1. Rational spirit of mathematics
The cultivation and development of this rational spirit is of great significance. It is the core of human civilization, especially western civilization. From the first mathematical crisis, philosophers represented by Plato (ancient philosophy and mathematics are inseparable) began to realize that human intuition is unreliable and the rational spirit of mathematics began to develop.
Therefore, it is the highest level of mathematics education to cultivate students' independent thinking and courage to criticize in teaching, and to focus on this and persistently cultivate people's rational spirit through mathematics teaching.
2. Mathematical ideas and methods
Mathematics is the product of human abstract thinking and a rational thinking paradigm and cognitive model. It is not only some operating rules and transformation skills, but also a way of thinking that can benefit people for life. Therefore, in teaching practice, we should always pay attention to this essential feature of mathematics, avoid the tendency of simply pursuing knowledge in mathematics learning, and pay attention to the cultivation of ability and thinking, so as to benefit students for life.
The mathematical thoughts in primary school mainly include axiomatization, symbol, set, model, reduction, identity and inequality, combination of numbers and shapes, function and correspondence, infinity and other important mathematical thoughts. Mathematical methods include comparison, analysis, synthesis, abstraction, generalization, induction, deduction, classification, transformation and deformation, correspondence, hypothesis, conjecture, observation, simplification and reasoning.
3. The beauty of mathematics
Mathematics is beauty and a spiritual space with a new aesthetic dimension. As the famous British philosopher Russell said, "Mathematics has not only truth, but also supreme beauty." The beauty of mathematics is not as bright, lively and chic as natural beauty and artistic beauty, nor even as intuitive and concrete as other social beauty. It is abstract, rigorous, profound, cold and implicit, and it is a rational beauty.
Therefore, in teaching practice, efforts should be made to explore the unique intellectual beauty of mathematics and guide students to appreciate and appreciate the beauty of mathematics. The aesthetic value of primary school mathematics mainly includes: dynamic beauty, static beauty, symmetrical beauty, asymmetrical beauty, intuitive beauty and abstract beauty …
4. The application value of mathematics
The cultural significance of mathematics lies not only in knowledge itself and its connotation, but also in its application value. Therefore, we should strengthen the connection between mathematics and real life in teaching, enhance the application of mathematics, and let students experience the application value of mathematics.
5. History and culture of mathematics
The connotation of mathematical culture is not only reflected in knowledge itself, but also in its history. It is a historical existence. Therefore, in the teaching process, the whole process of the generation and development of mathematical knowledge has been fully revealed. We believe that mathematics is both creative and inventive. It is as big as a subject and as small as a symbol, and always comes out of a certain thinking under a certain cultural background.
Our mathematics education should strive to restore and reproduce this process of discovery or invention, explore the source of mathematical knowledge, and rebuild the relationship between the separated mathematical knowledge and the realistic background.