Learn math skills through practice-suitable for learning facts and skills. Learn the general methods of solving problems by solving situations that do have certain characteristics, and use these characteristics to define a real problem-skills suitable for learning how to discover and explore, how to rediscover mathematics and how to learn.
13, the purpose of mathematics learning has changed from mastering "mathematical facts and skills" to mastering "general methods to solve problems", that is, "mathematical thinking", which is a major update of the concept of mathematics education.
14, four levels of understanding mathematics: 1, formal understanding. Logical thinking training should be the basic training in mathematics learning. 2. Understanding at the discovery level; 3. Intuition-concrete understanding; 4. Intuitive understanding.
15, Xiao Pingbangyan: "It is generally believed that mathematics is a science composed of strict logic, even if it is different from logic, it is roughly the same. But actually, mathematics has nothing to do with logic. Mathematics must follow logic, of course, but logic plays the same role in mathematics as grammar does in literature. Writing a grammatical article is completely different from writing a novel according to grammar. Similarly, carrying out correct logical reasoning and piling up logic to form mathematical theory are completely different problems. Mathematics and logic are essentially different.
16. In mathematics, never put the logical carriage in front of the heuristic horse.
17, only by knowing how the conclusion was drawn can we really understand the conclusion. Reproducing or experiencing the discovery process is a wonderful way for mathematicians to learn and study mathematics. The best way to learn is to do it-ask questions and solve problems. The best teaching method is to let students ask questions and solve problems, not just impart knowledge-encourage action.
18. Mathematics is very abstract. One aspect of understanding mathematics is to give it intuitive and concrete meaning.
It is wrong to overemphasize the formal structure of mathematics.
20. Abstraction is meaningful only on the basis of solid experience. In addition, after the introduction of abstract concepts, specific problems should be used to illustrate their usefulness.
2 1. The direction of learning modern algebra well is to emphasize several basic concepts, such as symmetry, continuity and linearity.
22. Geometrical intuition is still the most effective way to understand mathematics. Geometric intuition means that abstract things can be described and thought in your mind like painting.
23. The combination of mathematics teaching and people's quality development is the most important purpose of mathematics education.
24. Geometry is a mathematical coincidence, a "symbol of intuitive space to help memory" and a "graphic formula".
What mathematics really wants to do is to solve specific problems. The best way to understand a theory is to find a specific problem, and then study a sample example of this theory, a typical example that can explain everything.