In the new curriculum standard of 20 1 1 edition, the "two basics" (basic knowledge and skills) is changed to "four basics" (basic knowledge, basic skills, basic ideas and basic activity experience), and the two abilities are changed to four abilities, which makes the teaching goal of primary school mathematics more comprehensive and three-dimensional. 1. How to understand the reasons why "double base" changed to "four base" 1 and "double base" changed to "four base"? Double basics only involve the first goal of three-dimensional goals: knowledge and skills, and other two-dimensional goals: process and method, emotion, attitude and values are not involved; Some teachers only pursue a single goal of knowledge and skills, and they are not people-oriented in teaching, but people-oriented. The two new bases are people-oriented and conform to quality education; Double basics is a foundation for cultivating innovative and practical talents, but it is impossible to cultivate innovative and practical talents only by mastering existing knowledge and skills. More importantly, in the process of learning knowledge formation skills, students can learn to understand mathematical ideas, accumulate experience in mathematical activities, learn mathematical thinking, and find, ask, analyze and solve problems by themselves. 2. Changes in the connotation of "double basics" With the progress of society, the development of science and technology and the implementation of curriculum reform, the connotation of "double basics" in the new curriculum standard has also changed: the basic knowledge in the curriculum content includes not only basic concepts, properties, formulas, etc., but also the formation process and thinking methods of these basic knowledge. The content of the course has changed, and some difficult contents have been deleted directly, which has reduced the learning requirements for some knowledge points, and it has been implemented since the new textbook of Grade One in Senior High School. The content of the course aims at ten core concepts, emphasizing the importance of developing students' sense of number, symbol, space, geometric intuition, data analysis, calculation, reasoning, model thinking, application and innovation. (The content of the course explains the connotation of each core concept. ) Basic skills should not only enable students to form skills of operation, reasoning and graphic processing, but also increase skills of data processing (skills of exploring data laws from behind complex data information), skills of mathematical communication (skills of expressing and talking about mathematics) and skills of using information technology. (Use calculators and computers for calculation or data processing; The "double basics" emphasizes that students can't master mathematics knowledge by rote learning, but must constantly consolidate and deepen their knowledge application based on understanding. 3. The "double base" of basic ideas and basic activity experience is the foundation, and the basic ideas and basic activity experience are formed on the basis of "double base" and are the development of "double base". Mathematics classroom teaching should integrate mathematics knowledge, mathematics thinking method and mathematics activity experience. Only in this way can students' mathematics literacy be really improved. Mathematical thinking refers to the reflection of spatial forms and quantitative relations in the real world in people's consciousness, which is the result of thinking activities. It is an essential understanding and reflection of mathematical facts, concepts, propositions, laws, theorems, formulas, laws, methods and skills, and a new mathematical concept refined from some specific mathematical contents and the process of understanding mathematics. The basic ideas in mathematics mainly include: abstraction (classification, set, combination of numbers and shapes, symbolic representation, symmetry, correspondence, finite and infinite), reasoning (induction, deduction, axiomatization, transformation and classification, ideal analogy, gradual approximation, substitution and special generalization) and modeling (simplification, quantification, function, equation, optimization, randomness and sampling statistics). Abstraction is to extract the same and essential features from many things and discard their non-essential features. Reasoning is a form of thinking, and one or several known judgments lead to another unknown judgment. Generally including rational reasoning and deductive reasoning. Rational reasoning is used to explore ideas and find conclusions, from special to general; Deductive reasoning is used to prove conclusions, from general to special. The cultivation of reasoning ability should penetrate into various fields, such as algorithm summary and rule discovery in computing teaching. Participate in the whole process, give full play to students' subjectivity, encourage students to observe and discover, make bold guesses, carefully verify, compare and infer, etc. The generalized mathematical model includes various concepts, formulas and conclusions in mathematics; Narrow understanding only refers to the mathematical relationship structure that reflects a specific problem or a specific thing system. The process of establishing mathematical model is called mathematical modeling. The basic model of mathematical modeling is "problem situation-modeling-explanation and application". Through mathematical abstraction, human beings obtain mathematical concepts and laws from the objective world and establish a mathematical discipline. Through mathematical reasoning, they got many conclusions, which further developed mathematical science. Then, they applied mathematics to the objective world through mathematical models, which in turn promoted the development of mathematical science and produced the basic ideas of mathematical abstraction, reasoning and modeling. Mathematics thought is the foundation of mathematics development, exploration and research, and the essence of mathematics teaching. Basic activity experience: It is generally believed that in the process of "doing" mathematics, students turn some things that teachers can't teach through examples into their own things through experience, experience, sentiment and accumulation. These things are "basic experience in mathematical activities", that is, accumulating experience in solving problems with mathematics. Accumulating experience in mathematics activities emphasizes the process of mathematics learning and students' perceptual knowledge gained through personal experience. The accumulation of activity experience can make students apply what they have learned and form mathematical thoughts and wisdom, which is conducive to the promotion of students' emotional attitudes and values and the realization of three-dimensional goals. Mathematics-related activities are everywhere in life: shopping, traveling, decoration, investigation and statistics, investment and financial management, buying lottery tickets, predicting the results of sports competitions and so on. A variety of mathematical activities can be designed in class: hands-on operation, observation, experiment, guess, calculation, reasoning, verification and so on. The development from "two basics" to "four basics" makes our primary school mathematics teaching objectives more diverse and three-dimensional, makes the teaching content richer and more interesting, makes the teaching methods more flexible and connotative, makes the communication between teachers and students more attractive and influential, and makes students' understanding and application of mathematics knowledge more profound and creative. Second, how to implement the "four basics" in teaching can be realized from the following aspects: 1. We should really understand the importance of mathematical thinking methods and experience in mathematical activities to students' mathematical learning; Can promote students to learn mathematics knowledge better; Can cultivate students' creative ability. Knowledge and skills are the foundation and carrier, experience and thoughts are accumulation, perception and promotion, and literacy, wisdom and innovation are sublimation and realm. 2. The mathematical thinking method is implicit in the mathematical knowledge system and needs to be experienced and excavated. 3. Colorful mathematical activities are the main way for students to learn knowledge, acquire skills and feel ideas, and also the inevitable means to accumulate rich experience in mathematical activities; Mathematical activity is not a single operation activity, but contains positive thinking activities. 4. The acquisition of mathematical knowledge, mathematical skills and mathematical thinking methods should be unified in the activities of accumulating experience in mathematical activities. These four foundations are mutually integrated and infiltrated. Three, around the implementation of the "four basics", what should we pay attention to when preparing lessons? 1, read textbooks and students, and determine teaching objectives. First of all, when teachers preset the teaching process according to the curriculum standards, teaching materials, teaching reference materials, etc., they put the knowledge and skill goals in the first place. Because it is the basic goal of the three-dimensional goal, it is still the focus of mathematics learning, but teachers should also be clear that knowledge is the foundation of students' development, but it is not the ultimate goal of education. Secondly, teachers should pay attention to process and method objectives. Although processes and methods are implicit, their functions are very important, because the two dimensions of "knowledge and skills" and "emotion, attitude and values" are achieved through the goal of "process and method". If mathematics knowledge and skills are the "body" of mathematics discipline, then the inquiry process and inquiry method are the "soul" of mathematics discipline, and only the organic combination of them can reflect the overall connotation and thought of mathematics discipline. Then, teachers should be clear that the teaching goal of "emotion, attitude and values" is not incidental. Emotion not only plays an important role in starting, encouraging, maintaining and regulating the learning process, but also is closely related to the formation of students' learning attitude, the establishment of values and the perfection of personality. 2. The four basic objectives should be specific, accurate in wording and easy to implement and detect. Verbs that express the goal of results are: understanding, understanding, mastering and using; Verbs expressing process goals include: experience, experience, exploration, etc. Understanding: to know or explain the relevant characteristics of the object from specific examples; According to the characteristics of the object, identify or explain the object from the specific situation. Understanding: describe the characteristics and origin of an object, and explain the difference and connection between this object and related objects. Mastery: On the basis of understanding, apply objects to new situations. Application: comprehensively use the mastered objects, and choose or create appropriate methods to solve problems. Experience: Get some perceptual knowledge in specific mathematical activities. Experience: Take part in specific mathematical activities, actively recognize or verify the characteristics of the object, and gain some experience. Inquiry: participate in specific mathematical activities independently or in cooperation with others, understand or ask questions, seek ideas for solving problems, discover the characteristics of objects and their differences and connections with related objects, and gain a certain rational understanding. The teaching objectives are very rich, so just implement the "double-base" society, and don't engage in too much training and sea tactics. It should be based on curriculum standards and teaching materials, with moderate difficulty, and work hard on students' learning and music learning. Fourth, around the implementation of the "four basics", what should be paid attention to in 1 class, and create a good problem situation. Problems are the core of mathematics, and only good questions can arouse students' positive thinking. A good problem situation should be novel, challenging and feasible. The ideal situation is to pay attention to students' existing knowledge and experience, which can not only arouse the enthusiasm of learning, but also guide mathematics to go deeper. The realistic and life theme can be used as a problem situation, and so can the content of mathematics itself. 2. Classroom questions should be carefully designed to stimulate students' mathematical thinking. Classroom questioning can gradually refine and deepen the created problem situation, support and stimulate students' mathematical thinking, and guide students to think effectively, which is a direct embodiment of effective teaching. What is mathematical thinking? That is, in the face of all kinds of realistic problem situations, we can think about problems from the perspective of mathematics, that is, we can consciously apply mathematical knowledge, methods, ideas and concepts to discover mathematical phenomena and laws, and we can use mathematical knowledge and mathematical thinking methods to solve problems. As a "process goal", mathematical thinking is actually to let students experience the process of "doing mathematics", that is, to let students experience the process of discovering, asking, analyzing and solving problems. 3. Design colorful mathematical activities with students as the main body. Students should be the main body of the classroom, and pay attention to students' diverse learning methods: listening carefully, thinking actively, practicing, exploring independently, cooperating and communicating, etc. According to students' age characteristics and cognitive rules, the written things such as examples, explanations and conclusions in textbooks are transformed into colorful mathematical activities that students can participate in personally, so that students can fully experience the process of observation, experiment, guess, calculation, reasoning and verification. The focus of teaching should be to let students experience the process of activities, understand mathematical ideas and accumulate experience in activities. When guiding students' mathematical thinking, don't directly give the thinking mode of the problem; Don't deny students' ideas easily; It is necessary to present the questions or specific ideas put forward by students to other students in time for everyone to exchange and discuss. In teaching, we should pay attention to the abstract process of concepts, the derivation of formulas, the induction of methods, the generalization of laws, the synthesis of conclusions and the analysis of ideas. , so as to experience mathematical thought in the process of knowledge generation; In the process of solving problems, highlight mathematical ideas; In the process of summing up knowledge, sum up mathematical ideas. In teaching, students should be given more time to think, more space for activities, more opportunities to express themselves and more successful and pleasant experiences. 4. Effectively guide students to choose appropriate content in cooperative communication teaching, grasp the opportunity of cooperation, and let students have the need for cooperation. Generally, the following aspects are suitable for group learning: learning content with uncertain methods and unique answers; Explore and challenge the learning content; Content that individuals cannot complete; Some operational activities that need peer help to complete. 5. Pay attention to the cultivation of students' study habits that determine their lives. Attention should be paid to the cultivation of students' study habits in teaching. There are many good study habits in mathematics. In mathematics classroom teaching, teachers should pay special attention to cultivate students' good learning habits of mathematical thinking, practice, explore actively, cooperate and communicate, guide students to form the habit of reflection, and enhance students' application consciousness of mathematical thinking. In a word, the basic idea and characteristics of curriculum reform are the organic integration of three-dimensional goals, which are the three dimensions needed for students' development. They are a unified whole, interdependent and mutually based, and there is a relationship between you and me. Three aspects of three-dimensional goals are very important for students' development. Students must use certain methods to learn knowledge and skills, which can be scientific or unscientific; It must also go through a process, either actively exploring or passively accepting; In the process of learning, it will be accompanied by certain emotions and attitudes, either positive and serious, or passive and perfunctory. Therefore, the four basic goals or three-dimensional goals are not independent and inseparable. It is impossible to accomplish one goal before implementing another, and it is impossible for each goal to use its strength equally. How to fully implement the four basic goals and three-dimensional goals in teaching needs the teaching wisdom of our teachers. The goal of "knowledge and skills" dimension is to let students learn, the goal of "process and method" dimension is to let students learn, and the goal of "emotion, attitude and values" dimension is to let students enjoy learning. In classroom teaching, we should not only pay attention to the foundation, but also pay attention to the process, thinking and emotion. Only by combining the three goals can we finally realize the training goal of compulsory education: to face all students, to meet the needs of students' personality development, to let everyone get a good mathematics education and to let different people get different development in mathematics. Teachers and students in our mathematics classroom teaching will finally realize: teach people to fish-teach people to fish-teach people to have fun-enjoy learning-enjoy learning.