A careful understanding of students' psychological characteristics and acceptance ability is the premise of implementing the principle of combining rigor with ability. This is why the experience of "preparing lessons first and then preparing lessons" is relatively weak. In other words, only by fully understanding the students' situation, can the teaching plan and content arrangement be truly targeted and teach students in accordance with their aptitude, and this principle can be truly implemented.
In teaching, we should try our best to arrange the process and opportunities for students to adapt gradually, gradually improve their rigor and make the argument well-founded. For example, beginners in plane geometry are very uncomfortable with strict proof. In teaching, teachers should first give proof steps, so that students can only fill in the reasons for each step, encourage students to carry forward the spirit of "jumping is enough", reasonably put forward teaching requirements, and gradually transition to strict proof by students themselves. Finally, it is required to be well-founded and concise. But we must not passively adapt to students and artificially lower the theoretical requirements of teaching materials. We must organize teaching according to the scientific content and the actual situation of students.
In teaching, we should pay attention to cultivating rigor from accurate basic knowledge and language. This requires teachers to prepare teaching materials, be skilled and accurate, and make no mistakes. In addition, we should be wary of ignoring the conditions for the establishment of formulas, laws and theorems. We should also pay attention to gradually cultivate students' habit of accurate language. This requires teachers to have higher teaching language literacy, make their own language accurate, concise and standardized, and require accurate and appropriate teaching language.
In teaching, pay attention to cultivate comprehensive and thorough thinking habits and gradually improve the degree of rigor. General mathematics studies the nature of a class of things or the relationship between their elements, not just a single thing. Therefore, teachers are required to conduct a comprehensive and thorough examination.
In short, the rigor of mathematics should be well combined with ability. In teaching, we should pay attention to the "degree" of teaching, that is, pay attention to the depth and breadth of teaching materials, and start with rigor; In addition, we should pay attention to the stage, let the former prepare for the latter, and the latter become the development of the former, echoing before and after. Through the cultivation of students' rigor, students can develop good thinking habits.
Extended data:
Rigorous, description attitude is serious and cautious, meticulous, comprehensive and perfect, pursuing perfection.
The principle of prudence refers to the reasonable accounting of possible losses and expenses, and shall not overestimate assets or income or underestimate liabilities or expenses. ?
It means that when some economic businesses have several different accounting methods and procedures to choose from, under the premise of not affecting the reasonable choice, try to choose the method and procedures that have the least impact on the owner's rights and interests, and reasonably calculate the possible losses and expenses, that is, the so-called "predicting possible losses is not as good as predicting possible gains".
The ability principle, also known as the "acceptability principle". Refers to the moderate principle that teaching adapts to children's development level. From the practical possibility of children's development, teaching tasks, teaching materials, methods and organizational forms are acceptable to children. It should not be overburdened or relaxed. It should be higher than the current level of children, maintain a certain degree of difficulty, and guide children to work hard to solve problems in the "recent development zone" where their ability is still in its formative state.
To implement this principle, it is necessary to accurately understand and estimate children's acceptance ability and intellectual and physical development level, adopt a reasonable teaching structure, from near to far, from known to unknown, from simple to complex, from easy to difficult, from concrete to abstract, from local to whole, and conduct teaching appropriately.
Mathematics education is a social and cultural phenomenon, and its sociality determines that mathematics education should keep pace with the times and innovate constantly. A series of problems in mathematics education, such as educational objectives, educational content and educational technology, will change and develop with the progress of society. The background of mathematics education reform comes from at least nine considerations: knowledge economy, social relations, family pressure, international trends, examination reform, rejuvenating the country through science and education, deepening quality education, popularizing compulsory education and science and technology.
Reference link: Rigorous-Baidu Encyclopedia
Prudence Principle-Baidu Encyclopedia
Ability principle-Baidu Encyclopedia
Mathematical Education Principle System-Baidu Encyclopedia
Mathematics Education-Baidu Encyclopedia