One of the biggest changes in the revised edition of "New Mathematics Curriculum Standard for Compulsory Education (20 1 1)" is that knowledge and skills have changed from "two basics" to "four basics" and "two abilities" to "four abilities". The change is not only an increase in literal content, but more importantly, it will bring teaching ideas. Four basics, that is, students acquire necessary basic knowledge, basic skills, basic ideas and basic activity experience through study; Expanding "two basics" into "four basics" has increased students' basic mathematical thoughts and experience in basic mathematical activities. What's more, these two items reflect a comprehensive understanding of the value of mathematics courses. Students not only acquire the necessary knowledge and skills through mathematics learning, but also accumulate experience in the process of learning, and gain the idea of mathematics development and problem solving. In particular, basic activities put more emphasis on students' subjective experience, which embodies the basic concept of student-oriented. The four basic goals have two meanings, one is for real life, and the other is for further study. It can be seen that the new curriculum standard has changed from the original "two basics" to the current "four basics", which is very worthy of our consideration. Four abilities, emphasizing understanding the relationship between mathematics knowledge, mathematics and other disciplines, mathematics and life, using mathematical thinking mode to think, and enhancing the ability to find, ask, analyze and solve problems. From "double energy" to "four energy", it embodies the importance of the ability to find and ask questions. Finding problems more refers to finding new methods, new ideas and new ways that have not been taught in books, and knowing new things that were unknown before. This discovery is a kind of self-transcendence, which can not only gradually accumulate the experience of innovation and creation, but more importantly, cultivate students' interest in learning, establish confidence in progress and stimulate the passion of creation. Asking questions on the basis of discovery requires logical reasoning and theoretical abstraction, and needs accurate generalization. Questions must be put forward after in-depth thinking and self-organization, which can stimulate students' wisdom and mobilize students' body and mind to enter a positive state. This is a different way of thinking from following the teacher to verify and infer the existing conclusions. Only after many times of training in this way of thinking can students gradually form innovative consciousness, innovative spirit and innovative ability. Mathematics is a subject that lays the foundation for students' future development. It undertakes the task of laying a good foundation for students' future study, and also lays a foundation for students' future work and life. Mathematics discipline should not only enable students to master basic knowledge and skills, but also cultivate students' mathematical thinking methods, strategies and ideas, cultivate students' thinking ability and open students' intelligence. Second, preparation and design before class (1) How to control the teaching materials with the spirit of the new curriculum standard is to understand and read through the teaching materials? At least understand the intention of the textbook, make clear the key points and difficulties of the textbook, and have your own thinking and value judgment. If the curriculum standard is compared to the center of the circle, then the teacher's understanding and grasp of the textbook is the radius. No matter how big the circle is, it is inseparable from the core element of the center of the circle. Teachers understand curriculum standards through interpretation, and at the same time control teaching materials with their own understanding of the spirit of curriculum standards. First of all, we should sort out the context and have an overall grasp of the teaching materials. When preparing lessons, teachers should establish structural thinking, understand the role of a lesson in the teaching material unit, the position of a unit's knowledge in the whole knowledge field, clarify the module goal, unit goal and class goal, especially strengthen the structural consciousness of unit knowledge, look at the teaching material higher, and design each lesson from top to bottom, which is an important dimension to read the teaching material well. Ye Shengtao said, "Teaching materials can only be used as a basis for teaching. To teach well and benefit students, teachers must be good at using it. " Therefore, when preparing lessons, we must use teaching materials flexibly according to students' actual situation, and on the basis of understanding students' existing knowledge development level and experience, we should process the teaching materials, change the presentation mode of the teaching materials, or turn the static picture into a dynamic situation, or turn the cold beauty of the teaching materials into students' passionate thinking, thus stimulating students' interest in learning. In addition, although the textbook is the most important curriculum resource, teachers can make full use of the textbook, but at the same time, they can deal with some limitations in the textbook flexibly and boldly, so as to increase exploration, improve thinking difficulty, increase teaching density, improve teaching efficiency and optimize teaching resources, thus better serving teaching and students. (B) in-depth understanding of students' reality, identify the real starting point of students. Students are the main body of development and the master of learning. Analyzing and thoroughly understanding students' situation is an important part of preparing lessons. Without understanding students, it is difficult to teach students in accordance with their aptitude, and it is easy to fall into the embarrassing situation of casting pearls before swine, which leads to low teaching efficiency. Only by knowing ourselves and knowing ourselves can we prescribe the right medicine and even get rid of the disease. This requires teachers to prepare students, understand students' original knowledge and learning ability, understand students' interests and wishes, position teaching in the "nearest development zone", and combine teaching materials with students' life experience and emotional experience to make teaching full of life breath and vitality. Every teacher should seriously consider the following questions when preparing lessons: 1. Do students already have the necessary knowledge and skills to learn new knowledge? 2. Did the students understand the relevant content through preview, and how many people understood it? How much do you know? To what extent? 3. What knowledge is the key and difficult point that teachers need to teach and guide in class? 4. What content will arouse students' interest and thinking, and become the exciting point in the classroom? The above problems can be understood before or at the beginning of teaching, and teachers can organize teaching activities according to the actual situation. In this way, students can think what they want and worry what they are in a hurry, so that students can constantly find and solve problems in a class and always be in the main position. At the same time, it is necessary to understand students' interests and excitement and turn them into the focus or growing point of teaching; At the same time, the key and difficult points of teaching are transformed into students' interests and excitement. Let students preview independently before class, and students' colorful and distinctive preview notes become the "teaching reference" and the most dynamic curriculum resources for teachers to organize the next learning activities. Teachers' way of preparing lessons has changed from mainly teaching reference books and books for preparing lessons to mainly obtaining learning information from learning, which has identified the starting point of students' learning and naturally realized the change from learning to teaching. It is worth noting that when preparing lessons, we should consider the learning situation of most students and the learning difficulties of a small number of students, and provide tangible services for students with learning difficulties. It is also a knowledge point, what basic contents should students with learning difficulties master, to what extent, and what help teachers should provide. In the same exercise, students with learning difficulties should be divided into several steps and what kind of counseling should be given. Ask questions in class, which questions are aimed at students with learning difficulties. Classroom teaching, which time is arranged for students with learning difficulties, and so on, should be thought and designed when preparing lessons. Students with learning difficulties are constantly getting personalized counseling, making progress and enhancing their self-confidence. Over time, they stepped into the excellent ranks. (3) Determining teaching objectives Teaching objectives are not only the starting point of teaching activities, but also a preset possible result. The goal of primary school mathematics teaching includes not only the requirements of knowledge and skills, but also the requirements of mathematical thinking, problem solving and students' feelings and attitudes towards mathematics, both explicit and implicit. Different understanding of the goal will lead to different teaching designs, which will lead to different levels of classroom teaching. When making teaching objectives, teachers should at least include three different levels: learning period, unit and class hour. Only in this way can teachers complete their teaching tasks systematically, comprehensively, completely and effectively according to the requirements of curriculum standards. I think we should first make it clear that students are the main body of the classroom and teachers are the guides, helpers, organizers and guides of students' learning. Therefore, in the expression of teaching objectives, it is what activities teachers guide students to engage in and what knowledge and skills students gain in activities; Through what activity process, what learning methods students get from it; What emotions, attitudes and values students experience through what activities, it is necessary to study the corresponding requirements of curriculum standards, and make clear which are the outcome goals (knowledge and skills, processes and methods) and which are the experiential goals (emotions, attitudes and values). Therefore, when determining the teaching objectives, we should consider the following points: the relationship with the curriculum objectives. The classroom teaching goal is not equal to the curriculum goal. Classroom teaching should strive to meet the requirements of curriculum objectives, but the curriculum objectives are a big framework and general objectives, rather than the specific objectives of classroom teaching. It can be mastered flexibly and adjusted appropriately according to the overall plan and actual situation of teachers' teaching. Relationship with students' actual situation. Students are the main body of classroom teaching, and classroom teaching should be based on serving the growth and development of students. Teachers should fully understand the actual situation of students, including students' cognitive level and ability level, as well as the characteristics and problems of students' current ideological understanding, grasp the key, find the breakthrough point and the relationship with the subject knowledge system. Some teachers, because of their thinking inertia, mostly start from the structural system of subject knowledge, and rarely start from the learning needs and growth and development needs of students. This is a big misunderstanding and should be adjusted. We should fully consider how to rely on subject knowledge and fully tap the significance of subject knowledge to serve the growth and development of students. Relationship with teachers' personal factors. Some teachers seldom consider personal factors when designing classroom teaching. If teachers' own strengths and weaknesses are not brought into full play, the classroom teaching effect is difficult to reach the ideal state, which requires teachers to make full use of their own advantages, mobilize their own potential and fully display their own strengths and styles in classroom teaching. Relationship with classroom generation. The classroom teaching process should be based on the preset process. The success of classroom teaching is likely to exceed the teacher's preset, which requires teachers to exert their educational wisdom and make appropriate adjustments in time. Teachers should be psychologically prepared, analyze some uncertain possibilities in advance and put forward corresponding adjustment plans to deal with these unpredictable situations. These considerations should be properly reflected in the teaching objectives. Relationship with limited class time. There is also a key factor that determines the level and quantity of teaching objectives. A class is only 40 minutes, and time is very limited. When designing teaching objectives, we should consider how to teach in a limited time. Third, the specific strategies in the classroom The basic idea of the new curriculum standard is that "everyone can get a good mathematics education, and different people can get different development in mathematics". How do we understand this sentence, face individual differences, and how to implement the four basics and four abilities in teaching is a problem that every teacher should think about. (A) opening up the situation and developing the "four abilities" situation is the first step to implement the four basics and four abilities and realize an efficient classroom. Fundamentally speaking, the initial starting point of mathematics is the real world, and a considerable part of primary school mathematics teaching content can be found in the reality of children's lives. Teachers can use these prototypes to create teaching situations and guide students to observe, study and discuss these prototypes when making teaching presuppositions. The methods and ideas summarized from it react to the reality of life, thus helping them "better explore the laws of the objective world." The creation of situations should be authentic, mathematical, attractive and developmental. In order to better implement the "four abilities" and improve students' ability to find and solve problems, teachers should "open" the problem situation. It is to throw students into a problem situation with different thinking strategies and problem-solving methods, so that students can think, analyze and solve problems from different angles and levels. For example, when teaching addition and subtraction within 100, I first show all kinds of clothes and mark the price, so that students can ask questions freely and help them solve problems. Then, I suggested that today is Xiaoli's mother's birthday, and Xiaoli wants to buy a suit for her mother with 100 yuan. If you were Xiaoli, how would you match it? There are many ways for students to speak freely. I appointed several student representatives to go on stage to match according to what he said, and then the following students evaluated the flowers they matched. Therefore, the students put forward different views according to their own life experience: "Mom likes dresses, but it's too monotonous to choose only one." "sneakers with skirts don't look good." ..... In this open learning process, every student's thinking has been fully developed and constantly innovated in mutual communication. At the same time, with the help of students' existing knowledge and life experience, we can solve some practical problems in life and further improve students' ability to solve problems. (2) Take the old knowledge as the growing point and promote the development of the four basics. Primary school mathematics is a highly systematic subject, and every new knowledge is often an extension and development of old knowledge, and it is also the basis of subsequent knowledge. Knowledge chains are interconnected, interlocking, supplementing the old with the new, and constantly changing the new into the old, forming a knowledge network. Only when students understand the relationship between knowledge can they deeply understand and master it. Mathematics teaching is to guide students from the old to the new, organize active migration, promote reasoning from the known to the unknown, understand the relationship between simple and complex problems, and train students' thinking with the logical relationship of mathematics itself. There is no fixed model in mathematics teaching. In actual teaching, some characteristics of teaching content should be considered. When there is a close logical relationship between old and new knowledge or there is no substantial change between the learned knowledge and the old knowledge, it is only a special case of the original knowledge in the cognitive structure. When teaching, we should take the original knowledge as the growing point and directly change from the old to the new, that is, from the students' existing knowledge and experience. Because students always acquire knowledge with the participation of existing knowledge and experience, without the foundation of existing knowledge and experience, their original knowledge and experience can not participate in teaching, and the fracture of the connection between old and new knowledge will inevitably bring students difficulties in understanding, making it difficult for them to master what they have learned. For example, the knowledge of "checking calculation of division with remainder" should be based on the previous checking calculation of divisible division. Both types of checking computations should use "quotient multiplied by divisor", and the latter evolved into "addition remainder". In teaching, we should not only review the test method of divisibility, but also review the division with remainder with 127÷6 as an example. The key question is: "Is the average score of 127÷6 and quotient 2 1 in this question?" So what's the average score? Can I only multiply the quotient and divisor when checking the calculation? What should I do? This series of questions is discussed by everyone. " Only in this way can we master the new laws and inspection methods smoothly. (3) Strengthening mathematics activities, acquiring more experience knowledge and combining it with practical activities, which not only conforms to the teaching principle of integrating theory with practice, but also conforms to the age characteristics of students; It not only stimulates students' interest, but also enables students to learn practical knowledge and skills and gain more basic activity experience. Students' learning activities are full of curiosity and conjecture. In order to make students' interest in learning develop in curiosity and conjecture, teachers need to use more interesting ways to stimulate students' curiosity and produce the relationship between the three forces, thus improving the effectiveness of mathematics classroom exercises. This requires teachers to understand students' interests and excitement and turn them into teaching priorities or growth points. At the same time, the key and difficult points of teaching are transformed into students' interests and excitement. Let students preview independently before class, and students' colorful and distinctive preview notes become the "teaching reference" and the most dynamic curriculum resources for teachers to organize the next learning activities. Teachers' way of preparing lessons has changed from mainly teaching reference books and books for preparing lessons to mainly obtaining learning information from learning, which has identified the starting point of students' learning and naturally realized the change from learning to teaching. How to ensure the smooth progress of activities and achieve the best results? First of all, teachers should give students room to read, taste and rethink in class, ensure that students have enough time and space to experience activities such as observation, experiment, guess, calculation and reasoning, and then help students accumulate basic activity experience through review and reflection. In addition, when guiding students to explore, we should pay attention to how to stimulate students' curiosity and induce students to take the initiative to discover and ask questions. Regarding classroom activities, many teachers have a puzzle: let students let go, what if there is not enough time? Yes! Every class has a certain learning task, and the time of each semester is certain, so it is a great challenge for teachers to complete the teaching task, which requires teachers to make full preparations before class, prepare lessons carefully, grasp the teaching materials as a whole, and relax in class. (4) Flexible use of teaching methods Only by using a variety of teaching methods flexibly and skillfully can teachers teach easily, students learn flexibly and teaching tasks be completed well. In actual teaching, we should choose different teaching methods according to different teaching contents and students' actual situation, and at the same time we need the cooperation between teachers and students to realize the flexible use of teaching methods. Teaching and learning activities are interrelated and inseparable. The implementation of teaching methods also includes two inseparable aspects: how teachers teach and how students learn. Only when teachers' teaching methods are coordinated with students' learning methods can the flexible use of teaching methods be realized. The application of any teaching method is to arouse students' initiative and creativity, so that they can quickly and firmly master relevant knowledge and solve problems they don't understand. In this way, the problem of teaching methods is not only how teachers teach and how students learn, but also how teachers and students cooperate. As long as this problem is solved and students' enthusiasm and initiative are mobilized, students can actively think along the teacher's ideas and carry out related activities according to the teacher's requirements. To use teaching methods flexibly, the most fundamental thing is to study and study teaching methods. According to the characteristics of the subjects taught, we should master a variety of teaching methods skillfully. With the continuous development of education, teaching methods are constantly changing, and a large number of new teaching methods appear, which poses new challenges to the research and application of our teaching methods. Therefore. It is the bounden duty and responsibility of every teacher to learn and study new teaching methods. (V) Importance of consolidating exercises The forgetting curve of memory in psychology is the basic basis for consolidating exercises, so appropriate exercises are necessary. The difficulty, quantity and time of consolidation exercises should be appropriate, and the feedback during practice is very important, so you can't simply raise your hand. It is necessary to patrol and fully understand the situation that students have mastered. Let the students who have made mistakes report their thoughts, analyze the causes of the mistakes and help them in a targeted manner. Make sure everyone gets a good math education. The practice of new curriculum is no longer completely dependent on classroom teaching, but an important content to rebuild and enhance the significance of curriculum and life. Therefore, under the background of the new curriculum, teachers should fully develop the educational resources of exercises, and pay equal attention to the knowledge function, evaluation function and education function of exercises. Every exercise should be used adequately, well and properly, so as to promote students' active learning and develop their creative potential. We should be open-minded in practical application and encourage innovation. Teachers face individuals with different foundations, abilities, personalities, habits and interests. Therefore, facing the whole group, we should consider the students at each level and practice in layers. According to students' differences, the homework is designed into different groups, so that students can choose the one that suits them according to their actual situation. Students with poor foundation can choose to do some exercises in knowledge understanding and application, while those with spare capacity can do more difficult exercises. This kind of design exercise can make each student gain something on the original basis through different degrees and different quantities of homework exercises, and all of them can enjoy the joy of success. With a strong interest, more practice, and a long time, the ability will naturally go up, and students who used to study poorly will slowly jump to the ranks of learning well. This requires teachers to provide students with interesting and varied buffet-style homework. You can also study in advance or do your own homework according to your actual ability. Four. Teaching examples Based on the above interpretation of the new curriculum standards and my understanding and understanding of the four basics and four abilities, I seriously thought about the teaching of the first volume of the first grade "Toys" class. First, combined with this lesson example, I specifically talked about how I practiced. The learning goal of this lesson is to correctly count the number of objects within 5 and read and write the number 1-5; Learn to express the number of objects within 5 by operation and drawing, and know the order of 5 numbers1-5; Learn to use numbers to describe the number of objects in life, and gradually develop good math learning habits. The goal of this lesson is not difficult to achieve. We often say: "money should be spent on the cutting edge", and for our teaching, "time should be spent on the cutting edge". Students already have this part of knowledge (basic knowledge) and the methods to solve this kind of knowledge (basic skills). I don't think we need to spend too much time on this. Our focus should be on guiding students to master basic mathematical ideas and gain basic activity experience. How to embody these two requirements? The basic ideas of the upper level include abstract thinking, reasoning thinking and model thinking, and the lower level ideas derived from these three basic ideas include the combination of numbers and shapes, symbolic thinking and classified thinking. When teaching this lesson, I lead my children to experience the abstract process of "counting the number of objects-indicating the number with pictures-indicating the number with numbers" again, so as to help students understand the meaning of numbers. When counting the number of toys, some children use sticks to represent numbers, some use disks to represent numbers, and some show their fingers ... At this time, I guide children to represent squares, triangles and circles with graphics ... From physical objects to graphics, children's thinking is blooming; Then lead children to express the number of objects with digital symbols, and abstract the digital symbols from the graphics. By expressing the quantity of things from different angles, children can learn to express the gradual abstraction process of numbers in different ways, and at the same time enrich their understanding of logarithm. Understanding the relationship among objects, figures and digital symbols in gradual abstraction is permeated with the basic idea of the combination of numbers and figures. And in the process of correct counting, establish a sense of number and realize the corresponding concept of number and thing. At the same time, I have accumulated experience in mathematical activities in the process of hands-on operation, cooperation and communication, and gradual abstraction.