Understand the meaning of mathematical rigor and ability: mathematical rigor means that the description of mathematical conclusions must be accurate, the argument of conclusions must be rigorous and thorough, and the whole teaching content should be organized into a strict logical system; The ability of mathematics, that is, to do what you can, requires neither more nor less, so that the knowledge taught can be accepted by students.
How to effectively apply the principle of combining rigor with ability in teaching: (1) Seriously study curriculum standards and teaching materials, and clearly grasp the rigor requirements of teaching materials; (2) In the teaching of specific concepts and theorems, don't tell all the contents of the concepts and theorems to be learned at once, but reflect the rigorous process step by step; (3) In teaching, we should consciously and gradually cultivate students' good thinking habits, which is the main symbol of students' rigorous mathematical thinking. (4) At ordinary times, efforts should be made to study the age characteristics, personality characteristics, intelligence and ability level of students.
2. The principle of combining abstraction with concreteness
Understand the meaning of abstraction in mathematics: abstraction is the basic feature of mathematics. The content of mathematics is highly abstract; Mathematical methods are also highly abstract; Abstraction also shows the characteristics of gradual progress; The abstraction of mathematics can reach areas that human perception cannot reach.
How to effectively apply the principle of combining concreteness with abstraction in teaching: (1) Introduce and clarify new mathematical concepts by using vivid, vivid, concrete and intuitive realistic materials and mathematical language. (2) Teachers should give full play to the leading role of teachers in introducing and clarifying new mathematical concepts with vivid, vivid, concrete and intuitive realistic materials, and guide students to summarize abstract and generalized mathematical concepts and conclusions. (3) After learning relevant and abstract mathematical theories, we should apply them to concrete practice, solve concrete problems and explain concrete phenomena, which is a process from abstract to concrete. (4) From concrete to abstract, and then from abstract to concrete, it is often not completed at one time, and sometimes it can only be completed through circulation.
3. The principle of combining theory with practice
On the one hand, we should improve the theoretical level, attach importance to the teaching of general principles and methods, give full play to the guiding role of theory, and overcome the bad phenomena such as emphasizing arithmetic over arithmetic, unilaterally emphasizing skills, and engaging in sea tactics. On the other hand, we should pay attention to practice, illustrate the application of mathematics with examples, and cultivate students' ability to use mathematical knowledge through examples.
4. The principle of combining development with consolidation
The process of mathematics learning is a development process of constantly consolidating and acquiring relevant knowledge and skills. Consolidation and development cannot be completely separated, but should be consolidated in development and developed on the basis of consolidation.
Carry out the principle of combining development with consolidation: First of all, we should understand the significance of combining development with consolidation, and learn new knowledge and review and consolidate old knowledge throughout the whole teaching process. We should not only pay attention to periodic review and summative review, but also pay attention to the review and consolidation of daily classroom teaching, and take review and consolidation as an important teaching link. Secondly, we should pay attention to the review and consolidation of students' knowledge, skills and methods.