knowledge that senior primary school students need to learn and master. First of all, it has great practical value, and some practical problems need to be solved in proportion. For example, draw a map, enlarge or reduce a graph, etc. ; Secondly, it is the basic knowledge for students to further study. Thirdly, it is an important field to cultivate students' comprehensive ability to solve problems with knowledge and mathematical thinking. The relevant mathematical knowledge that students have learned before has been comprehensively applied here. For example, drawing a simple map requires a lot of knowledge and skills such as scale, comparison and drawing. From the point of view of the movement and change of things, the various quantitative relations that students have known before are summarized as positive proportional relations and inverse proportional relations, which not only deepens students' understanding of quantitative relations, but also obtains the preliminary concept of functions, laying the foundation for middle school mathematics learning.
Compared with the previous syllabus, the teaching requirements of this part of the standard have been improved. Students are not only required to recognize the images in direct proportion, but also to "enlarge or reduce simple graphics in a certain proportion by using the form of grid paper." The arrangement of this part of teaching materials should not only reflect the requirements of standards and new ideas advocated, but also highlight the role and position of proportion in students' mathematical knowledge structure. Therefore, compared with the original general compulsory education textbooks, there are the following improvements.
(1) Concept teaching pays attention to integrating with practice and strengthening exploration. The concept of proportional unit is emphasized in teaching, and basic concepts such as proportion, positive proportion and inverse proportion are the important basis for subsequent learning. The arrangement of this textbook focuses on concept teaching in the first two sections. On the one hand, pay attention to guiding students to establish clear concepts through observation, comparison, judgment and induction; on the other hand, pay attention to connecting with reality, introduce concept learning from practical problems, and increase the exploratory nature of learning. At the same time, the teaching materials no longer provide detailed guidance and explanation on the research process, but only provide research materials and data, show key conclusions and give play to students' initiative.
(2) "Application of Proportion" adds content and provides rich learning materials. Proportion is widely used in real life. On the one hand, this textbook increases the content of enlarging and reducing graphics according to the requirements of the standard; On the other hand, the teaching of proportion is moved here, so that the "application of proportion" consists of three parts: proportion, zooming in and zooming out the figure, and solving problems with proportion, which enriches the teaching content. Among them, the teaching content of "scale" is richer than the original compulsory education textbook, and examples of how to express the scale to enlarge the actual distance are added, and examples of practical drawing are arranged by using the scale knowledge comprehensively. This part will not only consolidate the concept learning in the first two sections, but also provide students with good materials and opportunities to experience the application of proportion in real life and develop their application consciousness, problem-solving ability and practical ability.
(3) Pay attention to the thought of infiltration. Function is one of the important concepts in modern mathematics and is widely used in modern science and technology. Primary school stage, mainly through the study of some knowledge, infiltration function thought. The significance of direct proportion and inverse proportion in this unit is also an important content of osmotic function thought. This textbook continues to follow the arrangement method of the original general compulsory education textbook, and the concept of positive proportion is followed by the concept of inverse proportion, which is convenient for comparing the meanings of the two concepts; On the basis of examples, the relationship between variables is expressed in the form of list, and then the relationship between two variables is expressed in the form of. At the same time, the teaching of understanding scale images has been increased, and it is still "Do you know?" In this paper, the image of inverse proportion is introduced, so that students can understand the changing law of positive and negative proportion and understand the function thought initially.
3. Provide rich teaching content of space and graphics, pay attention to hands-on practice and independent exploration, and promote the development of students' space concept.
The main goal of space and graphics teaching in primary schools is to develop students' concept of space. Like the previous volumes, the arrangement of this textbook continues to pay attention to enabling students to develop their spatial concept, independent exploration and practical ability while gaining knowledge of space and graphics. The teaching content of this textbook is the last part of this field, "Cylinders and Cones".
Cylinders and cones are also traditional teaching contents. The arrangement of this part of the content has not changed much in content and requirements, but the appearance of the teaching material has changed greatly. Specifically, there are several changes:
(1) Strengthens the connection between the learned knowledge and real life. By enumerating a large number of objects with the characteristics of cylinders and cones in real life, the understanding of cylinders and cones is introduced intuitively, so that students can observe and think about the similarities and differences of the shapes of these objects and abstract their geometric figures from them. When students know their main features, they are required to find more objects with this feature from their lives, so as to deepen their understanding of cylinders and cones.
(2) The exploration process of graphic features, surface area and volume calculation methods has been strengthened. In the past teaching, the arrangement of these parts focused more on the understanding and mastery of the characteristics of graphics and the calculation methods of surface area and volume, but it was not enough to promote the development of students' spatial concept in learning materials and practical operation. Experimental teaching materials strengthen hands-on practice and independent exploration, so that students can experience the formation process of knowledge and get more training opportunities on independent exploration and spatial concepts. For example, the characteristics of a cylinder are obtained through students' hands-on experiments and independent exploration. When teaching the characteristics of cylinder expansion diagram, the textbook also allows students to operate it by hands. It is found that the length of this rectangle is equal to the circumference of the bottom of the cylinder and the width is equal to the height of the cylinder. It deepens students' understanding of cylindrical features and exercises students' spatial imagination.
(3) Strengthen students' thinking about space and graphics in operation. When arranging the understanding of cylinder and cone, the textbook adds the activity of sticking rectangular (or triangular) hard paper on a wooden stick to quickly turn out the cylinder (cone). This activity can not only stimulate students' interest in learning, but also understand the relationship and transformation between plane graphics and three-dimensional graphics; At the same time, students master the characteristics of cylinders and cones and develop the concept of space in the process of operation, observation, imagination and reasoning.
(4) Strengthen the guidance of learning methods, encourage students to think independently and cultivate their learning ability. In the experimental teaching materials, students are encouraged to use the existing knowledge to associate and guess the new learning content, and then through experiments and reasoning verification, students' good learning and thinking habits are cultivated. For example, the textbook links cuboid volume formula to encourage students to estimate the calculation method of cylindrical volume, and links cylindrical volume formula to encourage students to guess the calculation method of conical volume. The teaching of cone volume is designed according to the idea of asking questions, associating, guessing, experimental exploration and deducing formulas. Experiments and reasoning are carried out on the basis of guessing, so that students can be trained in research methods and ways of thinking, and develop and improve their autonomous learning ability.
4. Arrange the arrangement and review of mathematics learning in primary schools, so that students can systematize their mathematics knowledge and do a good job in the connection of mathematics teaching in primary and secondary schools.
This semester is the last semester of primary school study, and the last unit of this textbook is still arranged for "sorting and reviewing", which systematically sorts out the main contents learned in primary school and reviews them in the form of an outline, so that students can consolidate and deepen their understanding of the mathematics knowledge they have learned, further improve their ability, better realize the predetermined goal of primary school mathematics teaching, and make necessary preparations for middle school mathematics learning.
Sorting and reviewing is an important part of mathematics teaching in primary schools. Although the Standard divides the compulsory education stage into three periods in order to reflect the integrity of compulsory education, it makes the relationship between mathematics courses in each period closer. However, at present, school education in most areas of our country is actually still independent of primary school and junior high school, which makes the teaching of primary school and junior high school basically separate. From primary school to junior high school, students' mathematical knowledge and learning methods have changed a lot. Therefore, before primary school students finish their studies, a systematic and comprehensive review and arrangement of all the contents of mathematics learning will help students sort out the knowledge of scattered learning, help students improve their mathematical cognitive structure in their minds, enhance their lasting memory and improve their mathematical ability. Therefore, the unit of "arrangement and review" is not only one of the key teaching contents of this textbook, but also an important part of the whole set of primary school mathematics textbooks.
Compared with the original textbook for nine-year compulsory education, this textbook has the following improvements in the arrangement of "arrangement and review":
(1) According to the learning fields divided by standards, the learning contents of primary school mathematics are sorted and reviewed in turn. The standard divides the content of compulsory education into four fields: number and algebra, space and graphics, statistics and probability, practice and comprehensive application. According to this classification framework, four experimental textbooks are arranged in the "arrangement and review" unit, and some appropriate treatments are made according to the actual teaching needs. For example, the section "Common Quantity" is arranged in "Number and Algebra", which brings together the units of measurement that appeared in different fields in primary school, and systematically reviews them through the methods of list arrangement and recall rewriting.
(2) Streamline the content, highlight the key points of collation and review, and provide space for students to actively participate in knowledge collation. Compared with the original nine-year compulsory education textbook, this textbook has greatly simplified the content arrangement. Don't try to cover everything, cover the details of what you have learned and describe the concepts you have learned. Instead, highlight the key points, grasp the main content and main problems to sort out and review. On the one hand, it makes the teaching materials get rid of the situation of listing knowledge points and arranging concepts and rules, on the other hand, it also provides students with clues to sort out knowledge, leaving room for students to participate in the collation of knowledge. For example, when reviewing the meanings and methods of the four operations in "Number Operation", the textbook first creates a problem situation through the theme map, so that students can review the application of the four operations in solving problems, and then let students discuss the meanings of the four operations in groups, compare the calculation methods of integers, decimals and fractions, and find out their similarities and differences, so as to fully understand the meanings and methods of the four operations they have learned.
(3) Pay attention to the creation of problem situations and the application of what they have learned to develop students' ability to solve problems with mathematics. This textbook attempts to guide students to contact reality or mathematical examples through problem situations, including realistic situations and mathematical situations, deepen their understanding of what they have learned and strengthen their understanding of the internal relations of related knowledge. At the same time, we should pay attention to applying what we have learned, especially in practical problem situations, so as to apply what we have learned and promote understanding and consolidation in the process of "using". This is very beneficial to improve the effectiveness of review and students' ability to solve problems. For example, "number cognition", "number operation" and "graphic position" are all introduced from practical problem situations, while "formula and equation" and "graphic cognition and measurement" discuss the application of mathematics in mathematical situations.
(4) On the basis of basic exercises, provide comprehensive and challenging exercises to promote the continuous improvement of students' comprehensive application ability. In practice, we should not only pay attention to basic training, but also strengthen the practice of flexible and comprehensive application of knowledge, and also provide challenging exercises appropriately to further improve students' comprehensive mathematical ability.
5. Infiltrate mathematical thinking methods step by step to cultivate students' mathematical thinking ability and problem-solving ability.
One of the general ideas of this experimental textbook is to systematically and step by step infiltrate mathematical thinking methods, and try to present important mathematical thinking methods with vivid and interesting examples in a simple form that students can understand. Through teaching, students are influenced by mathematical thinking methods. Accordingly, in the "wide angle of mathematics" unit, the teaching of "pigeon hole principle" is arranged. Through intuitive and practical operation, let students experience the inquiry process of "pigeon hole principle", "model" some simple practical problems and solve them with "pigeon hole principle"; Through the flexible application of "pigeon hole principle", students can feel the charm of mathematics, promote the development of logical reasoning ability, cultivate the ability of analysis, reasoning, problem solving and interest in exploring mathematical problems.
Like the previous textbooks, this textbook still pays attention to integrating problem-solving teaching into the teaching of all parts, and cultivates students' ability to solve problems with mathematics through the teaching of all parts. At the same time, in the "mathematical wide angle" unit and comprehensive application of mathematics, the teaching of comprehensive application knowledge to solve problems and diversified problem-solving strategies has been strengthened, so that students can gradually improve their mathematical thinking ability and problem-solving ability. This textbook has designed five comprehensive application activities of mathematics, such as "Mathematics in Bicycle" and "Saving Water", so that students can comprehensively use the mathematics knowledge and methods they have learned, solve problems by hands, and enhance their awareness of applying mathematics. In the textbook, a section of "Mathematical Thinking" is set up in the number and algebra review of the "Arrangement and Review" unit, which permeates mathematical thinking methods, enables students to know more problem-solving methods and strategies, get training in mathematical reasoning, and further develop students' logical reasoning ability and problem-solving ability.
6. The cultivation of emotion, attitude and values permeates mathematics teaching, and stimulates students' interest and inner motivation with the charm of mathematics and the harvest of learning.
This mathematics curriculum reform emphasizes the cultivation of students' emotions, attitudes and values, and comprehensively improves students' quality. Senior pupils have gained some knowledge and life experience, and have a certain desire to explore natural and social phenomena. At this time, educators need purposeful inspiration and guidance. In mathematics teaching, students should form rich emotions, positive attitudes and correct values through mathematics learning activities. This experimental textbook not only covers all fields of mathematics teaching content, but also provides rich materials for students to explore the wonderful world of mathematics, and pays attention to arranging many reading materials and mathematical historical facts reflecting mathematics culture in combination with the teaching content to enrich students' mathematics learning activities. All these help students understand the close relationship between mathematics and human life, understand the value of mathematics, and stimulate their desire to learn mathematics.
(1) Provide rich materials to cultivate students' interest in learning mathematics.
We should pay attention to the selection of teaching materials with rich knowledge and connotation, so that students can be influenced by emotions, attitudes and values while learning mathematics. For example, the selection of "comprehensive application" content, pay attention to selecting topics that senior students care about and understand; The wide-angle teaching of "Pigeon Hole Principle" in mathematics implies finding the most essential mathematical model from the complicated realistic materials, so that students can experience the process of "mathematization" of specific problems and help improve their logical thinking ability. "Fibonacci series" arranged in "reading materials" allows students to understand its origin and characteristics, find its laws, feel the inner charm of mathematics and increase their interest in mathematics learning.
(2) Pay attention to the close relationship between mathematics and human life and the cultural value of mathematics.
Like the previous experimental textbooks, this textbook still pays attention to the form of reading materials, and arranges some relevant mathematical historical materials in combination with the teaching content to enrich students' overall understanding of the development of mathematics and cultivate students' interest and desire in exploring and learning mathematics. For example, several "Do you know?" "Mathematics in Life" and "Reading Materials". These contents can not only make students have a strong interest in mathematics itself, but also stimulate their desire to expand their knowledge and further explore and study, and also have the function of cultivating students' scientific sentiment and spirit.
(3) Through independent exploration activities, students can gain successful learning experience and enhance their confidence in learning mathematics well.
Combined with the age characteristics of students and the teaching content, this textbook has designed many activities that require students to explore independently. For example, when exploring the calculation method of cone volume, let students guess by association first, and then guide students to experiment and explore, and get the calculation method and formula of cone volume. Similarly, the teaching of drawing with scale allows students to discuss the specific steps to solve the problem independently-first determine the scale, then determine the length and width of the playground on the map according to the scale, and finally draw. Let students have more opportunities to apply mathematics knowledge and practice independent exploration, and enhance their confidence in learning and using mathematics.
This experimental textbook includes the following contents: negative number, cylinder and cone, proportion, statistics, wide angle and comprehensive application of mathematics, etc. And sort out and review the mathematical knowledge learned in the decimal stage.
(a) Numbers and algebra
First unit negative number
Third unit proportion
(b) space and graphics
Unit 2 Cylinder and Cone
(3) Statistics and probability
Unit 4 Statistics
(D) Mathematical thinking methods
Unit 5 Mathematics Wide Angle
(5) Comprehensive application
1. Mathematics in Bicycle
Please?Save?Water
(6) sorting and auditing
Unit 6 Arrangement and Review