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What is the meaning of "four basics" in the national mathematics curriculum standard? What does Sanneng mean?
Discussion content: 1. The national mathematics curriculum standard expands "two basics" to "four basics", namely basic knowledge and basic skills, and adds "basic mathematics activity experience" and "basic mathematics thinking method". Emphasis on foundation is for development. Adhering to the "four basics" in the reform of mathematics education can not only better promote the development of students, but also highlight the disciplinary nature of mathematics. Three abilities: (1) calculation ability (2) spatial imagination ability (3) logical thinking ability, in which logical thinking ability should be the synthesis of analysis, synthesis, comparison, abstraction, generalization and transformation, and the cultivation of mathematical ability is completed in the teaching process. Therefore, it is particularly important to make effective use of teaching time and cultivate mathematical ability reasonably, orderly and moderately. 2. The relationship between the "four basics" of mathematics. The meaning of "two basics" in mathematics is very rich, which can be expressed in three forms: knowledge form, teaching form and individual form [12]. From the teaching point of view, Professor Shao Guanghua and Mr. Gu Lingyuan pointed out: "The teaching of the two basics pays attention to the teaching of basic knowledge and skills, pays attention to intensive teaching and more practice, and advocates' practicing middle school'. The main teaching goal is to pursue the memory and mastery of basic knowledge and the exercise and proficiency of basic skills, so that students can acquire solid basic knowledge, skilled basic skills and high academic ability. " [13] Among them, "intensive speaking and more practice" and "practice makes perfect" are mainly around "deductive activities". Its purpose is to enable students to acquire formal result knowledge-systematic knowledge expressed in mathematical terms or formulas. Basic activity experience mainly refers to the process knowledge formed and accumulated in basic mathematical activities. Because China's mathematics teaching overemphasizes deductive activities and weakens or even ignores inductive activities, the experience of basic activities emphasizes inductive activities more. In the process of mathematics learning, "double basics" and basic activity experience are interdependent, mutually promoting and transforming. In their continuous integration and repeated practical application, a kind of knowledge experience with basic and universal guiding significance formed through reflection and refinement is the basic idea of mathematics. From this, we can give the following relational structure of the "four bases" of mathematics: from the perspective of knowledge, "double bases" is a rational and formal result knowledge. Basic activity experience is a kind of perceptual and situational process knowledge, each of which emphasizes one aspect of mathematical knowledge. The former forms a knowledge system, while the latter forms an experience system. Only by organically combining the two can a complete mathematical knowledge structure be formed. As far as the method is concerned, the "double basis" is mainly based on deduction, which is only a fixed premise (definition, axiom, theorem, etc. ). Using a relatively fixed reasoning program (syllogism), a fixed conclusion can be drawn, but the prediction and discovery of the conclusion, the exploration and adjustment of reasoning ideas and the practical application of knowledge cannot be deduced by deduction. In this sense, "children can't learn new mathematics knowledge through deduction!" The study of "double bases" needs a process of meaning construction. Based on the original experience and from the operating experience, the constructed meaning is finally stored in the students' brains in the form of experience, just as the famous educator Tao Xingzhi said in the analogy of grafting branches in the process of human knowledge acquisition: "We should take our own experience as the root and the knowledge generated from this experience as the branch, and then we can connect other people's knowledge. The knowledge of others has only become an organic part of our knowledge. " Therefore, "double basics" can really grow into students' mathematical literacy through experience. Compared with "double bases", "basic activity experience" is vague and imprecise, lacking a clear structural system, especially those "raw experiences" that have not been processed, and contain many subjective and one-sided non-essential factors. As the mathematician Chris Gore described it: "The knowledge gained in the process of mathematical activities is always inaccurate and one-sided, and its overall structure is like a virgin forest, or a tangled branch." Therefore, to make "basic activity experience" more accurate, reasonable and effective, it needs to go through a conceptualization and formalization process. Although, in the process of solving problems, some experience itself has a good guiding role and practical value. But after all, the essence of mathematical knowledge is to pursue rigor and certainty. After conceptualization and formalization, "basic activity experience" can be transformed or integrated into "double base", which not only sublimates "basic activity experience", but also makes "double base" gain some vitality because it is full of students' feelings. Mathematical activity experience refers to the perceptual knowledge, emotional experience and application consciousness formed by learners in the process of participating in mathematical activities. Emotional experience refers to the curiosity and thirst for knowledge about mathematics, the successful experience gained in mathematics learning activities, the feeling of mathematical rigor and certainty of mathematical results, and the feeling and appreciation of mathematical beauty. Application consciousness includes the belief that mathematics is useful, the confidence in applying mathematical knowledge, the consciousness of asking and thinking questions from the perspective of mathematics, and the innovative consciousness of expanding the application field of mathematical knowledge. Moreover, application consciousness is the core component of basic activity experience in mathematics. Professor Shi Ningzhong pointed out: "The basic idea mainly refers to deduction and induction, and it should be the main line and the highest idea of the whole mathematics teaching." [7] There are many discussions about the basic ideas of mathematics in the previous literature. Mr. Hu Jiongtao thinks: "The highest level of basic mathematics thought is the foundation and starting point of mathematics textbooks, and the whole middle school mathematics content develops along the track of basic mathematics thought ..." Symbolization and transformation thought ","set and correspondence thought "and" axiomatic and structured thought "constitute the highest level of basic mathematics thought." [15] The four basic ideas put forward by Mr. Ren Zichao have great influence in middle school mathematics teaching: the combination of numbers and shapes, the idea of classified discussion, the idea of function and equation, and the idea of transformation [16]. However, among many mathematical thoughts, inductive thinking and deductive thinking should also play a fundamental and leading role. Deductive thinking should be used when linking "intermediate problems", sorting out and expressing the transformation results, and the main strategies of transformation-"generalization" and "specialization" are the concrete manifestations of inductive thinking and deductive thinking. From the formation process, deductive thinking is mainly practiced in the formal training of "double basics". Inductive thinking is mainly cultivated in the continuous accumulation of "basic activity experience". Inductive thinking and deductive thinking are two wings of mathematical thinking system, and their coordinated development can make mathematical knowledge grow into students' wisdom healthily and harmoniously. In a word, the basic knowledge, skills, experience and ideas of mathematics are not only the core content and main goal of mathematics learning activities, but also the most important part of students' mathematics literacy. Together, they construct students' mathematics.