One way of thinking is to restore the formation process of mathematical knowledge, so that students can connect with their existing life experience, use their personal cognitive ability, abstract quantitative relations and graphic properties from specific situations through independent exploration and cooperative communication, and try to solve problems and accumulate experience instead of relying solely on imitation and memory. Remember that ready-made mathematical knowledge is more applicable than cat painting tiger.
The two motives are to make students feel that mathematics is both useful and interesting in the process of acquiring knowledge and solving problems through personal experience, and give full play to the external motives of "useful" and "interesting"
The three stages are the three stages of grasping the learning process from "perception" to "mastery" and then to "breakthrough" "Perception" is the initial discovery, perception and understanding of the internal relationship between new things and existing knowledge through exploration and thinking; "Mastering" refers to acquiring new knowledge through guessing, verifying, inducing and summarizing, and being able to use the acquired new knowledge to solve some problems in textbooks and life; "Infiltration" refers to integrating the acquired new knowledge into the existing knowledge structure, being able to flexibly use the new knowledge to solve some comprehensive problems, carrying out some deeper mathematical thinking, feeling the charm of mathematics in the process of solving problems and thinking deeply, and enjoying the fun of solving problems. The three stages vary from person to person, step by step, and students should be given sufficient practical opportunities and time to think, not eager for quick success. At the same time, we should proceed from the reality of students and admit that we are treated differently, so that every student can gain, have dignity, pursue and develop.
The four methods are to encourage and guide students by all means in teaching, and to acquire new knowledge by using the methods of association expansion, transformation and migration, combination of numbers and shapes, and using both hands and brains. "Lenovo expansion" is to find the intersection of old and new knowledge, popularize existing knowledge, and apply to new and old knowledge with quantitative change but no qualitative change. For example, from "addition and subtraction within 100" to "addition and subtraction within 10 thousand"; "Transformation and migration" means taking appropriate measures to turn new faces into old acquaintances, which is suitable for the similarity between new knowledge and old knowledge. For example, from "rectangular area" to "parallelogram area"; "The combination of numbers and shapes" means to reveal the abstraction of quantitative relations with the intuition of figures and the concealment of graphic properties with the clarity of quantitative relations; "Using both hands and brains" is the basic method of learning mathematics. Because mathematics is abstract, thinking hard will only increase the burden of thinking and the difficulty of learning, while thinking while calculating and drawing can enhance the intuition of problems, reduce the burden of thinking and reduce the difficulty of learning. In terms of brain thinking, students should be guided to learn the methods of comprehensive observation, orderly thinking and summary reasoning. In terms of hands-on operation, students should be guided to learn how to simply measure and draw line segments, schematic diagrams, geometric sketches, and sketch and extract key sentences and data. Cultivating students to develop the good habit of using their hands and brains from an early age plays a vital role in students' development, and must be taken seriously and persevered.