(1) will observe the mathematics in the real world from the perspective of mathematics, and provide people with an understanding and inquiry. From the perspective of mathematics, we can find from the objective phenomena in the real world that quantitative relations and spatial forms raise meaningful mathematical problems and can emerge. The research object of mathematics and its attributes form concepts, concerns and structures, so that we can understand the mathematical principles behind natural phenomena, realize the aesthetic value of mathematics and form curiosity about mathematics.
In the compulsory education stage, mathematical vision is mainly manifested in producing a single ability, including number sense, quantity sense, geometric symbol consciousness, intuitive space concept and innovation consciousness. By observing the basic quantitative relationship and spatial form in the real world, students can intuitively understand the mathematical knowledge they have learned and its realistic background, discover the simple relationship and laws between the basic mathematical research objects and their expressed things in life practice and other disciplines, find and put forward meaningful mathematical problems in the actual situation, conduct mathematical inquiry, gradually develop the meaning and habit of observing the real world from a mathematical point of view, and develop curiosity, imagination and innovative consciousness.
(2) Think about the real world with mathematical thinking. Mathematics provides a way of thinking for human beings to understand and explain the real world. Through mathematical thinking, we can reveal the essential attributes of objective things and make use of the logical connection between mathematics and the real world among mathematical objects. We can draw conclusions logically according to known facts or principles, construct a mathematical logic system and use symbolic operations. Mathematical methods such as formal reasoning can analyze and solve mathematical problems and practical problems, and can solve problems and design systems through various information such as computational thinking or formalization, so that the theoretical and logical thinking quality in travel can cultivate scientific attitude and rational spirit.
? In the compulsory education stage, mathematical thinking is mainly manifested as calculation ability, reasoning consciousness or reasoning ability. Through independent mathematical thinking process, students can understand the occurrence and development of basic mathematical concepts and laws, the relationship between basic mathematical concepts and between mathematics and the real world, logically explain or demonstrate the basic methods and conclusions of mathematics, analyze and solve simple mathematical problems and practical problems, explore mathematical laws contained in natural phenomena and real situations, form a scientific attitude of seeking truth from facts, initially develop rational and orderly thinking quality, and gradually form a rational spirit.